Optimizing Micromixer Surfaces To Deter Biofouling - ACS Applied

Subscriber access provided by UNIV OF DURHAM

Article

Optimizing Micromixer Surfaces to Deter Biofouling James T. Waters, Ya Liu, Like Li, and Anna C. Balazs ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b19845 • Publication Date (Web): 09 Feb 2018 Downloaded from http://pubs.acs.org on February 16, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

ACS Applied Materials & Interfaces is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Applied Materials & Interfaces

Optimizing Micromixer Surfaces to Deter Biofouling James T. Waters,1 Ya Liu,1 Like Li,2 and Anna C. Balazs1* 1

Chemical Engineering Department, University of Pittsburgh, Pittsburgh, PA 15261 2

Department of Mechanical Engineering, Mississippi State University, MS 39762

*Corresponding author’s e-mail: [email protected] Abstract Using computational modeling, we show that the dynamic interplay between a flowing fluid and the appropriately designed surface relief pattern can inhibit the fouling of the substrate. We specifically focus on surfaces that are decorated with three-dimensional chevron or sawtooth “micromixer” patterns and model the fouling agents (e.g., cells) as spherical microcapsules. The interaction between the imposed shear flow and the chevrons on the surface generates 3D vortices in the system. We pinpoint a range of shear rates where the forces from these vortices can rupture the bonds between two mobile microcapsules near the surface. Notably, the patterned surface offers fewer points of attachment than a flat substrate, and the shear flows readily transport the separated capsules away from the layer. We contrast the performance of surfaces that encompass rectangular posts, chevrons and asymmetric sawtooth patterns and thereby identify the geometric factors that cause the sawtooth structure to be the most effective at disrupting the bonding between the capsules. By breaking up nascent clusters of contaminant cells, these 3D relief patterns can play a vital role in disrupting the biofouling of surfaces immersed in flowing fluids. Keywords: antifouling, microcapsules, microvortex, adhesion, computer simulation,

ACS Paragon Plus Environment

1

ACS Applied Materials & Interfaces 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 39

I. Introduction Within microfluidic devices, angled ridges that jut out from the confining walls are used to generate vortices about the mean direction of flow. These vortices, in turn, enable the intermixing of different fluids at low Reynolds number1–4. Inspired by the utility of these geometrically patterned surfaces, we use computational modeling to show that the flow fields generated by ridged substrates can break bonds between microcapsules (e.g., cells) near the substrate, transport the separated particles away from the surface and inhibit the biofouling of the layer. Marine biofouling is the accretion of organisms on surfaces in aqueous solutions. In the case of commercial ships and military vessels, this build-up can lead to reduced performance and increased fuel consumption5,6. Additionally, it can lead to the transport of invasive species between marine ecosystems7. It is clear that mitigating this fouling is of great importance. Typically, biofouling occurs in several stages; after absorption of individual bacteria and marine diatoms, these species bind together to form larger clusters. Eventually, the surface is subject to macrofouling in the form of multicellular organisms8–10. By breaking up nascent clusters of contaminant cells, we can potentially disrupt the process of colonization by macrofouling species, which are responsible for most of the economic and environmental cost of biofouling5. Antifouling strategies such as biocidal paints have been effective, but are avoided due to negative environmental effects11,12. Recent work has instead focused on alternative methods, employing fouling release coatings13,14 and physical mechanisms to deter the growth of fouling organisms15–18.For example, micro-topographically patterned surfaces, involving pillars and ridges, have been used to prevent the binding of individual zoospores19 and bacteria20 to the surfaces. Structures with spacings on the scale of 2 µm have been designed to decrease the area available for attachment, and have demonstrated success against the growth of the green alga


2

Page 3 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Ulva in the laboratory21,22. More recent field trials have demonstrated the difficulty in safeguarding against the diversity of organisms in the marine environment and their wideranging settlement strategies23,24. In devising an alternative approach to inhibiting biofouling, we considered the performance of the so-called “herringbone chaotic mixers”4, which are highly effective at blending dissolved reagents at microfluidic scales. In this system, the rectangular ridges along the walls of the microchambers are arranged in a herringbone pattern. This arrangement and similar structural motifs can be applied to larger immersed surfaces, where no-slip conditions near the boundary create a region of laminar flow. By using the vortices created by the mixer, we can potentially separate clusters of cells near the surface and inhibit clusters from binding to the substrate. This new application requires a new set of design considerations, which in turn necessitates the use of models that allow us to capture the salient interactions in the system. Specifically, we must take into account not only the dynamics arising from the interactions of the cells with the flow field, but also the response of the flow to the moving cells. In addition, the unicellular species bind to form larger clusters. These intercellular bonding interactions will displace the species from ideal trajectories that correspond to the fluid streamlines. We note that researchers2 have simulated the interaction of herringbone micromixer surfaces with tracer particles, which simply follow the fluid streamlines. The latter study also neglected the formation of bonds between neighboring particles. In contrast to the previous study, 2 our aim is to utilize the flow generated around the relief patterns to separate bound clusters and convey the separated particles away from the surface. To determine whether the flow fields around the vortex-generating surface are sufficiently strong to disrupt the bonding between microcapsules and prevent settlement of


3


Page 4 of 39

clusters, we utilize a hybrid approach that combines the lattice Boltzmann method (LBM) for fluid dynamics and the lattice spring method (LSM) for the micromechanics of the capsules. Using this LBM-LSM technique, we can simulate the dynamic interactions between spherical microcapsules and the flowing fluid. We also introduce bonding interactions between the capsules; bonds can pull capsules closer together with a Hookean spring force, while the probability of rupture grows exponentially with the force acting along the bond. Via these LBM-LSM simulations, we identify mechanisms that lead to the separation of the capsules both within and between microvortices. With this insight, we design ridged surfaces that minimize the settlement of the clusters on the surface. In this study, a significant challenge is pinpointing the parameter space where the generated vortices are sufficiently strong to separate the cells, and transport the separated cells away from the surface. By varying the configuration of the ridges along the walls, we isolate designs that maximize the effectiveness of the microvortexgenerating surface to inhibit the settlement of clusters of capsules on the surface. II. Methods A. Description of the Hybrid LBM-LSM Model We anticipate that the cell-cell interactions will be strongly dependent on the local velocity of the host fluid. The flow fields will, in turn, depend on the 3D architecture of the surface, as well the motion of the capsules. Our hybrid LBM-LSM approach allows us to capture the complex fluid-structure interactions within this system. The lattice Boltzmann model (LBM)25 offers an efficient method to solve the Navier-Stokes equation for fluids flowing over complex surfaces and thus allows us to determine how the fluid velocity fields depend on the features of the substrate and presence of the mobile capsules. For this study, we used the 3DQ19 scheme, which uses a cubic lattice with nineteen lattice vectors.


