Computational Fluid Dynamics Analysis of Cold Plasma Plume Mixing with Blood Using Level Set Method Coupled with Heat Transfer

applied sciences

Article Computational Fluid Dynamics Analysis of Cold Plasma Plume Mixing with Blood Using Level Set Method Coupled with Heat Transfer

Mehrdad Shahmohammadi Beni and Kwan Ngok Yu *

Department of Physics and Materials Science, City University of Hong Kong, Hong Kong, China; [email protected] * Correspondence: [email protected]; Tel.: +852-3442-7182

Academic Editor: Xianchang Li Received: 27 April 2017; Accepted: 31 May 2017; Published: 3 June 2017

Abstract: Cold plasmas were proposed for treatment of leukemia. In the present work, conceptual designs of mixing chambers that increased the contact between the two ﬂuids (plasma and blood) through addition of obstacles within rectangular-block-shaped chambers were proposed and the dynamic mixing between the plasma and blood were studied using the level set method coupled with heat transfer. Enhancement of mixing between blood and plasma in the presence of obstacles was demonstrated. Continuous tracking of ﬂuid mixing with determination of temperature distributions was enabled by the present model, which would be a useful tool for future development of cold plasma devices for treatment of blood-related diseases such as leukemia.

Keywords: level set method; thermoﬂuid; plasma medicine; cold plasma; multiphase ﬂow

1. Introduction A novel technique and a conceptual design of a mixing chamber were presented in the current study that could be used in future development of effective cold plasma devices for treatment of blood related syndromes such as leukemia. Plasma medicine research has been progressing very rapidly in recent years [1–3]. Cold atmospheric plasmas have shown significant potentials in various biomedical applications such as wound healing [4,5], tooth bleaching [6], cancer therapy [7–9] and sterilization of infected tissues [10]. In recent years, cold atmospheric plasmas were explored for inactivating different microorganisms. They were found effective in decontaminating chicken skin and muscle inoculated with Listeria innocua [11]. Inhomogeneous inhabitation zones were generated in microcolonies by high flow rates of helium [12]. Furthermore, cold plasmas were found to show microbicidal and sporicidal effects but at the same time low toxicity for mammalian tissues [13]. Cold plasmas were also employed to treat the surface of polymers, including polyethylene with an ultra-high molecular weight used as joint replacements, and were additionally found able to enhance adhesion between the joint-replacement material and bone [14] as well as the wear performance of the polymer [15]. Therapeutic use of interaction between cold plasma and blood was successfully carried out [16]. Mixing between cold plasma and blood was also explored for treatment of large bleeding areas and for blood coagulation [17–19]. In relation, the viability and proliferation of human peripheral blood mononuclear cells upon exposures to atmospheric pressure argon plasma jets were studied, and signiﬁcant cell damages for short plasma exposures were not observed [20]. The effect of cold plasma jet on wound healing was also comprehensively studied, and no signiﬁcant effects from cold-plasma treatment were found on white blood cells, red blood cells, aspartate aminotransferase, alanine aminotransferase, blood urea nitrogen, or creatine contents [21]. More recently, possible use of

Appl. Sci. 2017, 7, 578; doi:10.3390/app7060578 www.mdpi.com/journal/applsci Appl. Sci. 2017, 7, 578 2 of 19 non-thermal gas plasma as an alternative treatment scheme against leukemia was explored for the first time by Barekzi et al., and it was found that the therapeutic effect of plasma on leukemia cells was not immediate (it has a delayed effect) and the increase in leukemia cell killing was achieved by increasing the contact time between the cold plasma plume and the cancerous human T-cell leukemia cells [22]. Furthermore, selective natural mechanisms of blood coagulation were triggered when blood samples were exposed to plasmas generated by non-thermal atmospheric pressure dielectric barrier (DBD) discharge at room temperature and pressure [23]. Moreover, the difficulty in directly treating blood with cold plasmas due to the coagulation was noted by Chen et al., so injection of cold plasma solution into the blood around the tumor was explored by the authors, involving three different carrier gases, i.e., helium (He), argon (Ar) and nitrogen (N2)[24]. It was pointed out by Shimizu et al. that cold plasma discharges had very low gas temperatures due to weak ionization rate for electron collisions and reactions [25]. The concentration of reactive species in the plasmas could be altered by the applied voltage [15]. In order to enhance the plasma chemistry while maintaining a low plasma temperature, very short voltage pulses (in the range from nanoseconds to microseconds) could be applied [22]. Moreover, the chemical reactions in plasmas were affected by the vibrational temperature, since the molecules were dissociated through their vibrational and electronic excitations [26]. On the other hand, the plasma characteristics were also affected by the plasma frequency since the very short lifetime of the charged particles could be comparable or even shorter than the applied pulse width. For example, in a previous study, the plasma frequency was set to be at 5 kHz and the pulse width was set at 0.50 µs [22]. Moreover, the fractions of plasma constituents were found to be small and therefore no significant additional heat was produced as a result of reactions in the discharge, so the bulk temperature of the carrier gas would be the dominating factor in determining the plume temperature [27–29]. From the previous studies, the two main challenges regarding the treatment of blood related diseases such leukemia are: (1) the contact between the plasma and the blood needs to be maximized; and (2) at the same time the blood coagulation needs to be minimized so that maximum contact could be achieved. In order to maximize the efficiency and effectiveness of these treatments and at the same time overcome the mentioned challenges, the contact/mixing between the plasma plume and blood needs to be enhanced dynamically; this requires a versatile multiphysics model for thermofluid analysis of the cold plasmas which has been somehow overlooked in most previous investigations. A parameterized model was set up by Schröder et al. [30] to simulate the species densities generated by a plasma needle and also the heat transfer to a skin layer. However, the model developed by Schröder et al. did not consider the plasma plume and its transfer to the treatment zone. Finite element analyses were also previously employed in simulation of atmospheric pressure plasma needles, without considering thermofluid analyses [31,32]. In the present work, two different conceptual designs of the mixing chamber were studied to accomplish a better mixing and to increase the contact between the blood and plasma plume by modifying the previous multiphysics model based on the level set method coupled with heat transfer [29]. It is remarked here that the present designs (i.e., with and without obstacles) of mixing chambers for blood and plasma only serve to demonstrate the concept of enhanced mixing by addition of obstacles to the flow. To the best of our knowledge, there were no previous designs in the literature. Upon an even mixing between the cold plasma and blood with precise probing of thermofluid parameters, an effective mixing could be achieved despite the relatively higher blood viscosity [24] compared to the plasma. Furthermore, information would be provided by dynamic tracking of both fluids in the mixing chambers on the underlying mechanism of mixing between the blood and cold plasma plume. Appl. Sci. 2017, 7, 578 3 of 19

2. Materials and Methods

2.1. Mathematical Models The level set function coupled with heat transfer, continuity and Navier–Stokes equations were discretized and solved numerically using the finite element method (FEM). The blood and cold plasma plume in the mixing chamber domain were tracked with the level set method using the level set variable (φ). The standard heat equation was used to model the heat transfer between the two fluids within the mixing chamber. The present theoretical model consisted of two main parts: (1) fluid dynamics with level set interface module; and (2) heat transfer module, which were coupled to each other. The results were obtained using parallel computing. In the present work, the level set method was used to capture the mixing and evolution of blood in cold plasma in two different mixing chamber designs in three-dimensional coordinate system, which was a continuation of our previous work in which the level set method was used to simulate cold plasma plume propagation in a cell buffer medium [29]. The level set method has been extensively used in simulation of two-phase fluid systems in which a liquid–gas interface is present [33–36]. Applications of 3D computational fluid dynamics (CFD) simulations were aimed at providing realistic information and data [37] and at demonstrating the versatility and capability of the model over simplified models such as 2D axisymmetric models for cylindrical chambers. The present model was based on our previously developed theory and here it was modified for the present two-phase fluid systems [29]. The plasma carrier gas was assumed to be helium (He) and its evolution in the mixing chamber that got filled with the injected blood was explained using the level set function as

∂φ ∇φ + u · ∇φ = γ∇ · ε∇φ − φ(1 − φ) (1) ∂t |∇φ| where φ was the level set function, ε was the interface thickness equivalent to the largest mesh element size mainly to allow a better interface reconstruction between the two ﬂuids [29] and its value here was 4 × 10−4 m. Oscillations in the level set function were reduced by the parameter γ to keep the interface thickness constant to achieve better numerical stability, and γ was set to be the largest initial velocity in the system to effectively decrease the oscillations in the level set function [29], which in this case was 0.1. The continuity equation deﬁned in the mixing chamber involving blood and cold plasma is given by

