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Dynamics and Structure of Colloidal Aggregates Under Microchannel Flow† Cite This: Soft Matter, 2019, 15, 744 Ming Han, a Jonathan K

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Dynamics and Structure of Colloidal Aggregates Under Microchannel Flow† Cite This: Soft Matter, 2019, 15, 744 Ming Han, a Jonathan K Soft Matter PAPER Dynamics and structure of colloidal aggregates under microchannel flow† Cite this: Soft Matter, 2019, 15, 744 Ming Han, a Jonathan K. Whitmer b and Erik Luijten *bcd The kinetics of colloidal gels under narrow confinement are of widespread practical relevance, with applications ranging from flow in biological systems to 3D printing. Although the properties of such gels under uniform shear have received considerable attention, the effects of strongly nonuniform shear are far less understood. Motivated by the possibilities offered by recent advances in nano- and microfluidics, we explore the generic phase behavior and dynamics of attractive colloids subject to microchannel flow, using mesoscale particle-based hydrodynamic simulations. Whereas moderate shear strengths result in shear-assisted crystallization, high shear strengths overwhelm the attractions and lead to melting of the Received 15th July 2018, clusters. Within the transition region between these two regimes, we discover remarkable dynamics of Accepted 19th December 2018 the colloidal aggregates. Shear-induced surface melting of the aggregates, in conjunction with the DOI: 10.1039/c8sm01451e Plateau–Rayleigh instability and size-dependent cluster velocities, leads to a cyclic process in which elongated threads of colloidal aggregates break up and reform, resulting in large crystallites. These rsc.li/soft-matter-journal insights offer new possibilities for the control of colloidal dynamics and aggregation under confinement. 1 Introduction been studied separately under ideal conditions, with uniform shear and localized particle motion, typically induced by the Colloidal gelation plays an important role in the creation of relative motion of two parallel boundaries. However, in many wide classes of materials, resulting in stable nonequilibrium realistic applications colloidal gels are driven by a flow through aggregates of (sub)micron-sized particles that may be deformed confined geometries, necessarily coupling nonuniform shear by modest stress. The mechanical properties of such gels are and directional hydrodynamic forces. related to their internal structure. Small clusters formed during One ubiquitous example is the flow of colloidal dispersions the early stages of colloidal aggregation already lack the mobility through a microchannel, as realized in the transport of red to efficiently adjust their positions. As a result, they become blood cells in a microcapillary13 and the pumping of ink for 3D dynamically arrested and percolate in disordered, loose printing through a slot channel.6,14 This has motivated recent networks1 that are firm in a quiescent environment but floppy attempts to explore the diffusion of individual colloids subject under shear. Colloidal gels have attracted considerable attention to a channel flow.15,16 Developments in nano- and micro- as a model system for kinetic arrest;1–4 gelation has been fluidics17–20 and in particular corresponding applications in exploited to generate porous patterns for tissue engineering particle assembly21–23 further reinforce the need to understand scaffolds5 and to synthesize gel-based ink for three-dimensional aggregation of (sub)microscopic particles driven within narrow (3D) printing.6 Moreover, when exposed to external driving forces, confinements. Nonuniformity of shear effects exerted by flow is these gels can display a variety of remarkable behaviors, both in established at length scales comparable to the channel cross- morphology and in dynamics. Examples include shear-induced section. In macroscopic channels, colloidal clusters are typically aggregation,7 crystallization8 and melting9 as well as shear small compared to this scale and hence different clusters thinning10,11 and thickening.12 Most of these phenomena have experience different shear strengths depending on their location within the channel. By contrast, clusters within a (sub)microchannel a Graduate Program in Applied Physics, Northwestern University, Evanston, can have sizes comparable to the channel cross-section and thus Illinois 60208, USA different shear forces are exerted simultaneously on each individual b Department of Materials Science and Engineering, Northwestern University, cluster. Meanwhile, the global flow causes additional rheological Evanston, Illinois 60208, USA. E-mail: [email protected] effects on the aggregates, including jamming, merging, and c Department of Engineering Sciences and Applied Mathematics, densification.24 Conversely, the presence of clusters leads to Northwestern University, Evanston, Illinois 60208, USA d Department of Physics and Astronomy, Northwestern University, Evanston, considerable disturbances of the flow profile. This rich combination Illinois 60208, USA of factors makes the behavior of attractive colloids under micro- † Electronic