4

Page 5 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The interaction of the fluid with the solid surface is handled via a bounce-back scheme that maintains the total mass of fluid in the system, and enforces a no-slip condition at the interface of the fluid and the surface. Any arbitrary solid object on the substrate can be defined by a set of vertices, and a set of triangular faces linking those vertices. The boundary between solid objects and the free fluid is identified by ray-tracing, beginning from the substrate and moving upwards along the z-dimension while checking for intersections with any of the faces. Unlike the mobile capsules, this solid boundary does not change over the course of the simulation. The fouling agents (cells) are modeled as fluid-filled capsules. We use the lattice spring method (LSM)26 to model the surface of each capsule as two concentric spherical shells of point masses. Hookean springs link mass points to their neighbors, approximating an elastic surface. For this study, the springs comprising the structure of each capsule are assumed to be relatively stiff, so that the capsule maintains a spherical shape. The interface between the fluid and the capsule is handled by using a bounce-back scheme similar to that employed at the solid boundaries27. As the boundary of the capsule is mobile, this is subsequently adjusted based upon the velocity of the capsule wall, determined from a weighted average of the velocity of nearby capsule nodes. A corresponding pressure is distributed over nodes of the capsule from the local fluid velocity, summed over the neighboring fluid lattice sites. This hybrid methodology has been validated by comparing the results from the LBMLSM simulations of the breathing modes of a fluid-filled capsule with the findings from analytical theory28. Other predictions from LBM-LSM simulations of microcapsule-substrate interactions29 have been validated with subsequent experimental studies30.


5


Page 6 of 39

Bonds between capsules, and between capsules and the surface, are described by a Hookean potential. Additionally, a short-range repulsion is used to prevent capsules from crossing into each other, or into the surface of the ridges. The formation and rupture of bonds is modeled through use of the Bell model31, where the rate of bond rupture increases exponentially with the applied force. The rate of bond formation can be found from the distance-dependent potential energy in the resulting bond, and the equation of detailed balance. Each node in the capsule and on the surface has a fixed limit on how many bonds it can form. When bonds are formed above this limit, one of the node's bonds is randomly selected for deletion until the number of bonds at the node is no longer in excess. To generate the shear flow, the y-velocity of the top surface is set to a specified value, called the wall velocity,

. This gives a shear flow that increases linearly between the top of

the ridges and the top of the simulation box. This gradient in the velocity will induce rotation in the capsules. The fields surrounding spheres aligned in shear flow have been extensively studied, 32,33

showing that two such objects will either separate after a collision or become trapped in an

orbital pair. Initializing the spheres with a separation of 2.4

, where

is the capsule

radius, places them outside the regime of closed trajectories formed by an orbiting pair, and we find that for the bond potential strength used in this study, the interaction between the two capsules is insufficient to pull them into the trapped regime. This means that shear-aligned capsules will eventually become separated (along the shear direction), irrespective of surface topology. Consequently, we focus on capsules that become separated along the transverse (x) direction; these capsules would gradually be pulled together under the influence of inter-capsule bonds in the absence of any effects from the surface. B. Surface Topologies


6

Page 7 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The geometry of a given “chevron mixer” can be described by the width of the chevron pattern, i.e., how far it extends along the transverse (x) direction, and the length, or extension along the shear (y) direction (Indicated by ‘W’ and ‘L’ in Fig 1). The point at the largest y coordinate of the chevron will be referred to as the “apex”, and the point at the lowest value will be referred to as the “base”. The features of the vortices induced under shear flow will then depend on the dimensions of the chevron and the spacing between the rows of chevrons along the shear direction. If the transverse separation between the centers of adjacent vortices is similar to the separation between the centers of bonded capsules, we can maximize the contrast in the transverse component of the fluid velocity at the locations of the two capsules (as detailed further below), and thereby maximize the range of shear flow for which the mixer is effective at separating the capsules. To achieve this effect, we set the transverse width of each arm of the chevron to be slightly more than twice the capsule radius. By shifting the transverse position of the apex, the chevron pattern can be transformed into a sawtooth wave pattern on the surface (Fig. 2). As we show further below, this shift introduces two important new features. First, by lengthening one arm of the chevron, we increase the width of one of the rolls of fluid at the cost of narrowing the other. This broadening of one vortex increases the fraction of transverse coordinates over which the mixer can separate capsules, allowing the sawtooth surface to remain effective for more initial conditions at lower shear. Additionally, this change produces a net transverse (x-direction) flow that will gradually sweep capsules from regions that are ineffective at separating the capsules to effective regions. Due to the incompressibility of the fluid, there must be a commensurate flow from the effective regions of the mixer into the ineffective regions; however, if the capsules are already separated


7


Page 8 of 39

along the shear direction, motion of one or both capsules along the transverse direction will not cause them to rebind. Surfaces covered with square posts have been the subject of numerous antifouling studies23. To highlight the utility of the ridged surfaces, we also simulate the motion of capsules in the presence of an array of posts, shown in Fig. 3. As discussed below, we find that for surfaces with posts, the vertical and transverse components of the flow lack the strength or spatial scale to significantly impact capsule-capsule bonding. Furthermore, there is no significant net flow in the vertical or transverse direction when averaged over a full period of the surface along the shear direction. Disruption of capsule-capsule pairs in this case is instead governed by differences in post adhesion between the two capsule trajectories. This severely reduces the range of initial conditions for which the surface topology can separate clusters. Finally, we note that the patterned surfaces introduce an additional benefit. Namely, the three-dimensionally patterned surfaces offer fewer points of attachment for a particle in solution than a flat substrate. For the all but the lowest shear rates considered here, all the particles were transported away from the surface. At the lowest shear rate, a particle remained bound to the surface in only 3% of the simulation runs for the number of time steps considered here. C. Model Parameters Capsules representing contaminant cells were assumed to have an outer radius ( 7.5 µm, consistent with the size of common algal spores such as ulva linza

