Available online at www.sciencedirect.com JOURNAL OF ENVIRONMENTAL SCIENCES ISSN 1001-0742 CN 11-2629/X Journal of Environmental Sciences 2012, 24(7) 1157–1164 www.jesc.ac.cn

Investigation of the hydrodynamic behavior of diatom aggregates using particle image velocimetry

Feng Xiao1,2,∗, Xiaoyan Li2, Kitming Lam2, Dongsheng Wang1

1. State Key Laboratory of Environmental Aquatic Chemistry, Research Center for Eco-Environmental Sciences, Chinese Academy of Sciences, Beijing 100085, China 2. Environmental Engineering Research Centre, Department of Civil Engineering, University of Hong Kong, Hong Kong, China

Received 13 October 2011; revised 05 December 2011; accepted 12 January 2012

Abstract The hydrodynamic behavior of diatom aggregates has a significant influence on the interactions and flocculation kinetics of algae. However, characterization of the hydrodynamics of diatoms and diatom aggregates in water is rather difficult. In this laboratory study, an advanced visualization technique in particle image velocimetry (PIV) was employed to investigate the hydrodynamic properties of settling diatom aggregates. The experiments were conducted in a settling column filled with a suspension of fluorescent polymeric beads as seed tracers. A laser light sheet was generated by the PIV setup to illuminate a thin vertical planar region in the settling column, while the motions of particles were recorded by a high speed charge-coupled device (CCD) camera. This technique was able to capture the trajectories of the tracers when a diatom aggregate settled through the tracer suspension. The PIV results indicated directly the curvilinear feature of the streamlines around diatom aggregates. The rectilinear collision model largely overestimated the collision areas of the settling particles. Algae aggregates appeared to be highly porous and fractal, which allowed streamlines to penetrate into the aggregate interior. The diatom aggregates have a fluid collection efficiency of 10%–40%. The permeable feature of aggregates can significantly enhance the collisions and flocculation between the aggregates and other small particles including algal cells in water. Key words: diatom aggregate; fluid collection efficiency; fractal; particle image velocimetry DOI: 10.1016/S1001-0742(11)60960-1

