Analogue tuning of particle focusing in elasto-inertial flow

I Banerjee,L Brandt,A Russom,M E Rosti,T Kumar

doi:10.1007/s11012-021-01329-z

I Banerjee, L Brandt + Show 3 more

Open Access

https://doi.org/10.1007/s11012-021-01329-z

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Abstract

We report a unique tuneable analogue trend in particle focusing in the laminar and weak viscoelastic regime of elasto-inertial flows. We observe experimentally that particles in circular cross-section microchannels can be tuned to any focusing bandwidths that lie between the “Segre-Silberberg annulus” and the centre of a circular microcapillary. We use direct numerical simulations to investigate this phenomenon and to understand how minute amounts of elasticity affect the focussing of particles at increasing flow rates. An Immersed Boundary Method is used to account for the presence of the particles and a FENE-P model is used to simulate the presence of polymers in a Non-Newtonian fluid. The numerical simulations study the dynamics and stability of finite size particles and are further used to analyse the particle behaviour at Reynolds numbers higher than what is allowed by the experimental setup. In particular, we are able to report the entire migration trajectories of the particles as they reach their final focussing positions and extend our predictions to other geometries such as the square cross section. We believe complex effects originate due to a combination of inertia and elasticity in the weakly viscoelastic regime, where neither inertia nor elasticity are able to mask each other’s effect completely, leading to a number of intermediate focusing positions. The present study provides a fundamental new understanding of particle focusing in weakly elastic and strongly inertial flows, whose findings can be exploited for potentially multiple microfluidics-based biological sorting applications.

Highlights

We study particle focusing in strongly inertial and weakly elastic flows, whose importance is defined by two critical dimensionless numbers: the Reynolds and Weissenberg numbers
We found that particle focusing in elasto-inertial microfluidics is tuneable at this regime, and the particle focusing bandwidth is not restricted to the bistability scenario, but rather can be engineered to any analogue value that lies between the centreline focusing and the Segre-Silberberg annulus positions
We study the phenomenon of particle elasto-inertial focusing in presence of moderate inertia and weak fluid elasticity and found a general tendency of the particle to assume multiple equilibrium positions based on competitive effects of inertia and elasticity

Summary

Introduction

We study particle focusing in strongly inertial and weakly elastic flows, whose importance is defined by two critical dimensionless numbers: the Reynolds and Weissenberg numbers. The Weissenberg number is defined as Wi 1⁄4 kUc=H, where k is the relaxation time of the polymer additives The ratio between these two parameters gives the elasticity number El 1⁄4 Wi=Re. In Newtonian fluids, it has been well recognized that in the laminar flows typical of microfluidic channels (Re [ 1 and Re\2300) [1], inertia does play a role and particles tend to migrate to equilibrium positions at distances of order 0:6 of the channel hydraulic diameter, R, from the center, closer to channel centerlines, as initially predicted by Segreand Silberberg [2]. The equilibrium position in inertial microfluidic flows result from the balance of two opposing forces: (1) the wall-induced lift force arising out of the interaction between the particle and the adjacent wall, which directs the particle away from the wall and (2) the shear-gradient force, induced by the velocity profile curvature, pushing the particle away from the flow channel centreline and towards the wall [1, 8, 9]

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