34,35

) of

. The lattice

Boltzmann lattice spacing was chosen to give sufficient resolution of these capsules, with , meaning the capsules have an outer radius of 7.5 µ within the lattice Boltzmann code is defined as 1/6

The kinematic viscosity . Setting this value to 1.0 x10-6

m2/s to match water at room temperature defines a time step

= 1.67 x 10-7 s. The inner


8

Page 9 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


radius of the capsules is 6.0

, resulting in a shell thickness of 1.5

, chosen to be

larger than the lattice Boltzmann spacing. Both shells are represented by 362 points, representing 720 triangular facets. Each point is assumed to have unit mass

in the simulation units, corresponding to

g in

physical units. Each point on the outer shell is connected to the corresponding point on the inner shell, as well as to neighbors within the same shell that lie on the same face. Each point on the outer shell is also connected diagonally to any points on the inner shell within a specified radius, set at 2.3

in this model. These connections give a total of 4682 internal springs that

provide structure to each capsule. The equilibrium distance for each spring is determined from the separation between the nodes in the initial structure. Springs within one shell, and directly between the inner and outer shell, have a spring constant 0.01

, while the diagonal

springs between the inner and outer shell nodes have a spring constant 0.02 The chevron ridge used to generate the rolls of fluid is 15 wide. The arms are angled at 45º, and have a thickness of 5.66 of 8

high, and 40 , corresponding to a length

when measured along the shear direction (see Fig. 1). The sawtooth ridge is designed

to fit the same spatial periodicity, consisting of two arms with widths along the transverse direction of 32 and 8

, respectively (see Fig. 2). The arms are oriented at angles of 43.2º

and 75.1º with respect to the transverse axis, to meet at an apex 30 measured along the shear direction. The height is again 15 direction is 8

, and the length along the shear

. This leads to a thickness of 5.84

for the short arm. The square posts are 15

for the long arm and 2.05

high, and measure 8

are spaced on a square lattice, with a spacing of 20

from the base,

8

wide. These

along both the shear and transverse

directions.


9


Page 10 of 39

Capsule-capsule and capsule-surface bonds exert a spring-like force when stretched away from the equilibrium distance. This force takes the form (1) where the equilibrium extension for both the inter-capsule bonds and capsule-surface bonds is taken to be 2 capsule-capsule

,

with the cutoff distance defined as twice this value. The strength of both

and

capsule-surface

bonds

is

given

, corresponding to 1.73

.

by

the

spring

constant

The short-range repulsion is

chosen to match the repulsive term in the Morse potential36, falling to zero outside a radius and obeying the following law within that radius:

(2) For the short-range repulsion, the cutoff distance is repulsion is scaled by a coefficient

7200

0.75

, and the strength of

.

Bond formation within the cutoff distance is parameterized by rate constants for capsule-capsule bonds, and

for capsule-

surface bonds. Bond rupture is parameterized by the constant

for both

capsule-capsule and capsule-surface cases. Creating or removing bonds is done stochastically, integrating the rates given above to obtain the probability of rupture within a given time step as: (3) and the corresponding expression for bond formation as: ) where the displacement

is equal to

for

probability of bond formation is constant below

(4) , and zero for

. This means the

, but falls off quickly above this separation.


10

Page 11 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


We impose a cutoff distance of equal to

or

is

, depending on the type of bond.

The constant rate of

, beyond which no bonds can form. The constant

in eqs. (3) and (4) is set equal to 0.9; this choice results in a bond rupture

for both capsule-capsule and capsule-surface bonds at the relaxed distance

increasing to 605

,

at the cutoff distance. The rupture rate in the unstressed bonds is

comparable to that found in other biological binding interactions37. Formation rates are generally assumed to be a couple orders of magnitude greater than the rupture rates; in this case, we have ratios

= 100 and 250 for the capsule-surface and capsule-capsule bonds, respectively.

D. Computer Simulations The lattice Boltzmann fluid described above was simulated in a box measuring 120 60

80

. The chevron pattern is arranged in a square lattice on the substrate, with a

separation of 40

in both the transverse and shear directions. This allows six iterations of

the structure within the space. The x and y boundaries are handled with periodic boundary conditions, allowing the capsule to re-emerge at y = 0 once it crosses the y =

plane. The z

boundaries are handled with reflecting boundary conditions, where every fluid particle propagating across the top or bottom surface of the simulation space is compensated by a particle coming from outside the simulation space with an opposite z-velocity.25 Over the course of our simulations, the capsules did not collide with the z = 0 or z = 60 plane. The system is equilibrated for 1000 time steps before the shear flow is induced. This time allows a number of bonds to form between the capsules before inducing any flow that will drive them apart. The wall velocity

was varied from 5.28x10-4 to 1.69x10-2

; this is

equivalent to a range of 3.17 x 10-3 to 1.01x10-1 m/s in physical units, with the Reynolds number characterizing the flow falling in the range

to

. The shear velocity decays linearly


11


towards the patterned surface, producing a flow rate ranging from

Page 12 of 39

to

m/s at

the initial height of the capsules. This range overlaps with flow rates employed in micromixer experiments2. The lower end of this range should coincide with flow rates found in the viscous sublayer near a fixed substrate in the surf zone34, where the free stream velocity is of the order 110 m/s. This same regime should be equivalent to flow rates near the hull of a vessel moving under a speed of ~20 knots38.. The parameters for the inter-capsule and capsule-surface bonds were kept constant across all simulations. (The underlying assumption is that in studying a competition between bonding and fluid flow, decreasing the strength of the flow field has an analogous effect on the dynamics as increasing the strength of the bonds.) In earlier studies39, a square lattice on the flat substrate was used to designate the surface sites to which the capsules could bind. For an arbitrarily shaped ridge or post, we instead choose a random set of points evenly distributed on the triangular faces describing the structure. The number of points chosen should be proportional to the total area, and in this instance, we chose a ratio of 1:1, to match the density of bonding sites on the flat substrate. For the chevron ridge used for these simulations, this led to 2023 bonding sites per repetition of the structure. For the sawtooth ridge, this value is 2578. Fluid flow was advanced in time using the lattice Boltzmann method, and the nodes comprising the capsules were advanced in time using a fourth-order Runge-Kutta integration scheme. Forces on each node were calculated from a sum of bond forces, internal spring forces, and pressure from the surrounding fluid. Ridges and posts on the surface were assumed to remain static throughout the simulations. Capsules were initialized at a height of 25.5 ridged surface at 15