Introduction the collision efficiency by ignoring the influences of the hydrodynamic behavior and the structural morphology of Algal blooms have become one of the most serious water aggregates on the interaction and flocculation between pollution problems in the coastal waters of Hong Kong suspended particles in water. and mainland China. Algal coagulation, which transforms Diatom aggregates are highly porous with properties de- small cells to larger and faster settling aggregates, has scribed by fractals (Logan and Kilps, 1995; Li and Logan, been considered as an important mechanism of algal bloom 1995; Li et al., 1998). The interior flow through the diatom termination in marine systems (Jackson et al., 1995; Li and aggregates caused by the porous-fractal structure has been Logan, 1995; Jackson and Burd, 1998). proventoaffect the hydrodynamic behavior significantly, Based on field observations and particle coagulation and hence the particle flocculation and biomaterial trans- theories, Jackson (1990) proposed a model combining both port (Li and Logan, 1997; Li et al., 2003). To describe algal growth kinetics and particle coagulation to describe more accurately the flocculation of an algal bloom, Zhang the algal flocculation dynamics. A similar modeling ap- and Li (2003) developed a fractal-curvilinear model to proach has been used by Boehm and Grant (1998) for describe the flocculation process based on previous work better understanding the physical and biological factors by Han and Lawler (1992). Many conventional settling which addressed the algal population dynamics. However, column experiments (Li and Logan, 1997) were carried out both models were derived from Smoluchowski’s model to find out the inherent relationship between the reduction (also called the rectilinear model) assuming that parti- factor and the permeability of the particles. However, cles approach each other straightforwardly until collision these experiments just predicted the floc permeability from occurs (O’Melia and Tiller, 1998). Therefore, the algal the floc terminal velocity and could not provide detailed cell concentrations predicated by the models are much information about the hydrodynamics in the creeping flow higher than those actually observed in the field (Millgan field. A bubble-tracking technique was utilized to visualize and Hill, 1998). Apparently, these models overestimated the flow field near the settling floc (Tsou et al., 2002; Wu and Lee, 1998; Wu et al., 2002; Pietsch et al., 2002). How- * Corresponding author. E-mail: [email protected] ever, this technique does not follow the motions of water 1158 Journal of Environmental Sciences 2012, 24(7) 1157–1164 / Feng Xiao et al. Vol. 24 molecules induced by the falling particle. It just shows the structure of the grown diatom aggregates was highly the trajectories of the buoyant bubbles. Thus, the bubble- porous as shown by microscopic observation (Fig. 1c). tracking technique cannot give the exact information of 1.2 Particle image velocimetry (PIV) technique the flow field. Therefore, there is still a lack of direct evidence of the internal flow through particle aggregates. It PIV is a whole-flow-field technique providing instanta- is desirable to have streamline information for specifying neous velocity vector measurements in a cross-section of the hydrodynamic features and the internal permeation of a flow (Raffel et al., 1998). The use of modern charge- diatom aggregates. coupled device (CCD) cameras and dedicated computing With the development of optical techniques, particle hardware results in real-time velocity maps. PIV results are image velocimetry (PIV) does provide us an opportunity similar to computational fluid dynamics, i.e., large eddy to examine the curvilinear model. PIV is a non-intrusive simulations, and real-time velocity maps are an invaluable optical method to capture whole velocity fields in flows tool for fluid dynamics researchers. within a millisecond and to study flow sensitive to small PIV was carried out to investigate the creeping flow field perturbations. These advantages indicate the great poten- around falling diatom aggregates and capture the whole tial for PIV use in various flow fields. To date, PIV has velocity field within a millisecond, and to study the flow not been widely applied to study flow related to water sensitivity to small perturbations. According to the PIV treatment processes. Most studies have only utilized this principles, a program written by Matlab (Mathworks Inc., technology to identify the local velocity gradient during USA) was employed to obtain the conventional parameters flocculation process (Cheng et al., 1997; Coufort et al., provided by PIV, such as particle displacements and cor- 2005; Xiao et al., 2011; Zhong et al., 2011a, 2011b). responding velocity components. In addition, the images The aim of this study is to characterize the hydrody- were also analyzed by direct observation to outline the namic behavior of diatom aggregates by using an advanced moving trajectory of a seeding particle induced by the flow visualization technique in PIV. The PIV experiments larger falling object. This was used to set up a fixed set of were performed to capture the detailed spatial information coordinates through the center of the larger falling object. surrounding falling diatom aggregates from the motion of Then, the positions of relevant seeding particles could be seeding particles. Hence, the permeability, fluid collec- digitized using the software WINDIG, which is by far tion efficiency and collision frequency function of diatom the most effective software to extract data from graphs aggregates could be determined. In addition, the hydrody- in the Windows system. The procedure was repeated on namic interactions and the flow patterns were considered consecutive PIV images selected to acquire more digitized under different hydraulic conditions. points of the same trace particles. The points of the trace particles on different images display their apparent position 1 Materials and methods displacement caused by the falling object. Finally, the digitized points for the same trace particle were connected, 1.1 Diatom bloom and flocculation which formed a trajectory curve of the seeding particle relative to the falling object. By repeating the image Diatom blooms were produced in rectangular glass tanks treatment procedure, a group of trajectories around the ff × × with an e ective volume of 6 L (20 cm 20 cm 15 cm, falling object could be obtained. The trajectories of the × × L W H). The tanks were filled with autoclaved artificial PIV tracers would show the flow field, i.e. streamlines, = / seawater (salinity 30 ppt). Stock standard f 2 media was around the falling object. Figure 2 schematically illustrates ff added to o er enough nutrients for diatom culturing based the trajectories of the seeding particles, or the streamlines, on the guidance described by Guillard (1975). Artificial around and through a falling object. light was set at a cycle of 12 hr light and 12 hr darkness For a permeable aggregate, its internal permeation may in the incubator operated at room temperature (20–22°C). be measured by the fluid collection efficiency (η), which is Slight aeration was used to provide a mixing environment the ratio of the flow passing through the aggregate to the and prevent the diatom mass from sedimentation. Thalas- flow approaching the aggregate (Veerapaneni and Wiesner, siosra, Chaetoceros gracilis (Fig. 1a, b), which are long 1996). The fluid collection efficiency can be estimated chain cells, were inoculated into the growth tank. After one from the streamlines around and through the aggregate, or week, an algae flocculation bloom could be observed and 2 η = (di–d) , where di is the span of the streamlines flowing