∂ρ + ∇ · (ρu) = 0 (2) ∂t The Navier–Stokes momentum equation is given by

∂u 2 ρ + ρu · ∇u = −∇P + ∇ · µ ∇u + (∇u)T − µ(∇ · u)I + F (3) ∂t 3 where ρ is density, P is pressure, u is the velocity of the ﬂow, F is given by F = ρg + Fst + Fvf, ρg is the body force, Fst is the surface tension and Fvf is the volume force. Furthermore, the heat transfer in the mixing chamber is explained using the heat equation, with the use of the thermophysical properties of blood and plasma carrier gas:

∂T ρC + ρC u · ∇T = −∇ · (−k∇T) + Q (4) p ∂t p where Cp is the specific heat capacity, ρ represents the density, k is the thermal conductivity and Q represents any external source of heat energy, which can be evaluated as heat energy generated per unit volume. In the present work, instead of defining an external heat source Q, the initial temperatures Appl. Sci. 2017, 7, 578 4 of 19 of the fluids at the inlet boundaries of the nozzles were chosen. Furthermore, Equation (4) can be written as

∂T ∂T ∂T ∂T ∂ ∂T ∂ ∂T ∂ ∂T ρC + ρC u · + + = k + k + k + Q (5) p ∂t p ∂x ∂y ∂z ∂x ∂x ∂y ∂y ∂z ∂z

In the present work, all the boundaries except the inlets and outlet were assumed to be thermally insulated as −n·q = 0. Furthermore, the temperatures for blood and plasma at the inlet nozzles were assumed constants as 310 and 303 K, respectively [38,39].

2.2. Solver Since the domain Ω was divided into ﬁnite elements connected at the nodes, the global equations for Ω were assembled from equations for the elements in Ω. The shape function for temperature interpolation inside the ﬁnite elements would be

T = [N]{T} [N] = [N1, N2, N3,...] (6) {T} = {T1, T2, T3,...} Differentiation of the temperature interpolation equation led to temperature gradients as shown in Equation (7)    ∂N N  ∂T 1 ∂ 2 ...  ∂x  ∂x ∂x ∂T =  ∂N1 ∂N2 { } = [ ]{ } ∂y  ∂y ∂y ...  T B T (7)  ∂T  ∂N1 ∂N2 ∂z ∂z ∂z ... where {T} represented the vector temperature at the nodes, [N] was the matrix of shape functions and [B] was the matrix for temperature-gradient interpolation. Applying the Galerkin method, the heat transfer equation would became

R ∂ ∂T ∂ ∂T ∂ ∂T ∂T ∂T ∂T ∂T ∂x k ∂x + ∂y k ∂y + ∂z k ∂z − Q + ρCp ∂t + ρCpu · ∂x + ∂y + ∂z NidΩ = 0 (8) Ω After applying the divergence theorem and discretization, the obtained linear system was solved using the Generalized Minimal Residual Method (GMRES) iterative solver [40]. For a linear system of equations Ax = b, the general idea behind the GMRES solver with left preconditioning for Krylov subspace with initial guess of v to the solution would have the form

2 i−1 (i) −1 −1 −1 Kle f t M(v) = v, M Av, M A v,..., M A v (9)

The approximate solution x was chosen in a way to minimize the residual that had the form of r = Ax − b. The algorithm of the left-preconditioned GMRES method is described in AppendixA. Due to the complexities involved in the multi-physics system, the present model was solved in parallel using the Message Passing Interface (MPI) which allowed numerical simulations to be performed on multiple compute units. In the present work, the MPICH2 package was employed for parallel computing [41]. The source of the “heat” used to regulate the temperature of the injected blood and plasma was characterized by constant temperatures at the inlet boundaries, i.e., Tﬂuid = T0, where T0 was 310 and 303 K for blood and plasma, respectively.

2.3. Test Case Geometry Moreover, the proposed conceptual design of the chambers contained three inlet nozzles, two of which used to inject plasmas into the chamber while the third used to inject blood simultaneously. Initially, the chamber was assumed to be ﬁlled with cold plasma that enabled the interface initialization for the level set variable (φ). In addition, movement of blood and plasma into the chamber and their Appl. Sci. 2017, 7, 578 5 of 19 subsequent mixing until their ﬁnal discharge from the outlet nozzle were continuously tracked by the level set method. The geometries of the mixing chambers with and without obstacles are shown in

FigureAppl. Sci.1 a,b,2017, respectively. 7, 578 5 of 20

(a) (b)

Figure 1. Mixing chambers ( a) with and ( b) without obstacles, with inlets and outlets shown.

The dimensions of blood and cold plasma inlet nozzles were (5 × 1 × 1) × 10−6 m3 and (1 × 1 × 1) × The dimensions of blood and cold plasma inlet nozzles were (5 × 1 × 1) × 10−6 m3 and (1 × 10−6 m3, respectively, while those of the outlet nozzle were (5 × 2 × 1)×10−6 m3. The total length of the 1 × 1) × 10−6 m3, respectively, while those of the outlet nozzle were (5 × 2 × 1)×10−6 m3. The total mixing chamber was 0.1 m and the width was 5 × 10−2 m. The dimensions of the obstacles were (1 × 2 length of the mixing chamber was 0.1 m and the width was 5 × 10−2 m. The dimensions of the × 1) × 10−6 m3. The blood flowrates in portal vein and cardiac output were 1.92 and 9.33 m3 s−1, obstacles were (1 × 2 × 1) × 10−6 m3. The blood flowrates in portal vein and cardiac output were respectively, so the average blood flowrate was 5.63 m3 s−1 [42]. For the two mixing chamber 1.92 and 9.33 m3 s−1, respectively, so the average blood flowrate was 5.63 m3 s−1 [42]. For the two configurations shown in Figure 1a,b, the blood inlet velocity was chosen as 0.1 m s−1 to generate a mixing chamber configurations shown in Figure1a,b, the blood inlet velocity was chosen as 0.1 m s −1 matching blood flowrate. It is remarked that the velocity of the plasma carrier gas could vary [43], to generate a matching blood flowrate. It is remarked that the velocity of the plasma carrier gas and the plasma inlet velocity from the (1 × 1) × 10−4 m2 inlet nozzle was also set as 0.1 m s−1 here for could vary [43], and the plasma inlet velocity from the (1 × 1) × 10−4 m2 inlet nozzle was also set as simplicity. The fluid flow in the present work was in the laminar regime, since the largest Reynolds 0.1 m s−1 here for simplicity. The fluid flow in the present work was in the laminar regime, since the number (Re = ρVD/μ) was ~530 which was far below ~4000 for the turbulent regime. Moreover, the largest Reynolds number (Re = ρVD/µ) was ~530 which was far below ~4000 for the turbulent regime. material properties of plasma carrier gas and blood used as inputs to the present model are Moreover, the material properties of plasma carrier gas and blood used as inputs to the present model summarized in Table 1. are summarized in Table1.

Table 1. Summary of material properties used in the present work.work. Material Density Thermal Conductivity Specific Heat Capacity Dynamic Viscosity BloodMaterial 1060 kg/m Density3 [44] Thermal0.505 W/m.K Conductivity [45] Specific4000 Heat J/kg.K Capacity [46] Dynamic4.00×10 Viscosity−3 Pa.s [46] CarrierBlood gas [28] 0.1601060 kg/m kg/m3 3[ 44] 0.5050.200 W/m W/m.K·K[45 ] 40005200 J/kg J/kg.K·K[46] 4.00 ×2.10×1010−3 Pa−5·s Pa.s [46] Carrier gas [28] 0.160 kg/m3 0.200 W/m·K 5200 J/kg·K 2.10 × 10−5 Pa·s 2.4. Boundary Conditions 2.4. Boundary Conditions In order to solve the system of partial differential equations (PDEs), the boundary conditions for fluidIn dynamics order to solveand heat the systemtransfer of module partial would differential be needed. equations The (PDEs), no‐slip the boundary boundary condition conditions (u = for 0, fluidwhere dynamics u is the velocity and heat field) transfer was moduleassigned would to the beinner needed. boundary The no-slipof the device, boundary which condition indicated (u =the 0, wherepresenceu is of the adhesion velocity between field) was fluids assigned and the to solid the inner wall. boundaryIn the heat of transfer the device, module, which the indicated surrounding the presencewall was ofassumed adhesion as between thermally fluids insulated and the (–n solid∙q = wall.0, where In the q is heat the transfer heat flux). module, The inlet the surrounding nozzles for wallinjection was of assumed cold plasma as thermally had the insulatedform uleft = ( u−x+n and·q = u 0,right where = ux‐ forq is the the left heat and flux). right The nozzle inlet as nozzles shown for in injectionFigure 1a,b, of cold respectively. plasma had The the values form ofuleft ux+= and ux+ andux‐ wereuright set= u tox− befor 0.1 the ms left−1 for and the right two nozzle different as shown cases −1 inused Figure to study1a,b, the respectively. mixing phenomena The values and of theux+ leveland usetx− variablewere set at to the be inlets 0.1 ms was for = the 0; this two indicated different casesthe presence used to of study plasma. the Considering mixing phenomena the blood and inlet the nozzle level ( set = 1 variable at the inlet at the nozzle), inlets the was inletφ = velocity 0; this indicatedof the blood the u presenceupward = uy+ of was plasma. set as Considering 0.1 ms−1, so the that blood mixing inlet chamber nozzle ( φfilling= 1 at and the steady inlet nozzle),‐state could the inlet be −1 velocityfully obtained of the bloodduringu upwardthe simulation= uy+ was time set as of 0.1 10.0 ms s. In, so addition, that mixing linear chamber discretization filling and was steady-state employed couldusing an be average fully obtained element during quality the of simulation~2 × 10−4 m. time Numerical of 10.0 convergence s. In addition, was linear verified discretization by considering was simulations with different grid resolutions and no inconsistencies were observed in numerical convergence and the final results. The mesh figures for the two configurations of the mixing chamber are shown in Figure 2. Appl. Sci. 2017, 7, 578 6 of 19 employed using an average element quality of ~2 × 10−4 m. Numerical convergence was verified by considering simulations with different grid resolutions and no inconsistencies were observed in numerical convergence and the final results. The mesh figures for the two configurations of the mixing