, near enough to form bonds with the

, but high enough to clear the top surface of the ridges. The transverse


12

Page 13 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


separation was initially 18

between the capsule centers, leaving a separation of 3

between the neighboring edges of the capsules. This starting configuration was chosen to represent the most difficult case for separating the capsules, as misalignment along the vertical direction will cause the capsule higher in the flow to race ahead of the lower capsule. Misalignment along the shear direction will raise the leading capsule along the vertical axis, eventually leading to greater separation along the shear direction. Generally, misalignment should cause capsules to separate more quickly, or to separate under lower applied shears. Simulations are run for 106 time steps at lower shear values, and 105 time steps at the highest shear value, corresponding to 0.167 seconds and 0.0167 seconds of real time, respectively. Each set of initial conditions was simulated six times to determine the standard deviation in the separation. The six trials were conducted with six different randomly generated sets of bond sites on the surface of the posts, chevron or sawtooth ridges. III. Results and Discussion We determine how the flow fields generated by the interactions between the driven fluid and the patterned surfaces affect the bonds linking a pair of capsules near the surface. Through these studies, we can establish how to pattern immersed substrates so that the generated flows inhibit small clusters from binding to the surface or hinder the binding of incoming cells to those already near a wall. In this way, we isolate scenarios where the generated flows act to impede the fouling of the substrate. A. Flow Fields We first consider the fluid-filled chamber that encompasses the chevron-shaped ridges shown in Fig. 1. In the absence of capsules, the application of a shear along the top surface of the fluid induces rolls in the plane orthogonal to the direction of the shear; these rolls are clearly


13


Page 14 of 39

visible in Fig. 4A. The handedness of such rolls is dictated by the sign of the angle of the ridges on the surface (Fig. 4B), with flow circulating upward at the apex of the chevron, and circulating downward at the base. The alternating direction of this circulation dictates whether streamlines originating in adjacent rolls will converge or diverge above the height of the ridges. The width of the rolls is determined by the dimensions of the repeating chevron pattern; in a periodic coordinate system, it will be independent of the domain size. The maximum amplitude of the transverse component of the flow occurs just below the height of the top of the ridges (z = 14

), while the vertical component is greatest slightly

above the height of the ridges (z = 19

). The maximum amplitude (“strength”) of these

rolls scales with the applied shear at the top surface. At the initial height of the capsule centers, the maximum value of the transverse flow is 9.8 x10-3 vertical flow is 2.1x10-2

where

, while the maximum value of the

is the wall velocity described previously. The minimum

value of both quantities has the same magnitude, but the opposite sign. Both terms decay away from the patterned surface. Taking an average of the flow field along the shear direction, over one iteration of the periodic surface, we find a net maximum transverse component of 2.7 x10-3 and a net maximum vertical component of 5.9 x10-3

. These non-zero average values

imply that the flow field from the chevron surface can induce a significant deflection in the trajectories of the capsules as they pass over multiple ridges. A visualization of these transverse and vertical components at the initial capsule height is given in supplemental Fig. S1A and S1B, allowing us to see the top of the fluid rolls depicted in Fig. 4A. The transverse component drives capsules away from the apex of the chevron and toward the base. The vertical component pushes capsules away from the surface as they pass over the apex, and pulls them down as they pass over the base.


14

Page 15 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The square posts used for comparison have a height 15 periodicity of 20

and width

, with a

in the shear and transverse directions. In this environment, the

transverse component of the flow field has a maximum value of 6.3x10-4 component has a maximum value of 3.4x10-3

and the vertical

, an order of magnitude weaker than the

corresponding results for the chevron flow field. More significantly, when we consider the average amplitude of these fluid velocity components averaged over one period along the shear direction, we see much weaker amplitudes of 3.0x10-7

and 4.7x10-7

in the transverse and

vertical directions, respectively. Owing to the symmetry of the square post, these quantities largely cancel out, resulting in average velocities roughly four orders of magnitude smaller, meaning that the alternating flow field surrounding square posts will not act in a particular direction for a sufficiently long time to have an effect in separating the capsules. B. Modes of Disruption Focusing on a pair of initially bonded capsules, we observe that the bonding interactions can be disrupted by two predominant mechanisms under the influence of the chevron mixer. In particular, the capsules can be separated in the transverse (x) direction by divergent rolls that are produced about the apex of the chevron. Alternatively, the capsules can be driven apart in the vertical (z) direction by rotation within a single roll. The dominant mechanism will depend on the initial positions of the bound capsules, as indicated by the examples in Figs. 5 and 6. The capsules in Fig. 5 are situated symmetrically about the apex of a chevron. This position places the capsules in diverging rolls, and as the shear flow moves them over several ridges (Fig. 5 B,C), they are gradually pulled apart along the transverse (x) direction (as in Fig. 5D). The motion of the capsules along the y-direction is characterized by a sinusoidal rise and fall on top


15


Page 16 of 39

of the overall trend toward separation (Fig. 5A), with the period determined by the rate at which the capsules traverse over the chevron ridges. The other distinct scenario occurs when the capsules are initialized along one arm of the same chevron, as in Fig. 6. In this case, they lie within the same roll and will be subject to a difference in flow along the vertical (z) direction, orthogonal to the surface. The gradient in shear velocity along the height of the channel will cause capsules that rise in the flow to accelerate, and capsules that fall in the flow to slow down. A small displacement along the vertical direction (Fig. 6C) can eventually lead to a separation of the capsules along the shear (y) direction (Fig. 6D). The effect on capsule-capsule distance along each coordinate is shown in Fig. 6A. Notably, for arbitrary initial orientations of the pair of capsules, both mechanisms can contribute to the disruption of the bonds. A range of starting positions and the resulting effect of the flow field on the inter-capsule bonding over time are displayed in Fig. 7. The difference in the vertical component of the flow field between its minimum and maximum values, however, is nearly twice the corresponding difference in the transverse component. Consequently, the vertical-shear separation mode is more effective at lower shear values than the corresponding transverse separation mode at separating the capsules. To gain insight into the general effectiveness of the chevron pattern in separating the bound capsules, we plot the phase map in Fig. 8A as a function of the imposed shear and the initial positions of the capsules. To generate the map, we simulated the system under different shear values ranging from 5.28x10-4

to 1.69x10-2

, and a uniform

sampling of initial transverse positions. Each set of initial conditions was repeated over six trials to determine the average time before separation. If no separation occurred after 106 time steps, the conditions were recorded as a failure. In this map, the circles represent cases where the