abc

20 μm 10 μm 500 μm Fig. 1 Diatom seeds and aggregates. (a) Thalassiosra, (b) Chaetoceros gracilis, (c) aggregates. No. 7 Investigation of the hydrodynamic behavior of diatom aggregates using particle image velocimetry 1159

Interior flow expanding a laser beam with a combination of cylindrical and spherical lenses, illuminated a thin vertical planar flow region (< 0.5 mm). Polyamid seeding particles (PSP, Approaching flow U Dantec Dynamic Corp., Denmark) with a diameter of 10 μm were placed in the settling column as tracers to represent the streamlines of the fluid. The cultured diatom aggregate samples taken from the incubator was carefully released in the laser sheet from the top of the column and settled at a terminal velocity of U. The movements of the d Projected A, i seeding particles induced by falling aggregates were then Tracers, ds Floc, d captured by a recording device, a high speed CCD camera Exterior flow with a resolution of 1280 × 1024 (1200.hs, PCO.imaging). Fig. 2 Schematics of the trajectories of seeding tracers and the subse- The image was continuously recorded and sent to the quent determination of the fluid collection efficiency of an aggregate. workstation for further data processing. The stored images were analyzed in an interrogation box. Autocorrelation of into the aggregate relative to the span of the streamlines (d) the seeding particle coordinates was then applied within approaching it (Fig. 2). In addition, a curvilinear reduction the interrogation box to determine a coherent seeding factor may be used to relate the curvilinear collision particle displacement. In addition, the structural features frequency function, β , with the conventional rectilinear cur of the diatom aggregates, such as size, shape factor collision frequency function, β ,inE = β /β . The rec cur cur rec (4×pi×area/circumference2;0= line, 1 = circle (4πA/C2)) E value can be calculated using the curvilinear collision cur and sphericity (min diameter/max diameter; 0 = line, 1 = model of Han and Lawler (1992). Using the PIV-based circle), were determined by using a computer-based image streamlines, Ecur for a large falling particle or aggregate 2 2 analysis system (Scion Image, Frederick, USA). can be estimated from Ecur = (di+ds) /(d+ds) , where ds is the diameter of the seeding particles. Since ds (ca. 10 μm) 1.4 Morphological analysis is so small compared to d that it can be neglected, it can be i Diatom aggregates formed by particle flocculation are regarded that E = η. Obviously, η = 0 means there are cur porous and fractal (Jackson, 1990). It is well known for no permeable effects in evaluating hydrodynamics of the aggregates that the mass (m) of the aggregate scales with interactive aggregates; while η = 1 means the aggregates its size d according to Eq. (1) are 100% permeable. 1.3 Settling experiments m ∼ dDf (1) Figure 3 schematically describes the experimental setup. In the present work, the settling experiments were conducted in a settling column which is a rectangular glass (Borofloat where, Df is three dimensional fractal dimension. For 33, Schott) column with dimensions (L × W × H) of 40 an aggregate made up of N particles each of mass m0 mm × 40 mm × 500 mm. A laser light sheet, generated by and volume v0, the mass of an aggregate is related to the number of particles in the aggregate by m = Nm0.