Appl.chamber Sci. 2017 are, 7 shown, 578 in Figure2. 6 of 20 Appl. Sci. 2017, 7, 578 6 of 20

Figure 2. Seamless mesh employed for two mixing chambers with different configurations. Figure 2. SeamlessSeamless mesh mesh employed for two mixing chambers with different configurations.configurations. 2.5. Grid Sensitivity Analysis (GSA) 2.5. Grid Sensitivity Analysis (GSA) Grid sensitivity analysis (GSA) was performed for the mixing chambers with obstacles, mainly Grid sensitivity analysisanalysis (GSA) (GSA) was was performed performed for for the the mixing mixing chambers chambers with with obstacles, obstacles, mainly mainly to to assess the reliability and accuracy of the present model. The two main parameters chosen for GSA toassess assess the the reliability reliability and and accuracy accuracy of the of presentthe present model. model. The The two two main main parameters parameters chosen chosen for GSA for wereGSA were the blood volume fraction exiting the outlet boundary of the mixing chamber (which werethe blood the volumeblood volume fraction fraction exiting the exiting outlet the boundary outlet ofboundary the mixing of chamberthe mixing (which chamber demonstrated (which demonstrated the reliability and accuracy of fluid dynamics with level set interface module) and the demonstratedthe reliability andthe reliability accuracy ofand fluid accuracy dynamics of fluid with dynamics level set with interface level module) set interface and module) the temperature and the temperature of the outlet nozzle (which demonstrated the reliability and accuracy of the heat transfer temperatureof the outlet of nozzle the outlet (which nozzle demonstrated (which demonstrated the reliability the and reliability accuracy and of accuracy the heat of transfer the heat module). transfer module). Three different grid sizes were considered using the concept of grid refinement factor (r) Threemodule). different Three grid different sizes weregrid sizes considered were considered using the concept using the of gridconcept refinement of grid factorrefinement (r) defined factor as (r) defined as defined as rr = = h hcoarsecoarse/hfinefine (10)(10) r = hcoarse/hfine (10) where hcoarse was the mesh or grid size before refinement while hfine was the mesh or grid size after wherewhere hhcoarsecoarse waswas the the mesh mesh or or grid grid size size before before refinement refinement while while hhfinefine waswas the the mesh mesh or or grid grid size after refinement. In practice, r should be greater than 1.3 [47], and the chosen average grid sizes of 2 × 10−−4, refinement. In practice, rr shouldshould bebe greatergreater than than 1.3 1.3 [ 47[47],], and and the the chosen chosen average average grid grid sizes sizes of of 2 2× ×10 10−4,, 1 × 10−4− and4 3 × 10−5 m− gave5 r values of 2.0 (=0.02/0.01) and 3.3 (=0.01/0.003). The blood volume fractions 1 × 1010−4 andand 3 × 3 10×−510 m gavem gaver valuesr values of 2.0 of(=0.02/0.01) 2.0 (=0.02/0.01) and 3.3 and (=0.01/0.003). 3.3 (=0.01/0.003). The blood The volume blood fractions volume exiting the outlet boundary of the mixing chamber and the temperature of the outlet nozzle are shown exitingfractions the exiting outlet the boundary outlet boundary of the mixing of the chamber mixing and chamber the temperature and the temperature of the outlet of nozzle the outlet are shown nozzle in Figure 3. Variations in the obtained results for significantly different grid sizes (i.e., r = 2.0 and 3.3) inare Figure shown 3. in Variations Figure3. Variations in the obtained in the results obtained for results significantly for significantly different different grid sizes grid (i.e., sizes r = 2.0 (i.e., andr = 3.3) 2.0 were not significant, so the grid or mesh convergence of the present model was ensured. wereand 3.3) not were significant, not significant, so the grid so the or mesh grid or convergence mesh convergence of the present of the present model modelwas ensured. was ensured.

(a) (b) (a) (b) Figure 3. Grid sensitivity analysis (GSA) for: (a) blood volume fraction exiting the outlet boundary of Figure 3. Grid sensitivity analysis (GSA) for: (a) blood volume fraction exiting the outlet boundary of theFigure mixing 3. Grid chamber; sensitivity and ( analysisb) temperature (GSA) for: of the (a) outlet blood nozzle volume for fraction chosen exiting average the grid outlet sizes boundary of 2 × 10− of4, the mixing chamber; and (b) temperature of the outlet nozzle for chosen average grid sizes of 2 × 10−−4, the mixing−4 chamber;−5 and (b) temperature of the outlet nozzle for chosen average grid sizes of 2 × 10 , 1 × 10−4 and 3 × 10−5 m. 1 × 1010− and4 and 3 × 3 10× 10 m.−5 m. 3. Results and Discussion 3. Results and Discussion

3.1. Experimental Benchmarking 3.1. Experimental Benchmarking The main aim of the present model was to simulate the mixing phenomena in two‐phase fluid The main aim of the present model was to simulate the mixing phenomena in two‐phase fluid systems, which was coupled with the heat transfer module to keep track of temperature dispersion systems, which was coupled with the heat transfer module to keep track of temperature dispersion during mixing. In order to exhaustively benchmark the present model, the previous experimental during mixing. In order to exhaustively benchmark the present model, the previous experimental Appl. Sci. 2017, 7, 578 7 of 19

3. Results and Discussion

3.1. Experimental Benchmarking

Appl. Sci. 2017The, 7 main, 578 aim of the present model was to simulate the mixing phenomena in two-phase ﬂuid7 of 20 systems, which was coupled with the heat transfer module to keep track of temperature dispersion resultsduring from mixing. Akhlaghi In order et al. to[43] exhaustively regarding benchmarkthe propagation the present of plasma model, plume the previous in ambient experimental air were used, whereresults the frommeasurements Akhlaghi et al.were [43 ]focused regarding on the temperature propagation ofvariations plasma plume versus in ambient distance air away were used,from the where the measurements were focused on temperature variations versus distance away from the outlet outlet nozzle. Furthermore, experimental data on temperature variations associated with mixing nozzle. Furthermore, experimental data on temperature variations associated with mixing between between the discharged plume and the ambient air were needed for the present benchmarking. the discharged plume and the ambient air were needed for the present benchmarking. Therefore, it is Therefore,remarked it is that remarked the present that experimental the present benchmarking experimental directly benchmarking focused on directly the mixing focused between on the the two mixing betweenﬂuids the (in thistwo case fluids plasma (in this plume case and plasma air) with plume subsequent and air) temperature with subsequent dispersion. temperature In addition, dispersion. for the In addition,sake of benchmarking, for the sake aof similar benchmarking, experimental a setupsimilar of Akhlaghiexperimental et al. [ 43setup] was of modeled. Akhlaghi The et results al. [43] of was modeled.this benchmarking The results of are this shown benchmarking in Figure4. are shown in Figure 4.

FigureFigure 4. Comparison 4. Comparison between between temperatures temperatures at different distances distances from from the the outlet outlet for 6for kV 6 operating kV operating voltagevoltage obtained obtained experimentally experimentally by by Akhlaghi Akhlaghi etet al. al. [ 43[43]] and and from from theoretical theoretical predictions. predictions.