16

Page 17 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


capsules that were initially bound together are pulled apart by the flow in the majority (four or more) of the six cases and the crosses indicate the conditions where the capsules remain bound to each other in three or more of the cases. The map clearly indicates the failure of the chevron pattern to separate capsules initialized symmetrically about an apex ( values of 1.056x10-3

= 20

) at shear

and lower, where the bound capsules are subject only to the

transverse mode of disruption. Initial conditions away from this point are subject to a combination of both the transverse- and vertical-shear mode, and are consequently still separated at this shear value. There are, however, initial capsule locations that are not subject to either mode of disruption. An example of such an “ineffective” initial location is shown in Fig. 1, where the capsules are symmetrically placed about the base of two adjacent chevrons. In this case, the streamlines originating from the capsules’ centers do not diverge, but rather, the velocity profiles converge, as can be seen in Fig. 4A at x = 40

. Figure 7A shows that in this case, the

number of bonds between the capsules grows over time, eventually achieving a plateau when the capsules are nearly touching. The phase map in Fig. 8A demonstrates that such conditions fail to separate the two capsules even under the highest shear tested (0.016896

).

For the array of square posts, no vortices on the scale of the capsule size are generated, and so neither of these mechanisms influences the capsule-capsule interactions. Instead, we see separation occur for particular initial conditions, when one capsule is aligned with posts in the array and the neighboring capsule is not, as seen in the phase diagram in Fig. 8B. Under these conditions, one capsule will form bonds with the posts, slowing its motion in the shear direction and dragging it down towards the surface. Over time, this interaction will separate the capsules if the shear flow is sufficiently strong. Unlike the vortex separation mechanisms, which grow


17


Page 18 of 39

stronger with increasing shear flow, this mode of separation loses its efficacy at high shear, when the capsules pass more quickly over the posts. This adhesion-driven mode is absent in the mixer geometry, as the ridge extends across all transverse coordinates. Thus, while only some of the capsules pass directly over the posts, all capsules must pass over the ridges. A comparison of the phase maps in Figs. 8A and 8B clearly shows the advantage of the chevron pattern over the array of posts in separating the cells. Nevertheless, initial positions of contaminant particles are not a matter of choice in practical applications, so instead we seek to modify the pattern in a way that will ameliorate this deficiency. C. Sawtooth Flow Field The sawtooth ridge is obtained by shifting the apex of the chevron along the transverse direction, as displayed in Fig. 2. This arm of the chevron is also stretched forward along the shear direction, to maintain approximately the same angle with the transverse axis. Lengthening one arm of the chevron pattern has the effect of spreading the resulting roll out over a greater width along the transverse direction, while shrinking the roll centered on the compressed arm, as seen in Fig. 9A . We noted above that for the chevron pattern, the vertical-shear separation of capsules within one roll was more effective at lower shear values than transverse separation between neighboring rolls. The sawtooth pattern increases the range of initial conditions over which the vertical-shear separation mechanism can operate, thereby improving the fraction of initial conditions for which the surface can split bonded capsules relative to the chevron pattern. This improvement is in spite of the fact that the overall difference between the minimum and maximum values of transverse and vertical flow (5.4 x 10-3

and 11.0x 10-3

, respectively)

are not significantly increased from the corresponding values for the chevron mixer.


18

Page 19 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The asymmetry also induces a net transverse flow. We find that the average x-component of the velocity field at z = 25.5

(the initial height of the capsules) is 4.4x 10-3

, falling

off linearly as we approach the top surface. (A visualization of the transverse and vertical components of the flow at this height is included in supplemental Figure S1C and S1D, for comparison with the corresponding flow field from the chevron.) This flow can move bonded capsules from ineffective regions to effective regions of the flow pattern. This net transverse motion is, however, sufficiently slow that capsules in an effective region of the mixer will remain there long enough to be separated. D. Effective Range of Parameters for Surfaces The effectiveness of different surface geometries for separating capsule pairs is determined by the shear rate and the initial position of the capsules. An array of posts must rely on differential adhesion between the two capsules, implying high sensitivity to the capsule positions relative to the posts (Fig. 8B). This means of separation is ineffective at both low shear, when the capsules move slowly, and high shear, when they do not get significant traction on the posts. Micromixers like the chevron and sawtooth pattern can instead make use of the velocity field to pull capsules apart. Under low shear, the local differences in the fluid velocity are not sufficiently large to overcome the bonding attraction between the capsules (Fig. 8A). As the shear is increased, the transverse and vertical components of the flow will grow as well, and the mixer will succeed in separating capsules for more initial positions. For the chevron pattern, the mixer remains ineffective at some positions even under high shear, as the force from the local fluid velocity does not exceed the force from the bonding interaction. When localized about the converging arms of the chevron, the two capsules will be


19


Page 20 of 39

forced together by the flow, creating a “dead spot” where they cannot be separated. This can be seen in Fig. 8A as the column of red crosses, indicating initial conditions where the mixer fails. The phase map also displays how the transverse separation mode in the chevron mixer gradually loses effectiveness as shear is reduced, as noted above. Altering the design of the mixer by introducing an asymmetry has multiple advantages. Increasing the length of one arm of the chevron relative to the other increases the region where the vertical separation mechanism is effective, as evidenced by the phase map in Fig. 8C. This vertical separation mechanism is more effective at lower shears than the transverse separation mechanism, and so allows the sawtooth mixer to separate a larger fraction of capsule pairs under low shear relative to the symmetric chevron. The sawtooth pattern provides the further advantage of inducing a net transverse flow into the system. This transverse flow brings pairs of capsules initially near the “dead spot” of the mixer into a region where they can be effectively separated, giving the sawtooth effectiveness independent of starting position at high shear values. In Fig. 10, we plot the displacement of the center of mass for the two capsule system between the start of the simulation and the time that the capsules separate. As with the chevron mixer, the region where the two vortices converge ( = 42) is not able to split apart two capsules. Once these capsules have moved away from this part of the flow field, though, the bonds between them begin to break, leading to separation near

=

55 Finally, we emphasize that the particles were transported away from all the surfaces in all instances, except for a very small number of cases at the lowest shear rate consider here. In the latter case, only 3% of the simulations revealed that a particle remained bound to the surface at the end of the simulation run time.


