Impact of inertia and channel angles on flow distribution in microfluidic junctions

S Blonski,T Wacławczyk,M Jachimek,S Jakiela,P M Korczyk,D Zaremba

doi:10.1007/s10404-020-2319-6

Abstract

In the present paper, we provide evidence of the vital impact of inertia on the flow in microfluidic networks, which is disclosed by the appearance of nonlinear velocity–pressure coupling. The experiments and numerical analysis of microfluidic junctions within the range of moderate Reynolds number (1 < Re < 250) revealed that inertial effects are of high relevance when Re > 10. Thus, our results estimate the applicability limit of the linear relationship between the flow rate and pressure drop in channels, commonly described by the so-called hydraulic resistance. Herein, we show that neglecting the nonlinear in their nature inertial effects can make such linear resistance-based approximation mistaken for the network operating beyond Re < 10. In the course of our research, we investigated the distribution of flows in connections of three channels in two flow modes. In the splitting mode, the flow from a common channel divides between two outputs, while in the merging mode, streams from two channels join together in a common duct. We tested a wide range of junction geometries characterized by parameters such as: (1) the angle between bifurcating channels (45°, 90°, 135° and 180°); (2) angle of the common channel relative to bifurcating channels (varied within the available range); (3) ratio of lengths of bifurcating channels (up to 8). The research revealed that the inertial effects strongly depend on angles between the channels. Additionally, we observed substantial differences between the distributions of flows in the splitting and merging modes in the same geometries, which reflects the non-reversibility of the motion of an inertial fluid. The promising aspect of our research is that for some combinations of both lengths and angles of the channels, the inertial contributions balance each other in such a way that the equations recover their linear character. In such an optimal configuration, the dependence on Reynolds number can be effectively mitigated.

Highlights

Classical microfluidics is seen as a domain of viscousdominated flows, where simple Ohm-like circuit analysis can be applied with sufficient precision (Oh et al 2012)
We show the experimental evidence of the angle’s impact on the flow distribution in a microfluidic junction, on the example of a specially designed microfluidic rectangular device
Using the new model we analyse numerically the microfluidic junctions to investigate the possibilities for the mitigation of inertial effects by the adjusting of angles

Summary

Introduction

Classical microfluidics is seen as a domain of viscousdominated flows, where simple Ohm-like circuit analysis (analogical to electric circuits) can be applied with sufficient precision (Oh et al 2012). The ratio of inertial and viscous interactions is described by the Reynolds number. For the flow through a long channel, the Reynolds number is defined as Re = UW∕ , where and are density and dynamic viscosity of the liquid, respectively, U—mean velocity of the fluid, W—the width of the channel. In the case of a circular pipe, experimentally obtained critical Reynolds number Re ≈ 2300 gives the upper limit for which the inertial effects can be neglected. In this range, the flow through a pipe is thought to be laminar. According to Hagen–Poiseuille’s law, stationary, viscous, laminar and incompressible flow satisfies the linear relation

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