supplementary information (ESI) available. See DOI: 10.1039/c8sm01451e channel flow an interesting topic of practical relevance, which we 744 | Soft Matter, 2019, 15, 744--751 This journal is © The Royal Society of Chemistry 2019 Paper Soft Matter pursue here via mesoscale particle-based hydrodynamic simulations. chosen, yielding an overall interaction with range Drc = zsc o We find that the colloids, which display gel-like behavior under 0.1sc and strength Eb = À8kBT. This ensures the system resides resting conditions,25 undergo shear-assisted crystallization. within the coexistence region and therefore crystallization Remarkably, not only does the degree of ordering depend would occur if the system could attain equilibrium. Given its sensitively on the flow conditions, but the order is also attained short-ranged nature, the precise form of the interaction is through a cyclic process in which colloidal aggregates repeatedly immaterial to the phase behavior.1,29 break up and merge again. The colloids are embedded inpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a solvent with kinematic 2 2 This paper is organized as follows. First, we provide a viscosity n B 4sc /t (where t ¼ mcsc =kBT is the colloidal detailed description of our simulation model in Section 2. After diffusion time, mc the colloidal mass). The entire suspension is demonstrating the nonuniform shear of a microchannel flow in pumped by a pressure gradient through a narrow channel of Section 3.1, we discuss its effect on the phase behavior of a cross-sectional dimensions W  W, with W ranging from 4sc to colloidal gel in Section 3.2. In Sections 3.3 and 3.4, we show 15sc. Periodic boundary conditions are applied on the inlet and that the nonuniform shear also leads to a unique rheology as the outlet. A long channel of length L =80sc, containing 132 to well as the Plateau–Rayleigh instability for colloidal aggregates. 1850 colloids (depending on W), is employed to avoid artifacts Lastly, we conclude the paper with a brief summary in Section 4. due to the periodicity. To include both thermal and hydrodynamic effects, we 2 Method and model couple our system to a multi-particle collision30 (MPC) hydro- dynamic solver with Andersen thermostat. The system is divided We employ molecular dynamics (MD) simulations to model a into a 3D grid with resolution Nx  Ny  Nz,withNx = Ny =4(W/sc) colloidal suspension being pumped through a narrow channel. and Nz =4(L/sc), for a total of 81 920 to 1 152 000 cells. Each cubic The suspension contains monodisperse colloids with diameter cell (linear size a0) on average contains five point-like fluid sc and volume fraction fc = 0.054. The colloids interact via particles with mass m =0.004mc, which exchange momentum strong short-range attractions mediated by nonabsorbing polymers, with nearby colloids. This yields a solvent comprised of whosepresenceisimplicitlymodeledbyanAsakura–Oosawa(AO) 4.096  105 to 5.76  106 fluid particles. The pressure gradient potential26,27 between the colloids, is implemented via a constant force acting on each fluid particle. "# 3 3 To avoid spurious (additional) depletion forces induced by the 1 þ z 3r=sc 1 r=sc U ðrÞ¼ Àk Tf 1 À þ ; fluid particles, we set sc =4.3a0 whereas the colloid-fluid radius is AO B p z 2ð1 þ zÞ 2 1 þ z set to scf =2a0, as suggested by previous work on colloidal gelation.31,32 TheMDtimestepissetto2 10À4t and the fluid sc r ð1 þ zÞsc; collision step size to 2  10À2t. The mass density of the fluid (1) particles rf gives rise to a dynamic viscosity m = rfn B 5.12mc/tsc. All hydrodynamic surfaces, i.e., channel walls and colloidal where fp is the volume fraction of the implicit polymers and z denotes the size ratio between the polymers and the colloids. To surfaces, impose stick boundary conditions on the fluid and 33 avoid discontinuity in forces, the AO potential is rounded with a are treated via the bounce-back approach. The colloid-wall and quadratic function near the colloidal surface,28 fluid-wall interactions are modeled by purely repulsive shifted- ( truncated Lennard-Jones potentials. The Reynolds number 2 Bðr À sÞ þ C; 0 r o ð1 þ azÞsc Re = U W/n (where U is the flow velocity at the centerline and U ðrÞ¼ (2) 0 0 att W the channel width) characterizing the channel flow ranges UAO ðrÞð1 þ azÞsc r ð1 þ zÞsc from 10À3 to 10. All runs are performed for 2  107 MD steps with parameter a = 0.1. The constants B and C are set to maintain (4000t), and repeated 30-fold for each flow strength. the continuity of both Uatt and its first derivative at the crossover point rm =(1+az)sc, Âà 3kBTfp 2 2 3 Results B ¼ 4 2 ð1 þ zÞ ð1 þ azÞ ; (3) 4az sc 3.1 Shear flow 2 2 2 In the absence of dispersed particles, the microchannel flow C = UAO(rm) À Ba z sc . (4) U(x,y) decays from its maximum U0 at the center to zero at the The excluded-volume effect of the colloids is implemented channel walls (Fig. 1a) whereas the opposite occurs to the _ by a soft-core repulsion, resultant shear rate g (Fig. 1b). This resembles the parabolic profile characteristic of Poiseuille flow,34,35 albeit distorted "# 18 2 sc 18 1 near the walls owing to the square cross-section.
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