20

Page 21 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


IV. Conclusions Our hybrid method, combining the lattice Boltzmann model for fluid flows with a lattice spring method to simulate capsule dynamics, allowed us to investigate the effect of different 3D surface features on fluid flows, and the effect that these flows have on capsule-capsule bonding interactions. Our aim was to pinpoint surface topologies that disrupt the bonds between the two capsules as they are driven to move over the surface. The breaking of these inter-capsule bonds not only prevents small clusters as a whole from binding to the surface, but also keeps the separated, shear-driven capsules from contacting the substrate. We find that the array of rectangular posts is highly ineffective at disrupting the bonding between the flow-driven capsules. On the other hand, the symmetric chevron pattern provides significant improvement over the array of posts in breaking the inter-capsule bonds. The utility and efficacy of the surface can, however, be improved further by employing an asymmetric sawtooth geometry. Lengthening one arm of the chevron in this fashion increases the width of one vortex at the expense of shrinking the other vortex in the periodic flow pattern. This feature is advantageous, as we have found that separation within one vortex, along the vertical direction, is effective at lower flow rates than separation between neighboring vortices along the transverse direction. Additionally, this asymmetry produces a net flow transverse to the shear flow, gradually sweeping particles across the surface. As the chevron mixer is ineffective at separating the capsules for some values of the initial coordinates, the asymmetric pattern has the benefit of moving nascent clusters from regions of the flow where they will not be separated to regions


21


Page 22 of 39

where they will. In particular, the sawtooth pattern is effective at transporting capsule pairs initially in converging rolls into the same roll or into diverging rolls, where they can be separated by the flow field. In contrast, capsules that begin in converging rolls of the symmetric chevron mixer will remain in that state for the entire length of the simulation run. While reducing the adhesion of individual cells on an immersed surface is vital for preventing biofouling, inhibiting the aggregation amongst these cells is also an important factor in thwarting fouling. Our findings demonstrate the potential utility of the “micro-vortex mixer” relief patterns to break apart clusters of cells and thus deter the formation of extensive biofilms. The success rate of these surfaces increases with the flow rate, determined here by the shear rate applied at the free boundary of the simulation box. The flows studied here, with Reynolds numbers between

, overlaps with the regime typically encountered in microfluidic

devices, and with the flow in the viscous sublayer near a ship’s hull.38 The sawtooth mixer represents a previously unexplored avenue for disrupting the process of marine biofouling. By making use of a non-biocidal physical mechanism, we can avoid unwanted environmental effects. Acknowledgements ACB gratefully acknowledges financial support from the ONR References (1)

Stroock, A. D.; Dertinger, S. K.; Whitesides, G. M.; Ajdari, A. Patterning Flows Using Grooved Surfaces. Anal. Chem. 2002, 74 (20), 5306–5312.

(2)

Forbes, T. P.; Kralj, J. G. Engineering and Analysis of Surface Interactions in a Microfluidic Herringbone Micromixer. Lab Chip 2012, 12 (15), 2634–2637.

(3)

Stott, S. L.; Hsu, C.-H. C.-H.; Tsukrov, D. I.; Yu, M.; Miyamoto, D. T.; Waltman, B. A.;


22

Page 23 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Rothenberg, S. M.; Shah, A. M.; Smas, M. E.; Korir, G. K.; Floyd, F. P.; Gilman, A. J.; Lord, J. B.; Winokur, D.; Springer, S.; Irimia, D.; Nagrath, S.; Sequist, L. V; Lee, R. J.; Isselbacher, K. J.; Maheswaran, S.; Haber, D. A.; Toner, M. Isolation of Circulating Tumor Cells Using a Microvortex-Generating Herringbone-Chip. PNAS 2010, 107 (43), 18392–18397. (4)

Stroock, A. D. Chaotic Mixer for Microchannels. Science (80-. ). 2002, 295 (5555), 647– 651.

(5)

Schultz, M. P.; Bendick, J. A.; Holm, E. R.; Hertel, W. M. Economic Impact of Biofouling on a Naval Surface Ship. Biofouling 2011, 27 (1), 87–98.

(6)

Champ, M. A. A Review of Organotin Regulatory Strategies, Pending Actions, Related Costs and Benefits. Sci. Total Environ. 2000, 258, 21–71.

(7)

Piola, R. F.; Johnston, E. L. The Potential for Translocation of Marine Species via SmallScale Disruptions to Antifouling Surfaces. Biofouling 2008, 24 (3), 145–155.

(8)

Cao, S.; Wang, J. D.; Chen, H. S.; Chen, D. R. Progress of Marine Biofouling and Antifouling Technologies. Chinese Sci. Bull. 2011, 56 (7), 598–612.

(9)

Bacchetti De Gregoris, T.; Khandeparker, L.; Anil, A. C.; Mesbahi, E.; Burgess, J. G.; Clare, A. S. Characterisation of the Bacteria Associated with Barnacle, Balanus Amphitrite, Shell and Their Role in Gregarious Settlement of Cypris Larvae. J. Exp. Mar. Bio. Ecol. 2012, 413, 7–12.

(10)

Kirschner, C. M.; Brennan, A. B. Bio-Inspired Antifouling Strategies. Annu. Rev. Mater. Res. 2012, 42 (211–229).

(11)

Guardiola, F. A.; Cuesta, A.; Meseguer, J.; Esteban, M. A. Risks of Using Antifouling Biocides in Aquaculture. Int. J. Mol. Sci. 2012, 13 (2), 1541–1560.