Settling colomn Settling particle Laser sheet

Cylindrical lens

CCD camera

Recovery system Computer

Laser source

X,Y adjuster

Fig. 3 Schematic of the PIV-settling experimental setup. 1160 Journal of Environmental Sciences 2012, 24(7) 1157–1164 / Feng Xiao et al. Vol. 24

Therefore, the porosity (p) can be derived in terms of of the graphs. The experimental terminal velocity of the falling diatom aggregate was 2.69 mm/sec, corresponding Nv (1 − p) = 0 (2) to a Reynolds number of 3.3. V a In Fig. 4a, three seed tracers indicated by arrows 1, 2 3 where, Va is the volume of aggregate expressed by Va∼d . and 3 were located beneath the diatom aggregate without And, Eq. (1) can be converted to movement when far away from the larger aggregate. In Fig. 4b, c, the seeds 1, 2 and 3 were pushed away ∼ Df N d (3) from the centerline of the falling aggregate when it was Combining Eqs. (2) and (3), we can therefore derive the approaching them. Subsequently, as Fig. 4d reveals, the fractal scaling relationship tracer 2 was missing and the tracer 3 just permeated the void of the aggregate because of the highly fractal-porous − (1 − p) ∼ dDf 3 (4) structure of the diatom aggregate, and the tracer 1 just swept over the aggregate surface. As the larger aggregate According to previous research (Johnson et al., 1996; continuously fell down at its terminal velocity, it can be Gmachowski, 2005; Bache and Gregory, 2010), the settling found that tracers 1 and 3 gradually shifted close to the velocity of the aggregate in the Stokes flow region can be centerline of the aggregate. Hence, the curvilinear features described as follows: and creeping flow surrounding the diatom aggregates were U ∼ (1 − p)d2 (5) directly demonstrated using the PIV technique. It clearly showed that the rectilinear model should overestimate the Therefore, the following fractal scaling relationship can collision potential. Moreover, it is necessary to account be obtained between settling velocity and aggregate size for the porosity and curvilinear effects to modify the − existing collision frequency functions and to improve the U ∼ dDf 1 (6) understanding of algae flocculation. 2 Results 2.2 Settling velocity and morphology The settling velocities in water of the investigated diatom 2.1 Visual observation of the creeping flow aggregates ranged from 1.88 to 5.84 mm/sec (Fig. 5). The frames in Fig. 4 represent the motions of the three The corresponding Reynolds numbers were in the range seeding particles induced by the larger falling diatom ag- of 1.59–11.79. The settling velocities measured were in gregate denoted as A3 (diameter 1256 μm) from a portion general agreement with those reported in previous studies

a b c

3 2 3 1 2 3 1 2 2 1 1 3 1 2

d e f

3

1 3 1 3 11 1

Fig. 4 Trajectories of seeding tracers related to falling diatom aggregates. Frames (a–f) show the position change of the seeding tracers (1–3). No. 7 Investigation of the hydrodynamic behavior of diatom aggregates using particle image velocimetry 1161