TheThe results results from from the the present present model model were inin aa good good agreement agreement with with previously previously obtained obtained experimentalexperimental data; data; this this proved proved the the capability capability of thethe present present model model to to precisely precisely predict predict the mixingthe mixing and and the subsequentthe subsequent heat heat distribution distribution during during plasma plasma dischargedischarge in in air. air. The The small small deviations deviations between between the the experimentalexperimental data data and and theoretical predictions predictions were were likely likely due to unknowndue to unknown and uncontrollable and uncontrollable external externalfactors factors involved involved in the experiments.in the experiments. Furthermore, since the present work dealt with mixing of blood (liquid) with helium plasma, Furthermore, since the present work dealt with mixing of blood (liquid) with helium plasma, the present model was also benchmarked using experimental results with liquid and gas interface, the present model was also benchmarked using experimental results with liquid and gas interface, including those for: (1) an air bubble rising in a water column; and (2) a water droplet moving in includingair and those impacting for: (1) a surface. an air bubble For (1), rising the vertical in a water velocities column; of a 2.77 and× (2)10 −a3 waterm air bubbledroplet at moving different in air −3 and heightsimpacting above a surface. the bottom For nozzle (1), the that vertical released velocities the air bubble of a into 2.77 the × 10 water m column air bubble were at employed different [48 heights]. aboveComparisons the bottom between nozzle vertical that released velocities the obtained air bubble by the into experiment the water and fromcolumn the presentwere employed model are [48]. Comparisonsshown in Figure between5, which vertical show velocities good agreement. obtained by To ensurethe experiment preservation and of from the interfacethe present between model are shownthe in air Figure bubble 5, and which water, show the contour good agreement. plots for the To bubble ensure at 0,preservation 0.02 and 0.04 of s arethe showninterface in Figure between6. the air bubbleThe capability and water, of our the present contour model plots in for preserving the bubble the at interface 0, 0.02 and between 0.04 thes are air shown bubble in and Figure water 6. The capability(i.e., the of liquid–gas our present system) model was in shown.preserving The the gradual interface change between in the volume the air fractionbubble and around water the (i.e., air the liquid–gasbubble (shownsystem) in was red) inshown. the water The column gradual (shown change in blue) in the demonstrated volume fraction that the presentaround model the air could bubble accurately track the degree of mixing between the gas (i.e., air) and the liquid (i.e., water) throughout (shown in red) in the water column (shown in blue) demonstrated that the present model could the simulation. For (2), the variations with time in the height of a 4.2 × 10−3-m-diameter water droplet accurately track the degree of mixing between the gas (i.e., air) and the liquid (i.e., water) throughout impacting onto a solid surface with a contact angle of 50◦ [49] were employed. Comparisons between −3 the simulation.heights obtained For (2), by thethe experiment variations andwith from time the in present the height model of area 4.2 shown × 10 in‐m Figure‐diameter7, which water show droplet impactinggood agreement. onto a solid The surface accuracy with of thea contact present angle model of in 50° simulating [49] were two-phase employed. ﬂuids Comparisons (i.e., liquid–gas) between heightssystem obtained was demonstrated by the experiment by the benchmarking and from the above. present model are shown in Figure 7, which show good agreement. The accuracy of the present model in simulating two‐phase fluids (i.e., liquid–gas) system was demonstrated by the benchmarking above.

Figure 5. Comparisons between vertical velocities of a 2.77 × 10−3 m air bubble at different heights above the bottom nozzle that released the air bubble into the water column obtained experimentally [48] (squares) and from the present model (circles). Appl. Sci. 2017, 7, 578 7 of 20 results from Akhlaghi et al. [43] regarding the propagation of plasma plume in ambient air were used, where the measurements were focused on temperature variations versus distance away from the outlet nozzle. Furthermore, experimental data on temperature variations associated with mixing between the discharged plume and the ambient air were needed for the present benchmarking. Therefore, it is remarked that the present experimental benchmarking directly focused on the mixing between the two fluids (in this case plasma plume and air) with subsequent temperature dispersion. In addition, for the sake of benchmarking, a similar experimental setup of Akhlaghi et al. [43] was modeled. The results of this benchmarking are shown in Figure 4.

Figure 4. Comparison between temperatures at different distances from the outlet for 6 kV operating voltage obtained experimentally by Akhlaghi et al. [43] and from theoretical predictions.

The results from the present model were in a good agreement with previously obtained experimental data; this proved the capability of the present model to precisely predict the mixing and the subsequent heat distribution during plasma discharge in air. The small deviations between the experimental data and theoretical predictions were likely due to unknown and uncontrollable external factors involved in the experiments. Furthermore, since the present work dealt with mixing of blood (liquid) with helium plasma, the present model was also benchmarked using experimental results with liquid and gas interface, including those for: (1) an air bubble rising in a water column; and (2) a water droplet moving in air and impacting a surface. For (1), the vertical velocities of a 2.77 × 10−3 m air bubble at different heights above the bottom nozzle that released the air bubble into the water column were employed [48]. Comparisons between vertical velocities obtained by the experiment and from the present model are shown in Figure 5, which show good agreement. To ensure preservation of the interface between the air bubble and water, the contour plots for the bubble at 0, 0.02 and 0.04 s are shown in Figure 6. The capability of our present model in preserving the interface between the air bubble and water (i.e., the liquid–gas system) was shown. The gradual change in the volume fraction around the air bubble (shown in red) in the water column (shown in blue) demonstrated that the present model could accurately track the degree of mixing between the gas (i.e., air) and the liquid (i.e., water) throughout the simulation. For (2), the variations with time in the height of a 4.2 × 10−3‐m‐diameter water droplet impacting onto a solid surface with a contact angle of 50° [49] were employed. Comparisons between heights obtained by the experiment and from the present model are shown in Figure 7, which show good agreement. The accuracy of the present model in simulating two‐phase fluids (i.e., liquid–gas) system wasAppl. Sci.demonstrated2017, 7, 578 by the benchmarking above. 8 of 19

Figure 5.Figure Comparisons 5. Comparisons between between vertical vertical velocities velocities ofof a a 2.77 2.77× 10× −103 m−3 airm bubbleair bubble at different at different heights heights above theabove bottom the bottom nozzle nozzle that that released released the the airair bubble bubble into into the waterthe water column column obtained obtained experimentally experimentally [48] Appl. Sci. (squares)2017, 7, 578 and from the present model (circles). 8 of 20 [48]Appl. (squares) Sci. 2017 ,and 7, 578 from the present model (circles). 8 of 20

Figure 6. Contour plots of the 2.77 × 10−3 m air bubble rising through the water column at: (a) 0; (b) × −3 −3 0.02;FigureFigure and (6.c 6.) Contour0.04Contour s. Blue plots plots color of of therepresents the 2.77 2.77 × 10 water10 m airandm airbubble red bubble color rising represents rising through through the the air thewater bubble. water column column at: (a at:) 0; (a ()b 0;) 0.02;(b) 0.02; and and (c) 0.04 (c) 0.04 s. Blue s. Blue color color represents represents water water and and red redcolor color represents represents the theair bubble. air bubble.

Figure 7. Comparisons between the heights of a 4.2 × 10−3‐m‐diameter water droplet impacting onto −33 a solidFigureFigure surface 7. 7. ComparisonsComparisons with a contact between angle theof 50° heights [49] (squares) ofof aa 4.24.2 ×× and 10 from‐m-m-diameter‐diameter the present water water model droplet droplet (curve). impacting impacting onto onto aa solid solid surface surface with with a a contact contact angle angle of of 50° 50◦ [49][49] (squares) (squares) and and from from the the present model (curve). 3.2. Computed Results 3.2.3.2. Computed Computed Results Results Due to employment of a finer mesh and a relatively long simulation time of 10.0 s, the present Due to employment of a finer mesh and a relatively long simulation time of 10.0 s, the present numericalDue simulation to employment was executed of a ﬁner on mesh a computer and a relatively cluster with long Intel simulation® Xeon E5 time‐2670 of 2.60 10.0 GHz s, the using present ® 48 numericalnumericalphysical cores simulation simulation and hyper was was ‐executedthreaded executed on onto 96.a a computer The computation cluster with time Intel to complete XeonXeon E5 E5-2670 the‐2670 simulations 2.60 2.60 GHz GHz using usingfor 48 physical cores and hyper‐threaded to 96. The computation time to complete the simulations for mixing48 physical chambers cores with and and hyper-threaded without obstacles to 96. was The ~2.96 computation × 104 and ~7.24 time × to 10 complete3 s, respectively. the simulations To make for 4 3 3 suremixingmixing that thechambers system with had and reached withoutwithout the obstaclesobstacles steady‐state was was ~2.96 over~2.96 the× × 10 simulation andand ~7.24 time×× 1010 ofs,s, respectively.10.0 respectively. s, the average To To make make velocitysuresure that in the the system mixingsystem had chamberhad reached reached domain the the steady-state steadywas scored,‐state over overand the simulationthethe resultssimulation timeare shown oftime 10.0 of s,in 10.0 the Figure average s, the 8a,b average velocity for chambersvelocityin the mixing with in the and chamber mixing without domainchamber obstacles, was domain scored, respectively. was and scored, the results and are the shown results in are Figure shown8a,b forin Figure chambers 8a,b with for chambersand without with obstacles, and without respectively. obstacles, respectively.

