# Role of shear induced diffusion in acoustophoretic focusing of dense suspensions

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TL;DR: An updated overview of the state of the art for passive label-free microparticle separation, with emphasis on performance and operational conditions is provided and the newly emerging approach based on shear-induced diffusion is highlighted.

Abstract: Massive growth of the microfluidics field has triggered numerous advances in focusing, separating, ordering, concentrating, and mixing of microparticles. Microfluidic systems capable of performing these functions are rapidly finding applications in industrial, environmental, and biomedical fields. Passive and label-free methods are one of the major categories of such systems that have received enormous attention owing to device operational simplicity and low costs. With new platforms continuously being proposed, our aim here is to provide an updated overview of the state of the art for passive label-free microparticle separation, with emphasis on performance and operational conditions. In addition to the now common separation approaches using Newtonian flows, such as deterministic lateral displacement, pinched flow fractionation, cross-flow filtration, hydrodynamic filtration, and inertial microfluidics, we also discuss separation approaches using non-Newtonian, viscoelastic flow. We then highlight the newly emerging approach based on shear-induced diffusion, which enables direct processing of complex samples such as untreated whole blood. Finally, we hope that an improved understanding of label-free passive sorting approaches can lead to sophisticated and useful platforms toward automation in industrial, environmental, and biomedical fields.

25 citations

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TL;DR: In this paper, the physics behind the separation of plasma from whole blood using acoustophoresis (movement driven by sound waves) is not well understood, and experiments and simulations are used to provide an improved understanding.

Abstract: Separating blood plasma in microchannels is of great relevance to microfluidics-based biodetection However, the physics behind the separation of plasma from whole blood using acoustophoresis (movement driven by sound waves) is not well understood This study uses experiments and simulations to provide an improved understanding of plasma separation from whole blood using acoustophoresis It is seen that acoustophoretic focusing of cells depend on two time scales: that of shear-induced diffusion, and that of actual acoustophoresis These results will help in designing highly efficient blood-plasma separation devices for lab-on-a-chip applications

15 citations

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TL;DR: In this article, the authors investigated the aggregation of a dense suspension of particles (volume fraction, = 0.1 ) in a PDMS microwell by employing surface acoustic wave (SAW) microcentrifugation.

Abstract: We investigate the aggregation of a dense suspension of particles (volume fraction, $$\varphi \sim 0.1$$
) in a PDMS microwell by employing surface acoustic wave (SAW) microcentrifugation. In spite of acoustic attenuation at the LiNbO3–PDMS interface, a significant portion of the energy (> 80%) is available for driving fluid actuation, and, in particular, microcentrifugation in the microwell via acoustic streaming. Rapid particle aggregation can then be affected in the microcentrifugation flow, arising as a consequence of the interplay between the hydrodynamic pressure gradient force $$F_{\text{p}}$$
responsible for the migration of particles to the center of the microwell and shear-induced diffusion force $$F_{\text{SID}}$$
that opposes their aggregation. Herein, we experimentally investigated the combined effect of the particle size $$a$$
and sample concentration $$c$$
on these microcentrifugation flows. The experimental results show that particles of smaller size and lower sample concentration (such that $$F_{\text{p}} > F_{\text{SID}}$$
) are concentrated efficiently into an equilibrium spot, whose diameter scales with the initial particle volume fraction as $$d_{\text{cs}} \sim \varphi^{0.3}$$
. In contrast, we found that as the local particle volume fraction at the center of the microwell approaches $$\varphi \sim 0.1$$
such that $$F_{\text{SID}} \ge F_{\text{p}}$$
, the particle aggregation fails. Additionally, we also investigate the effects of the well diameter, and the height, lateral positioning of microwell and the liquid volume on the microcentrifugation.

13 citations

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TL;DR: In this article, the authors studied the mechanism of cross-stream migration and the coalescence of aqueous droplets flowing in an oil-based ferrofluid with a co-flowing aouous stream in the presence of a magnetic field and revealed that the migration phenomenon is governed by the advection and magnetophoretic (τm) time scales.