6 2.4 Streamline determination

5 The positions of the seeding particles in relation to the falling particle can be identified directly from the PIV 4 video image. A streamline around the falling diatom aggregate can then be determined from the trajectory of a tracer. By repeating the procedure, a group of streamlines 3 surrounding the large falling particle can be formulated (Fig. 7). Figure 7 summarizes the positions of the seeding particles and presents the trajectories of the performed ex- Settling velocity (mm/sec) 2 periments. It can be found that the motions of the seeding D = 1.87 f particles can be classified as three groups. One is open- channel movement. The second is that the seeding tracers 1000 1500 2000 will clog in the diatoms, and the last is that some tracers Size (μm) will permeate through the aggregates. All of these three Fig. 5 Free-falling velocity as dependent on diatom aggregate size. group streamlines showed curvilinear effects and indicated the fractal-porous features of the diatom aggregates. The (Li and Yuan, 2002). The slopes of the settling velocity PIV results provide direct evidence for validation of the against size after log-log transformation were 0.87 (r2 = curvilinear model that has been used to calculate the curvi- 0.70). Therefore, according to the relationship between the linear reduction factor relative to the rectilinear prediction free-falling velocity and the size, the diatom aggregates of particle collisions (Han and Lawler, 1992). For diatom have an average fractal dimension Df = 1.87, indicating aggregates, the curvilinear reduction factors ranged from the fractal nature of marine aggregates. 0.008 to 0.42 (Fig. 8). However, the curvilinear reduction factors determined from the PIV study were generally 2.3 Flow pattern three orders of magnitude greater than those predicted by Once the images were captured and stored in the computer, the curvilinear model (Han and Lawler, 1992). From the the PIV interrogation program was applied to obtain the obtained streamlines, the fluid collection efficiency for A1, raw displacement vector data. In our approach, the interro- A2 and A3 also can be estimated from the dimensionless 2 2 gation area was 48 pixel × 48 pixels and the overlapping cross-sectional area Ecur = (di + ds) /(d + ds) as 0.12, size was half of the interrogation area so that there were 0.42, and 0.20 respectively. That is, 12%, 42% and 20% enough particle pairs to provide reasonable data. The of the approaching fluid flows through rather than flowing signal to noise ratio was employed to calculate the average around the investigated diatom aggregates. Clearly, the vector in one interrogation area. In the Fig. 6, typical flow highly porous diatom aggregate A2 could allow 42% the patterns under different conditions are presented. The sizes approaching fluid to flow through rather than around it, and of the diatom aggregates A1, A2 and A3 were 844, 1940 the extent of creeping flow was demonstrated to be higher and 1257 μm, respectively. for A3 (20%) than A1 (12%). Therefore, the role of the Figure 6 shows the three velocity fields of diatom creeping flow is significant and cannot be neglected. Figure aggregates A1, A2 and A3 corresponding with Reynolds 8 presents a summary of the characteristics of marine numbers (Re) of 1.75, 8.48, and 3.25 respectively. It can diatom aggregates from the PIV settling experiments. be noticed that the flow patterns were quite different. In Fig. 8, the diameter of the aggregate was plotted The length and the density of the vectors were increased against the estimated fluid collection efficiency. From the with increasing Re. These results indicated that higher results, it appears that the intra-flow within the diatom Re would enhance the hydrodynamic interaction between aggregate is not a function of the aggregate size. These approaching particles. The diatom aggregate A2 was very results are in good agreement with a previous study (Zhang special. There were some obviously hollow spaces in the and Li, 2003). middle of the aggregate.

0 0 0 -1 A1 -1 A2 -1 A3 -2 -2 -2 -3 -3 -3 -4 -4 -4 -5 -5 -5 Y (mm) Y (mm) Y (mm) -6 -6 -6 -7 -7 -7 -8 -8 -8 -9 -9 -9 -10 -10 -10 02 4 6 81012 0246 81012 0246 81012 X (mm) X (mm) X (mm) Fig. 6 Flow velocity vector display around falling diatom aggregates. A1: D = 844 μm, Reynolds numbers (Re) = 1.75; A2: D = 1940 μm, Re = 8.48; A3: D = 1257 μm, Re = 3.25. 1162 Journal of Environmental Sciences 2012, 24(7) 1157–1164 / Feng Xiao et al. Vol. 24

A1 A2 A3

Fig. 7 Streamlines around falling diatom aggregates. A1: D = 844 μm, Re = 1.75; A2: D = 1940 μm, Re = 8.48; A3: D = 1257 μm, Re = 3.25.