Figure 8. Average velocity magnitude of the mixture of fluids over the mixing chamber domain with andFigure without 8. Average obstacles velocity (Note: themagnitude mixing chamberof the mixture domain of isfluids marked over in the blue). mixing chamber domain with and without obstacles (Note: the mixing chamber domain is marked in blue). Appl. Sci. 2017, 7, 578 8 of 20

Figure 6. Contour plots of the 2.77 × 10−3 m air bubble rising through the water column at: (a) 0; (b) 0.02; and (c) 0.04 s. Blue color represents water and red color represents the air bubble.

Figure 7. Comparisons between the heights of a 4.2 × 10−3‐m‐diameter water droplet impacting onto a solid surface with a contact angle of 50° [49] (squares) and from the present model (curve).

3.2. Computed Results Due to employment of a finer mesh and a relatively long simulation time of 10.0 s, the present numerical simulation was executed on a computer cluster with Intel® Xeon E5‐2670 2.60 GHz using 48 physical cores and hyper‐threaded to 96. The computation time to complete the simulations for mixing chambers with and without obstacles was ~2.96 × 104 and ~7.24 × 103 s, respectively. To make sure that the system had reached the steady‐state over the simulation time of 10.0 s, the average Appl. Sci.velocity2017, 7, 578 in the mixing chamber domain was scored, and the results are shown in Figure 8a,b for 9 of 19 chambers with and without obstacles, respectively.

Figure 8.FigureAverage 8. Average velocity velocity magnitude magnitude of of the the mixture mixture of of fluids ﬂuids over over the the mixing mixing chamber chamber domain domain with with and withoutand without obstacles obstacles (Note: (Note: the the mixing mixing chamber chamber domain is is marked marked in blue). in blue).

The velocity magnitudes averaged over the mixing chamber domain for the two different conceptualAppl. designs Sci. 2017 of, 7, 578 the mixing chamber are shown in Figure8. The velocities in the mixing9 of 20 chamber domain with obstaclesThe velocity showed magnitudes fluctuations averaged for overt < the 2.0 mixing s, mainly chamber due domain to two for reasons: the two (1) different the steady-state was not yetconceptual reached fordesignst < 2.0of the s; and mixing (2) thechamber presence are shown of obstacles in Figure to 8. the The flow velocities when in chamber the mixing was getting filled wouldchamber significantly domain with affect obstacles the flow showed pattern fluctuations and the for t velocity < 2.0 s, mainly magnitude. due to two In reasons: contrast, (1) the the velocity steady‐state was not yet reached for t < 2.0 s; and (2) the presence of obstacles to the flow when variationschamber in the mixing was getting chamber filled would without significantly obstacles affect werethe flow found pattern negligible and the velocity since magnitude. a major In part of the flow remainedcontrast, undistorted the velocity (thevariations center in the part mixing of the chamber flow thatwithout was obstacles away fromwere found the mixing negligible chamber since walls). However, thea major steady-state part of the for flow the remained designs undistorted without any(the center obstacles part of would the flow also that be was fully away achieved from the at t ~ 2.0 s. After the steady-statemixing chamber was walls). fully However, achieved, the steady the‐state velocity for the magnitude designs without in any the obstacles mixing would chamber also domain be fully achieved at t ~ 2.0 s. After the steady‐state was fully achieved, the velocity magnitude in the would notmixing fluctuate chamber noticeably. domain Therefore,would not fluctuate the velocity noticeably. of the Therefore, flow would the velocity remain of the almost flow would constant while the mixingremain chamber almost was constant in operation while the mixing (i.e., when chamber the was blood in operation and cold (i.e., plasma when the were blood injectedand cold from the embeddedplasma nozzles). were Snapshots injected from for the spatial embedded evolution nozzles). of Snapshots the velocity for spatial over evolution the mixing of the chamber velocity domains are shownover in Figures the mixing9 and chamber 10, for domains mixing are chambers shown in Figures with and 9 and without 10, for mixing obstacles, chambers respectively. with and without obstacles, respectively.

Figure 9. DistributionFigure 9. Distribution of velocity of velocity streamlines streamlines over over the the mixing mixing chamber chamber with with obstacles obstacles at: (a) 0 at: s; ( ba)) 2 0 s; (b) 2 s; (c) 4 s; (d) 6s; s;(c) ( 4e )s; 8 (d s;) 6 and s; (e) ( f8) s; 10 and s. ( Differentf) 10 s. Different velocities velocities are are represented represented by by different different colors colors as shown as shown in −1 the color barin the (in color m s −bar1). (in m s ). Appl. Sci. 2017, 7, 578 10 of 19 Appl. Sci. 2017, 7, 578 10 of 20

FigureFigure 10. 10.Distribution Distribution of of velocity velocity streamlines streamlines overover thethe mixing chamber chamber without without obstacles obstacles at: at: (a) ( a0) s; 0 s; (b)( 2b) s; 2 (s;c) ( 4c) s; 4 (s;d )(d 6) s;6 (s;e )(e 8) s;8 s; and and (f ()f 10) 10 s. s. Different Different velocitiesvelocities are represented represented by by different different colors colors as as −1 shownshown in thein the color color bar bar (in (in m m s s−1).).

TheThe spatial spatial evolutions evolutions of of velocities velocities in in the the mixing mixing chamber chamber domain domain are are shown shown in in Figures Figures9 9and and 10 for10 mixing for mixing chamber chamber with with and and without without obstacles, obstacles, respectively. respectively. For For tt >> 2.0 s, s, the the velocities velocities did did not not changechange noticeably. noticeably. These These results results together together with with thosethose shownshown in Figure 8 supported that that steady steady state state waswas achieved achieved for fort > t 2.0> 2.0 s. s. Moreover, Moreover, velocities velocities awayaway from the walls were were higher higher than than those those closer closer to to thethe no-slip no‐slip walls walls due due to to adhesion adhesion between between the the fluid fluid and and solid.solid. The initial temperature of blood was set to be 310 K [38] and the initial cold plasma temperature The initial temperature of blood was set to be 310 K [38] and the initial cold plasma temperature was set to be at 303 K [39]. In the FEM technique, an element consisted of a number of nodes, each was set to be at 303 K [39]. In the FEM technique, an element consisted of a number of nodes, associated with a shape function (Ni) and a temperature (Ti), so the element temperature would be each associated with a shape function (Ni) and a temperature (Ti), so the element temperature would ∑ element M , where T was the temperature in the element, M was the total number of be Telement = ∑ (Ni × Ti), where Telement was the temperature in the element, M was the total number nodes in a specifici=1 element, Ni and Ti were the shape function and temperature of the ith node within of nodesthe element, in a specific respectively. element, TheN iaverageand Ti temperaturewere the shape of the function domain and was temperature determined of through the ith nodethe withinarithmetic the element, mean of respectively. temperatures The of elements average temperaturein the domain. of The the average domain temperatures was determined over through the outlet the arithmeticnozzle are mean shown of temperatures in Figure 11. For of elements t < 2.0 s, the in theaverage domain. temperature The average (i.e., the temperatures bulk temperature over the of outlet the nozzleflow) are of shownthe mixture in Figure in the 11 outlet. For tnozzle< 2.0 s, domain the average for the temperature mixing chamber (i.e., thewith bulk obstacles temperature was higher of the flow)than of that the mixturewithout inobstacles. the outlet The nozzle increase domain in the for temperature the mixing here chamber was explained with obstacles by the was chamber higher thanfilling that withoutand subsequent obstacles. mixing The increase between in the temperatureinjected blood here and was plasma. explained When by steady the chamber state was filling andachieved subsequent after mixingt > ~2.0 s, between the average the temperature injected blood of the and mixture plasma. in the When outlet steady nozzle state domain was for achieved both afterchamberst > ~2.0 became s, the average ~308.55 temperature K. Moreover, of the mixtureheat transfer in the between outlet nozzle these domaintwo different for both fluids chambers was becamecontrolled ~308.55 by K. the Moreover, heat flux the (q” heat) and transfer the spatial between distribution these two of different temperature, fluids so, was as controlled result of by the the heatincreased flux (q”) contact and the between spatial distribution blood and plasma of temperature, in the mixing so, as chamber, result of thethe increasedfinal temperature contact betweenof the bloodmixture and plasmawould be in regulated the mixing based chamber, on the theinitial final temperature temperature of both of the fluids. mixture In addition, would beit could regulated be basedconcluded on the initialthat heat temperature transfer could of bothbe enhanced fluids. In by addition, the increased it could contact be concludedas a result of that mixing, heat and transfer at couldthe besame enhanced time the by reaction the increased between contact the plasma as a result constituents of mixing, and and the at theblood same would time be the further reaction betweenenhanced. the plasma The results constituents of temperature and the distribution blood would inside be further the device enhanced. with Thethe flow results streamlines of temperature are shown in Figures 12 and 13 for mixing chambers with and without obstacles, respectively. The distribution inside the device with the flow streamlines are shown in Figures 12 and 13 for mixing chambers with and without obstacles, respectively. The snapshots were taken from the system every Appl. Sci. 2017, 7, 578 11 of 19 Appl. Sci. 2017, 7, 578 11 of 20 Appl. Sci. 2017, 7, 578 11 of 20 snapshots2.0 s over thewere total taken simulation from the runtimesystem every of 10.0 2.0 s s in over which the total the mixing simulation chamber runtime was of fully 10.0 filleds in which with snapshots were taken from the system every 2.0 s over the total simulation runtime of 10.0 s in which theblood mixing and plasma. chamber was fully filled with blood and plasma. the mixing chamber was fully filled with blood and plasma.