23


(12)

Page 24 of 39

Dafforn, K. A.; Lewis, J. A.; Johnston, E. L. Antifouling Strategies: History and Regulation, Ecological Impacts and Mitigation. Mar. Pollut. Bull. 2011, 62 (3), 453–465.

(13)

Lejars, M.; Margaillan, A.; Bressy, C. Fouling Release Coatings: A Nontoxic Alternative to Biocidal Antifouling Coatings. Chem. Rev. 2012, 112 (8), 4347–4390.

(14)

Magin, C. M.; Cooper, S. P.; Brennan, A. B. Non-Toxic Antifouling Strategies. Mater. Today 2010, 13 (4), 36–44.

(15)

Brzozowska, A. M.; Parra-Velandia, F. J.; Quintana, R.; Xiaoying, Z.; Lee, S. S. C.; ChinSing, L.; Jańczewski, D.; Teo, S. L. M.; Vancso, J. G. Biomimicking Micropatterned Surfaces and Their Effect on Marine Biofouling. Langmuir 2014, 30 (30), 9165–9175.

(16)

Shivapooja, P.; Wang, Q.; Orihuela, B.; Rittschof, D.; Lõpez, G. P.; Zhao, X. Bioinspired Surfaces with Dynamic Topography for Active Control of Biofouling. Adv. Mater. 2013, 25, 1430–1434.

(17)

Liu, Y.; McFarlin, G. T.; Yong, X.; Kuksenok, O.; Balazs, A. C. Designing Composite Coatings That Provide a Dual Defense against Fouling. Langmuir 2015, 31 (27), 7524– 7532.

(18)

Epstein, A. K.; Wong, T.-S.; Belisle, R. A.; Boggs, E. M.; Aizenberg, J. Liquid-Infused Structured Surfaces with Exceptional Anti-Biofouling Performance. Proc. Natl. Acad. Sci. 2012, 109 (33), 13182–13187.

(19)

Efimenko, K.; Finlay, J.; Callow, M. E.; Callow, J. A.; Genzer, J. Development and Testing of Hierarchically Wrinkled Coatings for Marine Antifouling. ACS Appl. Mater. Interfaces 2009, 1 (5), 1031–1040.

(20)

Epstein, A. K.; Hochbaum, A. I.; Kim, P.; Aizenberg, J. Control of Bacterial Biofilm Growth on Surfaces by Nanostructural Mechanics and Geometry. Nanotechnology 2011,


24

Page 25 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


22 (49), 494007. (21)

Long, C. J.; Schumacher, J. A Model That Predicts the Attachment Behavior of Ulva Linza Zoospores on Surface Topography. Biofouling 2010, 26 (4), 411–419.

(22)

Schumacher, J. F.; Long, C. J.; Callow, M. E.; Finlay, J. A.; Callow, J. A.; Brennan, A. B. Engineered Nanoforce Gradients for Inhibition of Settlement (Attachment) of Swimming Algal Spores. Langmuir 2008, 24 (9), 4931–4937.

(23)

Sullivan, T.; Regan, F. Marine Diatom Settlement on Microtextured Materials in Static Field Trials. J. Mater. Sci. 2017, 52 (10), 5846–5856.

(24)

Swain, G. W.; Kovach, B.; Touzot, A.; Casse, F.; Kavanagh, C. J. Measuring the Performance of Today ’ S Antifouling Coatings. J. Sh. Prod. 2007, 23 (3), 164–170.

(25)

Doolen, G. D.; Chen, S. Lattice Boltzmann Method. Annu. Rev. Fluid Mech. 1998, 30, 329–364.

(26)

Buxton, G. A.; Care, C. M.; Cleaver, D. J. A Lattice Spring Model of Heterogeneous Materials with Plasticity. Model. Simul. Mater. Sci. Eng. 2001, 9 (6), 485–497.

(27)

Buxton, G. A.; Verberg, R.; Jasnow, D.; Balazs, A. C. Newtonian Fluid Meets an Elastic Solid: Coupling Lattice Boltzmann and Lattice-Spring Models. Phys. Rev. E - Stat. Nonlinear, Soft Matter Phys. 2005, 71 (5), 56707.

(28)

Alexeev, A.; Verberg, R.; Balazs, A. C. Designing Compliant Substrates to Regulate the Motion of Vesicles. Phys. Rev. Lett. 2006, 96 (14), 148103.

(29)

Kolmakov, G. V.; Revanur, R.; Tangirala, R.; Emrick, T.; Russell, T. P.; Crosby, A. J.; Balazs, A. C. Using Nanoparticle-Filled Microcapsules for Site-Specific Healing of Damaged Substrates: Creating A “repair-and-Go” system. In ACS Nano; 2010; Vol. 4, pp 1115–1123.


25


(30)

Page 26 of 39

Kratz, K.; Narasimhan, A.; Tangirala, R.; Moon, S.; Revanur, R.; Kundu, S.; Kim, H. S.; Crosby, A. J.; Russell, T. P.; Emrick, T.; Kolmakov, G.; Balazs, A. C. Probing and Repairing Damaged Surfaces with Nanoparticle-Containing Microcapsules. Nat. Nanotechnol. 2012, 7 (2), 87–90.

(31)

Bell, G. Models for the Specific Adhesion of Cells to Cells. Science (80-. ). 1978, 200 (4342), 618–627.

(32)

Van de Ven, T. G. M.; Mason, S. G. The Microrheology of Colloidal Dispersions IV. Pairs of Interacting Spheres in Shear Flow. J. Colloid Interface Sci. 1976, 57 (3), 505– 516.

(33)

Kao, S. V.; Mason, S. G. Dispersion of Particles by Shear. Nature 1975, 253 (5493), 619– 621.

(34)

Granhag, L. M.; Larsson, A. I.; Jonsson, P. R. Algal Spore Settlement and Germling Removal as a Function of Flow Speed. Mar. Ecol. Prog. Ser. 2007, 344, 63–69.

(35)

Walker, G. C.; Sun, Y.; Guo, S.; Finlay, J. A.; Callow, M. E.; Callow, J. A. Surface Mechanical Properties of the Spore Adhesive of the Green Alga Ulva. J. Adhes. 2005, 81, 1101–1118.