Abstract: Manipulation of aqueous droplets in microchannels has great significance in various emerging applications such as biological and chemical assays. Magnetic-field based droplet manipulation that offers unique advantages is consequently gaining attention. However, the physics of magnetic field-driven cross-stream migration and the coalescence of aqueous droplets with an aqueous stream are not well understood. Here, we unravel the mechanism of cross-stream migration and the coalescence of aqueous droplets flowing in an oil based ferrofluid with a coflowing aqueous stream in the presence of a magnetic field. Our study reveals that the migration phenomenon is governed by the advection (τa) and magnetophoretic (τm) time scales. Experimental data show that the dimensionless equilibrium cross-stream migration distance δ* and the length Lδ* required to attain equilibrium cross-stream migration depend on the Strouhal number, St = (τa/τm), as δ* = 1.1 St0.33 and Lδ*=5.3 St−0.50, respectively. We find that the droplet-stream coalescence phenomenon is underpinned by the ratio of the sum of magnetophoretic (τm) and film-drainage time scales (τfd) and the advection time scale (τa), expressed in terms of the Strouhal number (St) and the film-drainage Reynolds number (Refd) as ξ = (τm + τfd)/τa = (St−1 + Refd). Irrespective of the flow rates of the coflowing streams, droplet size, and magnetic field, our study shows that droplet-stream coalescence is achieved for ξ ≤ 50 and ferrofluid stream width ratio w* < 0.7. We utilize the phenomenon and demonstrated the extraction of microparticles and HeLa cells from aqueous droplets to an aqueous stream.

13 citations

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TL;DR: In this article, the authors demonstrate the vibration-driven assembly of glass bead microparticles and iron oxide nanoparticles in contact with a photocurable hydrogel (PEGDA) over an area of 3000mm 2.

Abstract: In this study, we examine directed self-assembly of micro- and nanoparticles on a vibrating substrate as a viable pathway to large-scale assembly of microstructures and composite materials. We demonstrate the vibration-driven assembly of glass bead microparticles and iron oxide nanoparticles in contact with a photocurable hydrogel (PEGDA) over an area of 3000 mm 2 . The competition between acoustic radiation force and vibration-generated fluid flow in a viscous medium above a vibrating plate determines the particle transport characteristics. Based on a suspension balance model of this competition, we find that glass microparticles are dominated by displacement gradients and migrate towards displacement anti-nodes. Iron oxide nanoparticles that are smaller than the characteristic boundary layer generated by the flow will drive particles towards displacement nodes. We find close agreement between the observed experimental results when compared to a numerical solution to the 2D wave equation that governs this case. We also demonstrate that patterns assembled by vibration for glass microparticles or iron oxide nanoparticles dispersed in PEGDA can be immobilized by a UV light, allowing this approach to be used as a fabrication process for heterogeneously structured particle-polymer composites. The composites produced by this technique are robust and can be held by hand for application to tunable material properties for applications to bioelectronics and soft robotics. This work has been selected by the Editors as a Featured Cover Article for this issue.

10 citations

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TL;DR: In this article, it was shown that shear-induced migration of particles out of the sheared Couette gap and into the fluid reservoir, which reduces the particle concentration in the gap and thereby the observed viscosity, is consistent with a gap-limited shearinduced diffusion process normal to the plane of shear, with the relevant diffusion coefficient being proportional to the applied shear rate.