Figure 11. Average temperature of mixture over outlet nozzle domain (shown in blue) for mixing Figure 11. Average temperature of mixture over outlet nozzle domain (shown in blue) for mixing chambers with and without obstacles (Note: outlet nozzle domain is marked in blue). chambers with and without obstacles (Note: outlet nozzle domain is marked in blue).

FigureFigure 12. Distribution 12. Distribution of flow of flow streamlines streamlines and and temperature temperature over over the the mixing mixing chamber with with obstacles obstacles at: (a)at: 0 s; (a ()b 0) s; 2 s;(b) ( c2) s; 4 ( s;c) (4d s;) 6(d s;) 6 (e s;) ( 8e s;) 8 and s; and (f) (f 10) 10 s. s. Different Different temperatures temperatures are represented represented by by different different colorscolors as shown as shown in the in color the color bar (inbar K).(in K). Figure 12. Distribution of flow streamlines and temperature over the mixing chamber with obstacles at:The (a) temperature 0 s; (b) 2 s; (c) 4 distributions s; (d) 6 s; (e) 8 s; over and the(f) 10 mixing s. Different chambers temperatures shown are in represented Figures 12 by and different 13 show the temperaturecolors as shown variations in the color between bar (in K). the injected blood and plasma as a result of heat transfer and subsequent mixing. The temperature distributions over the mixing chamber with obstacles were more gradual when compared to those for no obstacles. As shown in Figure 12f, the final mixture temperature at the outlet boundary was ~308 K. The gradual color changes of the flow streamlines characterized the temperature distribution of the mixture of blood and plasma. As observed in Figure 13f, the temperature in the middle part of the outlet nozzle was almost equivalent to the Appl. Sci. 2017, 7, 578 12 of 19 temperature of the injected blood (~310 K). Moreover, the heat distribution tended to be less effective in a mixing chamber without obstacles, as shown in Figure 13f, which did not show gradual changes in the heat color map throughout the device’s domain. In addition, the distribution of blood and plasma volume fractions in both mixing-chamber designs when the chambers are fully filled and when steady-state is reached (i.e., t = 10.0 s) are shown in Figure 14a,b for chambers with and without obstacles,Appl. respectively. Sci. 2017, 7, 578 12 of 20

FigureFigure 13. Distribution 13. Distribution of ﬂow of streamlines flow streamlines and temperature and temperature over the over mixing the mixing chamber chamber without without obstacles at: (a) 0obstacles s; (b) 2 s; at: (c ()a 4) 0 s; s; ( d(b)) 6 2 s; s; ((ec)) 84 s; ( andd) 6 (s;f) (e 10) 8 s. s; Different and (f) 10 temperatures s. Different temperatures are represented are represented by different colorsAppl. Sci. asby shown 2017different, 7, 578 in colors the color as shown bar (in in the K). color bar (in K). 13 of 20

The temperature distributions over the mixing chambers shown in Figures 12 and 13 show the temperature variations between the injected blood and plasma as a result of heat transfer and subsequent mixing. The temperature distributions over the mixing chamber with obstacles were more gradual when compared to those for no obstacles. As shown in Figure 12f, the final mixture temperature at the outlet boundary was ~308 K. The gradual color changes of the flow streamlines characterized the temperature distribution of the mixture of blood and plasma. As observed in Figure 13f, the temperature in the middle part of the outlet nozzle was almost equivalent to the temperature of the injected blood (~310 K). Moreover, the heat distribution tended to be less effective in a mixing chamber without obstacles, as shown in Figure 13f, which did not show gradual changes in the heat color map throughout the device’s domain. In addition, the distribution of blood and plasma volume fractions in both mixing‐chamber designs when the chambers are fully filled and when steady‐state is reached (i.e., t = 10.0 s) are shown in Figure 14a,b for chambers with and without obstacles, respectively.

FigureFigure 14. Distributions 14. Distributions of mixture of mixture volume volume fractions fractions (between(between 0 0 and and 1) 1) in in mixing mixing chambers: chambers: (a) with (a) with obstacles;obstacles; and ( band) without (b) without obstacles. obstacles. The The colors colors representrepresent the the volume volume fractions fractions of the of themixture; mixture; red red correspondscorresponds to the to blood the blood (volume (volume fraction fraction = 0) = and0) and blue blue corresponds corresponds the the plasmaplasma (volume (volume fraction fraction = = 1). 1).

The volume fraction near ~0.5 (see color bar in Figure 14) represented a perfect mixing between the two fluids injected into the mixing chamber. Apart from the degree of mixing, special attention would be paid on the spatial distribution of this mixture, which determined the path along which the mixture propagated in a particular mixing‐chamber design. As shown by the flow profile Figure 14a, the mixing chamber with obstacles allowed a better mixing and at the same time directed the mixture of blood and plasma into the outlet nozzle. In contrast, the outlet zone in the mixing chamber without obstacles was almost completely filled with blood (see Figure 14b), and the blood at the center of the mixing chamber and the outlet nozzle did not have direct contact with the injected plasma from the side nozzles. In terms of treatment efficiency, it could be expected that the mixing chamber without obstacles would be less effective compared to one with obstacles, since the plasma which was initially present in the system was “pushed out” effectively by the blood without exhaustive mixing due to the higher density and dynamic viscosity of the blood (compared to the injected plasma). The volume fraction at the boundary of the outlet nozzle is quantitatively shown in Figure 15.

Figure 15. Average blood volume fractions scored over the outlet boundary of the nozzle (shown in blue) for mixing chambers with and without obstacles.

The average blood volume fractions scored over the outlet boundary of the nozzle for mixing chambers with and without obstacles are shown in Figure 15. When steady state was achieved after Appl. Sci. 2017, 7, 578 13 of 20

Figure 14. Distributions of mixture volume fractions (between 0 and 1) in mixing chambers: (a) with obstacles; and (b) without obstacles. The colors represent the volume fractions of the mixture; red corresponds to the blood (volume fraction = 0) and blue corresponds the plasma (volume fraction = Appl. Sci. 2017, 7, 578 13 of 19 1).

The volume fraction near ~0.5 (see (see color color bar bar in in Figure Figure 14)14) represented represented a perfect mixing between the two fluids fluids injected into the mixing chamber. Apart from the degree of mixing, special attention would be paid on the spatial distribution of this mixture, which determined the path along which the mixture propagated in a particular mixing mixing-chamber‐chamber design. As As shown shown by by the the flow flow profile profile Figure Figure 14a,14a, the mixing chamber with obstacles allowed a better mixing and at the the same same time time directed directed the the mixture of blood and plasma into the outlet nozzle. In In contrast, contrast, the the outlet outlet zone zone in in the the mixing mixing chamber chamber without without obstacles was almost completely filled filled with blood (see Figure 14b),14b), and the blood at the center of the mixing chamber and the outlet nozzle did not have direct contact with the injected plasma from the side nozzles. In In terms terms of of treatment treatment efficiency, efficiency, it could be expected that the mixing chamber without obstacles would be less effective compared to one with obstacles, since the plasma plasma which which was was initially initially present inin thethe systemsystem was was “pushed “pushed out” out” effectively effectively by by the the blood blood without without exhaustive exhaustive mixing mixing due due to the to thehigher higher density density and and dynamic dynamic viscosity viscosity of of the the blood blood (compared (compared to to the the injected injected plasma). plasma). The volume fraction at the boundary of the outlet nozzle is quantitatively shown inin Figure 1515..

Figure 15. Average blood volume fractions scored over the outlet boundary of the nozzle (shown in blue) for mixing chambers with and without obstacles.