0.5 streamlines of diatom aggregates were also successfully obtained. This proved that the PIV technique is able to 0.4 capture the flow field around not only falling solid spheres and particle aggregates but also highly porous diatom 0.3 aggregates. Diatom aggregates are of quite low fractal dimensions 0.2 (Df), ranging from 1.3 to 2.0 (Logan and Wilkinson, 1991; Jackson et al., 1995), compared with Df > 2.1 of common bioaggregates in water and wastewater (Li et al., 1998; Li 0.1

Fluid collection efficiency and Yuan, 2002). Logan and Wilkinson (1991) calculated diatom aggregates with fractal dimension of 1.52 ± 0.19. 0.0 The lower the fractal dimension is, the more porous the 800 1000 1200 1400 1600 1800 2000 2200 aggregate is. The curvilinear reduction factors of diatom D (μm) aggregates ranged from 0.008 to 0.42, which were two or Fig. 8 Fluid collection efficiency of the diatom aggregates in PIV three orders of magnitude greater than predicted by the experiments. curvilinear model (Han and Lawler, 1992). This suggests that the available curvilinear model may underestimate the 3 Discussion collision potential between particles. Compared with our previous PIV study (Xiao et al., 2007, 2011), the reduction The hydrodynamics of permeable aggregates is of interest factors of diatom aggregates were more than two orders of in the aggregation process. Theoretical work has been magnitude higher than those of similarly-sized solid falling conducted to characterize the permeability and the re- spheres, but close to those of aggregate flocs. It appears duction factors (Brinkman, 1947; Happel, 1958; Dullien, that the porous-fractal structure of the aggregates could 1992; Alder, 1981; Veerapaneni and Wiesner, 1996; Vanni, permit flow through the aggregate interior. This signifi- 2000). In addition, many conventional column experiments cant internal flow permeation would greatly enhance the (Li and Ganczarczyk, 1992; Li and Logan, 1997; Li et al., flocculation of marine aggregates with other particles as 2003) have been carried out to elucidate the inherent rela- well as material transfer through the aggregates. Although tionship between the reduction factor and the permeability determined with only limited data, the fluid collection of the particles. However, these experiments only predicted efficiency of diatom aggregates seems not to be a function the floc permeability from the floc terminal velocity and of the size of the aggregates. However, the values of other factors and could not provide detailed information the fluid collection efficiency are quite similar to those about the hydrodynamics in the creeping flow field. Hence, of aggregate flocs with similar fractal dimension. Hence, the floc permeability could not be accurately determined. this indicates that the fluid collection efficiency may be Tsou et al. (2002) employed a bubble-tracking technique associated with the fractal dimension and further research to observe the flow field to investigate floc permeability. may be needed to identify the relationship between them. This technique had the great advantage of being able to observe the fluid flow directly. However, this technique does not follow the motions of water molecules induced 4 Conclusions by the falling particle. It only showed the trajectories of the buoyant bubbles. In our previous study (Xiao et Settling experiments were performed in a settling column al., 2007, 2011), an advanced visualization technique PIV tank filled with a suspension of polyamide tracing parti- was successful in studying the creeping flow by analyzing cles. Particle image velocimetry (PIV) was carried out to the movements of tracers related to falling solid spheres examine the detailed spatial variations of many seeding and particle aggregates of microspheres. Here, based on particles when a free-falling diatom aggregate passed by. this technique, the flow pattern, hydrodynamic profile and The investigation directly observed the flow field sur- No. 7 Investigation of the hydrodynamic behavior of diatom aggregates using particle image velocimetry 1163 rounding diatom aggregates and noted the existence of ment measured using photographic and aperture impedance intra-flow through the aggregates. This shows that the PIV (Coulter and Elzone) techniques. Deep Sea Research Part technique is capable of studying the flow patterns, hydro- II: Topical Studies in Oceanography, 42(1): 139–157. dynamics and streamlines of falling marine aggregates. Johnson C P, Li X Y, Logan B E, 1996. Settling velocities of The PIV laboratory results indicate that the rectilinear fractal aggregates. Environmental Science and Technology, model largely overestimates the collision areas of the 30(6): 1911–1918. Han M, Lawler D F, 1992. 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