Abstract: In the course of viscometric measurements of concentrated suspensions of spheres in Newtonian fluids using a Couette device, Gadala-Maria & Acrivos (1980) observed a decrease in the suspension viscosity after long periods of shearing even though the viscosity of the pure suspending fluid remained constant under identical conditions. In the present work we demonstrate that this phenomenon is due to the shear-induced migration of particles out of the sheared Couette gap and into the fluid reservoir, which reduces the particle concentration in the gap and thereby the observed viscosity. We show further that this rate of viscosity decrease is consistent with a gap-limited shear-induced diffusion process normal to the plane of shear, with the relevant diffusion coefficient being proportional to is the applied shear rate.Additional experiments also uncovered a new phenomenon - a short-term increase in the viscosity upon initial shearing of a suspension in a Couette device - which was attributed to the diffusive migration of particles across the width of the Couette gap and thus was used to infer values of the corresponding diffusion coefficient within the plane of shear parallel to gradients in fluid velocity.In the theoretical part we demonstrate that the particle migrations that led to these observed phenomena may be explained in terms of the irreversible interparticle interactions that occur in these suspensions. From simple arguments, these interactions are shown to lead to effective diffusivities both normal to the plane of shear and normal to the direction of fluid motion within the plane of shear whose estimated magnitudes are comparable with those that were inferred from the experimental measurements. Furthermore, these interactions should induce, within a shear flow, particle drifts from regions of high to low shear stress, which are estimated to be of sufficient intensity to account for the observed initial viscosity increase mentioned above.

1,097 citations

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TL;DR: In this article, a constitutive equation for computing particle concentration and velocity fields in concentrated monomodal suspensions is proposed that consists of two parts: a Newtonian constitutive equations in which the viscosity depends on the local particle volume fraction and a diffusion equation that accounts for shear-induced particle migration.

Abstract: A constitutive equation for computing particle concentration and velocity fields in concentrated monomodal suspensions is proposed that consists of two parts: a Newtonian constitutive equation in which the viscosity depends on the local particle volume fraction and a diffusion equation that accounts for shear‐induced particle migration. Particle flux expressions used to obtain the diffusion equation are derived by simple scaling arguments. Predictions are made for the particle volume fraction and velocity fields for steady Couette and Poiseuille flow, and for transient start‐up of steady shear flow in a Couette apparatus. Particle concentrations for a monomodal suspension of polymethyl methacrylate spheres in a Newtonian solvent are measured by nuclear magnetic resonance (NMR) imaging in the Couette geometry for two particle sizes and volume fractions. The predictions agree remarkably well with the measurements for both transient and steady‐state experiments as well as for different particle sizes.

834 citations

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TL;DR: The theory of the acoustic radiation force is presented; a second-order, time-averaged effect responsible for the acoustophoretic motion of suspended, micrometre-sized particles in an ultrasound field.

Abstract: In this paper, Part 7 of the thematic tutorial series “Acoustofluidics – exploiting ultrasonic standing waves, forces and acoustic streaming in microfluidic systems for cell and particle manipulation ”, we present the theory of the acoustic radiation force; a second-order, time-averaged effect responsible for the acoustophoretic motion of suspended, micrometre-sized particles in an ultrasound field.

530 citations

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TL;DR: In this article, a simple model for the rheological behavior of concentrated colloidal dispersions is developed for a suspension of Brownian hard spheres, where two contributions to the macroscopic stress: a hydrodynamic and a Brownian stress.

Abstract: A simple model for the rheological behavior of concentrated colloidal dispersions is developed. For a suspension of Brownian hard spheres there are two contributions to the macroscopic stress: a hydrodynamic and a Brownian stress. For small departures from equilibrium, the hydrodynamic contribution is purely dissipative and gives the high‐frequency dynamic viscosity. The Brownian contribution has both dissipative and elastic parts and is responsible for the viscoelastic behavior of colloidal dispersions. An evolution equation for the pair‐distribution function is developed and from it a simple scaling relation is derived for the viscoelastic response. The Brownian stress is shown to be proportional to the equilibrium radial‐distribution function at contact, g(2;φ), divided by the short‐time self‐diffusivity, D0s(φ), both evaluated at the volume fraction φ of interest. This scaling predicts that the Brownian stress diverges at random close packing, φm, with an exponent of −2, that is, η’0 ∼ η(1 − φ/φm)−2, ...

463 citations