The average blood volume fractions scored over the outlet boundary of the nozzle for mixing Appl. Sci. 2017, 7, 578 14 of 20 chambers with and without obstacles are shown in Figure 15.15. When steady state was achieved after t > t~2.0> ~2.0 s, the s, the results results for forthe the two two chambers chambers overlapped, overlapped, which which showed showed that that similar similar amounts amounts of blood of blood exitedexited from from the the outlets outlets of ofthe the chambers. chambers. As As blood blood was was injected injected into into the the chambers, chambers, the the outlets outlets started started to to get filled filled until until saturation saturation was was reached. reached. The The blood blood volume volume fraction fraction exiting exiting the the outlet outlet boundary boundary was was foundfound to be to be~0.66 ~0.66 after after steady steady-state‐state was was achieved. achieved. The The spatial spatial distributions distributions of volume of volume fraction fraction in the in the outletoutlet nozzle nozzle for for the the mixing mixing chambers chambers (at (at t t== 10.0 10.0 s) s) are are also shown inin FigureFigure 16 16.. Figure Figure 16 16aa shows shows that thatthe the blood blood and and plasma plasma were were well-mixed well‐mixed in in the the presence presence of of obstacles. obstacles. In In contrast, contrast, Figure Figure 16 16bb shows shows that, that,in in the the absence absence of obstacles,of obstacles, mixing mixing was was insignificant insignificant in the in centralthe central part part of the of outlet the outlet nozzle, nozzle, and became and becamemore more significant significant towards towards the side the walls side walls of the of chamber. the chamber.

FigureFigure 16. 16. SpatialSpatial distributions distributions of volume of volume fraction fraction in the in the outlet outlet nozzle nozzle for for mixing mixing chamber: chamber: (a) (witha) with obstacles;obstacles; and and (b) (withoutb) without obstacles obstacles at 10.0 at 10.0 s. Blue s. Blue color color (i.e., (i.e., volume volume fraction fraction = 0) = represents 0) represents blood blood whilewhile red red color color (i.e., (i.e., volume volume fraction fraction = 1) = represents 1) represents plasma. plasma.

3.3. Importance of Obstacles in Mixing To the best of our knowledge, there were no reports in the literature on designs on mixing chambers for blood and cold plasma. However, to demonstrate the genericity of the results from using obstacles in mixing chambers and of the corresponding conclusions, three different mixing chamber designs with different dimensions and aspect ratios were analyzed. These chambers had: (a) a long width of 9 × 10−2 m; (b) small obstacles (1 × 1 × 10−4 m2); and (c) a long length (0.21 m) and two plasma inlets. Schematic diagrams of these chambers are shown in Figure 17a–c. The thicknesses of all chamber designs were set to be either 1 × 10−2 or 2 × 10−2 m. As such, each chamber design had four variations with or without obstacles, and with different thicknesses.

(a) (b) (c)

Figure 17. Schematic diagrams of mixing chambers with: (a) a long width of 9 × 10−2 m; (b) smaller obstacles (1 × 1 × 10−4 m2); and (c) a long length (0.21 m) and two plasma inlets.

Three‐dimensional snapshots of mixing chambers with a width of 9 × 10−2 m having thicknesses of 1 × 10−2 and 2 × 10−2 m, with and without obstacles, are shown in Figure 18a–d. Mixing of blood and cold plasma was enhanced by mixing chambers with obstacles when compared to those without obstacles. However, the central part of the mixing chambers was filled with blood not mixed with the injected plasma, which was explained by the insufficient volumetric flow rate of the plasma to achieve adequate mixing. Similarly, three‐dimensional snapshots of mixing chambers with small obstacles (1 × 1 × 10−4 m2) having thicknesses of 1 × 10−2 and 2 × 10−2 m, with and without obstacles, are Appl. Sci. 2017, 7, 578 14 of 20

t > ~2.0 s, the results for the two chambers overlapped, which showed that similar amounts of blood exited from the outlets of the chambers. As blood was injected into the chambers, the outlets started to get filled until saturation was reached. The blood volume fraction exiting the outlet boundary was found to be ~0.66 after steady‐state was achieved. The spatial distributions of volume fraction in the outlet nozzle for the mixing chambers (at t = 10.0 s) are also shown in Figure 16. Figure 16a shows that the blood and plasma were well‐mixed in the presence of obstacles. In contrast, Figure 16b shows that, in the absence of obstacles, mixing was insignificant in the central part of the outlet nozzle, and became more significant towards the side walls of the chamber.

Figure 16. Spatial distributions of volume fraction in the outlet nozzle for mixing chamber: (a) with obstacles; and (b) without obstacles at 10.0 s. Blue color (i.e., volume fraction = 0) represents blood while red color (i.e., volume fraction = 1) represents plasma. Appl. Sci. 2017, 7, 578 14 of 19

3.3. Importance of Obstacles in Mixing 3.3. Importance of Obstacles in Mixing To the best of our knowledge, there were no reports in the literature on designs on mixing chambersTo the for best blood of our and knowledge, cold plasma. there wereHowever, no reports to demonstrate in the literature the genericity on designs of on the mixing results from chambers for blood and cold plasma. However, to demonstrate the genericity of the results from using using obstacles in mixing chambers and of the corresponding conclusions, three different mixing obstacles in mixing chambers and of the corresponding conclusions, three different mixing chamber chamber designs with different dimensions and aspect ratios were analyzed. These chambers had: designs with different dimensions and aspect ratios were analyzed. These chambers had: (a) a long −2 −4 2 width(a) a long of 9 ×width10−2 ofm; 9 (b) × 10 small m; obstacles (b) small (1 obstacles× 1 × 10− 4(1m ×2 );1 and× 10 (c) m a long); and length (c) a (0.21long m)length and two(0.21 m) and plasmatwo plasma inlets. inlets. Schematic Schematic diagrams diagrams of these chambers of these chambers are shown inare Figure shown 17a–c. in Figure The thicknesses 17a–c. The of allthicknesses chamberof all chamber designs designs were set towere be either set to 1 be× 10either−2 or 1 2 ×× 1010−−2 2orm. 2 As× 10 such,−2 m. each As chambersuch, each design chamber had four design had variationsfour variations with or with without or without obstacles, obstacles, and with and different with thicknesses. different thicknesses.

(a) (b) (c)

−2 FigureFigure 17. 17.Schematic Schematic diagrams diagrams of mixing of mixing chambers chambers with: (with:a) a long (a) width a long of width 9 × 10 −of2 m;9 × ( b10) smaller m; (b) smaller obstaclesobstacles (1 (1× ×1 1× ×10 10−−44 mm22);); andand ( c()c) a a long long length length (0.21 (0.21 m) m) and and two two plasma plasma inlets. inlets.

Three-dimensionalThree‐dimensional snapshots snapshots of mixing of mixing chambers chambers with a widthwith a of width 9 × 10 of−2 9m × having10−2 m thicknesseshaving thicknesses of 11 ×× 10−22 andand 2 2 ×× 1010−−2 m,2 m, with with and and without without obstacles,obstacles, are are shown shown in in Figure Figure 18a–d. 18a–d. Mixing Mixing of blood of blood and andcold cold plasma plasma was was enhanced enhanced by mixingmixing chambers chambers with with obstacles obstacles when when compared compared to those to without those without obstacles. However, However, the the central central part part of of the the mixing mixing chambers chambers was was filled filled with with blood blood not mixed not mixed with with the theinjected injected plasma, plasma, which which was was explainedexplained by by the the insufficient insufficient volumetric volumetric flow rateflow of rate the plasma of the toplasma to achieve adequate adequate mixing. mixing. Similarly, Similarly, three-dimensional three‐dimensional snapshots snapshots of mixing of mixing chambers chambers with small with small obstacles (1 × 1 × 10−4 m2) having thicknesses of 1 × 10−2 and 2 × 10−2 m, with and without obstacles (1 × 1 × 10−4 m2) having thicknesses of 1 × 10−2 and 2 × 10−2 m, with and without obstacles, are obstacles, are shown in Figure 19a–d. Substantial mixing inside the mixing chambers with obstacles was achieved for distances as far as the outlet, which was not affected by an increase in the thickness of the chambers. When no obstacles were present, mixing between blood and plasma was poor and the central part of the mixing chambers was filled with blood not mixed with the injected plasma. Lastly, three-dimensional snapshots of the mixing chambers with a length of 0.21 m and two plasma inlets having thicknesses of 1 × 10−2 and 2 × 10−2 m, with and without obstacles, are shown in Figure 20a–d. Similar to previous designs, substantial mixing inside the mixing chambers could only be achieved in the presence of obstacles. According to the above analyses, obstacles within the mixing chambers were generically essential for achieving substantial mixing between the plasma and blood. Appl. Sci. 2017, 7, 578 15 of 20 Appl. Sci. 2017, 7, 578 15 of 20 Appl. Sci. 2017, 7, 578 15 of 20 shown in Figure 19a–d. Substantial mixing inside the mixing chambers with obstacles was achieved forshown distances in Figure as far19a–d. as theSubstantial outlet, whichmixing was inside not the affected mixing by chambers an increase with inobstacles the thickness was achieved of the shown in Figure 19a–d. Substantial mixing inside the mixing chambers with obstacles was achieved chambers.for distances When as farno asobstacles the outlet, were which present, was mixing not affected between by blood an increase and plasma in the was thickness poor and of thethe for distances as far as the outlet, which was not affected by an increase in the thickness of the centralchambers. part When of the nomixing obstacles chambers were was present, filled mixingwith blood between not mixed blood with and the plasma injected was plasma. poor and Lastly, the chambers. When no obstacles were present, mixing between blood and plasma was poor and the threecentral‐dimensional part of the mixingsnapshots chambers of the mixingwas filled chambers with blood with not a lengthmixed ofwith 0.21 the m injected and two plasma. plasma Lastly, inlets central part of the mixing chambers was filled with blood not mixed with the injected plasma. Lastly, havingthree‐dimensional thicknesses snapshotsof 1 × 10−2 andof the 2 ×mixing 10−2 m, chambers with and withwithout a length obstacles, of 0.21 are m shown and two in Figureplasma 20a–d. inlets three‐dimensional snapshots of the mixing chambers with a length of 0.21 m and two plasma inlets Similarhaving thicknessesto previous ofdesigns, 1 × 10− 2substantial and 2 × 10 −mixing2 m, with inside and withoutthe mixing obstacles, chambers are couldshown only in Figure be achieved 20a–d. having thicknesses of 1 × 10−2 and 2 × 10−2 m, with and without obstacles, are shown in Figure 20a–d. inSimilar the presence to previous of obstacles. designs, Accordingsubstantial to mixing the above inside analyses, the mixing obstacles chambers within could the mixingonly be chambers achieved Similar to previous designs, substantial mixing inside the mixing chambers could only be achieved werein the generically presence of essential obstacles. for According achieving tosubstantial the above mixing analyses, between obstacles the plasmawithin theand mixing blood. chambers in the presence of obstacles. According to the above analyses, obstacles within the mixing chambers Appl.were Sci. generically2017, 7, 578 essential for achieving substantial mixing between the plasma and blood. 15 of 19 were generically essential for achieving substantial mixing between the plasma and blood.