(36)

Morse, D. C.; Fredrickson, G. H. Semiflexible Polymers near Interfaces. Phys. Rev. Lett. 1994, 73 (24), 3235–3238.

(37)

Andersen, C.; Jordy, M.; Benz, R. Evaluation of the Rate Constants of Sugar Transport through Maltoporin (LamB) of Escherichia Coli from the Sugar-Induced Current Noise. J. Gen. Physiol. 1995, 105, 385–401.

(38)

Dean, B.; Bhushan, B. Shark-Skin Surfaces for Fluid-Drag Reduction in Turbulent Flow: A Review. Phil. Trans. R. Soc. A 2010, 368, 4775–4806.


26

Page 27 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(39)

Maresov, E. A.; Kolmakov, G. V.; Yashin, V. V.; Van Vliet, K. J.; Balazs, A. C. Modeling the Making and Breaking of Bonds as an Elastic Microcapsule Moves over a Compliant Substrate. Soft Matter 2012, 8 (1), 77–85.

Figure Captions

Figure 1: Diagram of the chevron mixer. The chevron ridge has a height of , and repeats every in the transverse direction ( . The distance along the shear direction from the base to the apex of the chevron ( ) is 20 The capsules are initialized in close enough proximity to bond to each other and to the surface. Under an applied shear, the angled arms of the chevron will induce rolls within the fluid that can separate the capsules. Figure 2: Diagram of the sawtooth mixer. This structure is formed by shifting the apex of the chevron along the transverse direction. While the asymmetry weakens the ability to separate capsules along the transverse direction, it increases the effective region for separation along the vertical direction. Additionally, it induces a net transverse flow that can move pairs of capsules from the ineffective regions of the mixer to effective regions Figure 3: Diagram of post array. Posts measure high, and are wide. The array has a periodicity of . Capsules can bind to the top and sides of the posts. Figure 4: (A) Transverse and vertical flow field for chevron mixer, averaged over one period along the shear direction. The chevron pattern induces rolls in alternating directions that can pull apart or push together capsules depending on the initial positions. This effect is strongest near the top of the ridges, and falls off further above them. (B) Diagram of the chevron mixer, showing how the vortex rolls align with the arms of the chevron. Figure 5: (A) Displacement between capsules over time, separated into components. Multiple snapshots of the system in the plane are shown. The two capsules are subject to a periodic stretching and compression along the transverse coordinate. (B) Capsules are initialized symmetrically about the apex of the chevron. (C) Separation has a local minimum just prior to passing over the ridge. (D) After multiple cycles, the effects of the flow field s overwhelm the bonding attraction between the capsules, and the capsules become separated. Figure 6: (A) Displacement between capsules over time, separated into components. Multiple snapshots in the plane are shown. (B) The capsules are initialized along one arm of the


27


Page 28 of 39

chevron, separated along the transverse direction. (C) The capsule closer to the chevron apex is displaced upward. (D) Owing to the gradient in the shear, this subsequently leads to the separation of the two capsules along the shear dimension. Figure 7: (A) Capsule-capsule bonds versus time for different starting positions in the chevron mixer. Shaded region indicates minimum and maximum values from six trials. Cartoons indicate initial position of capsules relative to chevron arms. Trajectories are taken from the shear = 2.11x10-3 simulations. (B) Capsules that begin about the base of the chevron are pushed together along the transverse direction by the flow, and fail to separate. Arrows indicate the direction and magnitude of the flow field, averaged over one cycle along the shear direction. (C,E,F) Capsules placed along the same arm within a single roll experience a small vertical separation, and are subsequently separated by the gradient in the shear. The transverse component can act to accelerate (E) or hinder (C) this process, leading to faster or slower separation. (D) Capsules that are initially symmetric about one point of the chevron will be gradually pulled apart along the transverse direction. Magnitude of arrows ranges from for (B) and (D) to for (F). Figure 8: (A) Phase diagram showing success of chevron mixer in separating capsules for different initial conditions. Blue circles represent conditions for which the majority (four or more) of six trials resulted in a success. Red crosses represent conditions where half or more of the trials resulted in a failure. A “dead spot” exists in the chamber with the chevron mixer where particles are not separated. This occurs about the point where the two straight edges meet (Y=0, Y=40), with the width of the ineffective region decreasing with increasing shear. Additionally, the apex of the chevron (Y = 20) becomes ineffective at low shear as the transverse mode is not strong enough to separate capsules. (B) Phase diagram for the post array. The array cannot separate capsules when both are positioned over posts, or when both are positioned over gaps between posts. Under intermediate shears, the array can separate capsules when there is a significant difference in post adhesion. This effect goes away at high shear. (C) Phase diagram for sawtooth mixer. The asymmetric surface is able to break up a larger number of bonded capsules, independent of shear. A dead spot is again created near one junction of the angled arms. As the vertical flow is not symmetric about this point, however, capsules are separated near here even under comparatively weaker shear. Additionally, the influence of the dead spot vanishes under larger shear velocities, as the transverse flow becomes strong enough to bring the capsules into an effective region over the course of the simulation. Figure 9: (A) Transverse and vertical flow field averaged over one period along shear direction for the sawtooth mixer. The sawtooth geometry broadens the vortex roll along one arm while shrinking the other. Additionally, the asymmetry of the sawtooth induces a net transverse flow in one direction at all transverse positions. The result of this is that bonded capsules initialized in a region that does not separate them effectively will be gradually swept to a region that does. (B) Diagram of sawtooth mixer, showing how the broader vortex roll aligns with the longer arm of the mixer. Figure 10: Trajectory of center of mass for two capsules from initialization to time of break-up for sawtooth mixer under high shear ( ). The converging fluid


28

Page 29 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


rolls at are unable to separate the capsules. Once the capsules are swept to another region of the sawtooth mixer, they are eventually pulled apart.

Figure 1


29


Page 30 of 39

Figure 2


30

Page 31 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 3


31


Page 32 of 39

Figure 4


32

Page 33 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 5


33


Page 34 of 39

Figure 6


34

Page 35 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 7


35


Page 36 of 39

Figure 8


36

Page 37 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 9


37


Page 38 of 39

Figure 10


38

Page 39 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



Optimizing Micromixer Surfaces To Deter Biofouling - ACS Applied

Recommend Documents