Figure 18. Three‐dimensional snapshots of mixing chambers with a width of 9 × 10−2 m having a −2 thicknessFigure 18. of Three 1 × 10‐−dimensional2 m: (a) with obstacles;snapshots andof mixing (b) without chambers obstacles; with and a width having of a 9 thickness × 10 − 2m ofhaving 2 × 10 −a2 Figure 18. Three-dimensional snapshots of mixing chambers with a width of 9 × 10−2 m having Figure 18. Three‐dimensional−2 snapshots of mixing chambers with a width of 9 × 10 m having a−2 m:thickness (c) with of obstacles; 1 × 10 m: −and2 (a) (withd) without obstacles; obstacles. and (b ) without obstacles; and having a thickness of 2 × 10 athickness thickness of of 1 × 1 10×−210 m: (am:) with (a) withobstacles; obstacles; and (b and) without (b) without obstacles; obstacles; and having and having a thickness a thickness of 2 × 10 of−2 m: (c) −with2 obstacles; and (d) without obstacles. 2m:× (c10) withm: obstacles; (c) with obstacles; and (d) without and (d )obstacles. without obstacles.

Figure 19. Three‐dimensional snapshots of mixing chambers with small obstacles (1 × 1 × 10−4 m2) Figure 19. Three-dimensional snapshots of mixing chambers with small obstacles (1 × 1 × 10−4 m2) havingFigure a19. thickness Three‐dimensional of 1 × 10−2 m: snapshots (a) with obstacles; of mixing and chambers (b) without with obstacles; small obstacles and having (1 × 1a ×thickness 10−4 m2) havingFigure a19. thickness Three‐dimensional of 1 × 10−2 m:snapshots (a) with of obstacles; mixing andchambers (b) without with obstacles;small obstacles and having (1 × 1 a × thickness 10−4 m2) ofhaving 2 × 10 a− 2thickness m: (c) with of obstacles;1 × 10−2 m: and (a) with(d) without obstacles; obstacles. and (b ) without obstacles; and having a thickness ofhaving 2 × 10 a −thickness2 m: (c) with of 1 obstacles;× 10−2 m: (a and) with (d) obstacles; without obstacles. and (b) without obstacles; and having a thickness of 2 × 10−2 m: (c) with obstacles; and (d) without obstacles. of 2 × 10−2 m: (c) with obstacles; and (d) without obstacles.

Figure 20. Three-dimensional snapshots of mixing chambers with a length of 0.21 m and two plasma Figure 20. Three‐dimensional snapshots of mixing chambers with a length of 0.21 m and two plasma inlets having a thickness of 1 × 10−2 m: (a) with obstacles; and (b) without obstacles; and having inletsFigure having 20. Three a thickness‐dimensional of 1 snapshots× 10−2 m: (ofa) mixingwith obstacles; chambers and with (b )a withoutlength of obstacles; 0.21 m and and two having plasma a −2 aFigure thickness 20. Three of 2 ×‐dimensional10 m: (c) withsnapshots obstacles;−2 of mixing and (d chambers) without with obstacles. a length of 0.21 m and two plasma thicknessinlets having of 2 ×a 10thickness−2 m: (c) ofwith 1 ×obstacles; 10 m: ( aand) with (d) withoutobstacles; obstacles. and (b) without obstacles; and having a inlets having a thickness of 1 × 10−2 m: (a) with obstacles; and (b) without obstacles; and having a thickness of 2 × 10−2 m: (c) with obstacles; and (d) without obstacles. thickness of 2 × 10−2 m: (c) with obstacles; and (d) without obstacles. 4. Conclusions 4. Conclusions 4. ConclusionsInIn the present work, work, a a model model based based on on our our previously previously developed developed theory theory [29] [29 was] was employed employed to tostudy studyIn cold the cold plasmapresent plasma plume work, plume mixinga model mixing with based with blood on blood withour previously witha view a viewto enhance developed to enhance the theorymixing. the mixing.[29] The was level The employed set level method set to In the present work, a model based on our previously developed theory [29] was employed to methodwasstudy used cold was toplasma usedcapture plume to capturethe mixingmixing the withand mixing bloodevolution and with evolution ofa view blood to of enhancein blood cold inplasma the cold mixing. plasmain two The different inlevel two set different methodmixing study cold plasma plume mixing with blood with a view to enhance the mixing. The level set method mixingchamberwas used chamber designsto capture designs in thea in threemixing a three-dimensional‐dimensional and evolution coordinate coordinate of blood system. in system. cold Simultaneousplasma Simultaneous in two determination determinationdifferent mixing ofof was used to capture the mixing and evolution of blood in cold plasma in two different mixing temperaturechamber designs distributions in a inthree simulated‐dimensional mixing coordinate chambers assystem. plasma andSimultaneous blood were determination injected from theof inletchamber nozzles designs were enabledin a three by the‐dimensional heat transfer coordinate coupling. Enhancementsystem. Simultaneous of mixing betweendetermination blood and of plasma in the presence of obstacles to the ﬂow was demonstrated by the present results. The present conceptual designs of mixing chambers would be useful in future development of cold plasma medicine devices for treatment of blood related diseases and at the same time the present model would be an important tool for further investigation of mixing phenomena with subsequent temperature distributions between blood and cold atmospheric pressure plasmas. In addition, the present model could be used to simulate mixing phenomena between the blood and different plasma carrier gases. Appl. Sci. 2017, 7, 578 16 of 19

Acknowledgments: We acknowledge the support from the Neutron computer cluster from the Department of Physics and Materials Science, City University of Hong Kong, for the computational work involved in this paper. This research was supported by the research grant 7004641 from City University of Hong Kong. Author Contributions: M.S.B. and K.N.Y. conceived and designed the experiments; M.S.B. and K.N.Y. performed the experiments; M.S.B. and K.N.Y. analyzed the data; M.S.B and K.N.Y. contributed reagents/materials/analysis tools; and M.S.B. and K.N.Y. wrote the paper. Conﬂicts of Interest: The authors declare no conﬂict of interest.

Appendix A

The algorithm of the left-preconditioned GMRES method is described in the following

Algorithm A1 The left-preconditioned GMRES method

1: Choose initial guess x(0) 2: for j = 1,2, . . . 3: solve r from Mr = b − Ax(0) (1) 4: v = r/||r||2 5: s := ||r||2e1 6: for i = 1,2, . . . ,m 7: solve w from Mw = Av(i) 8: for k = 1, . . . ,i (k) 9: hk,i = (w,v ) (k) 10: w = w − hk,iv 11: end

12: hi+1,i = ||w||2 (i+1) 13: v = w/hi+1,i 14: apply J1, ... ,Ji−1 on (h1,i, ... ,hi+1,i) th th 15: construct Ji, on i and (i+1) component of h:,i, such th 16: that (i+1) component of Jih:,i is 0 17: s:= Jis 18: if s(i+1) is small enough then UPDATE(ex,i) and exit 19: end 20: end

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