Flow of Non-Newtonian Fluids in a Single-Cavity Microchannel

Abstract

Having a basic understanding of non-Newtonian fluid flow through porous media, which usually consist of series of expansions and contractions, is of importance for enhanced oil recovery, groundwater remediation, microfluidic particle manipulation, etc. The flow in contraction and/or expansion microchannel is unbounded in the primary direction and has been widely studied before. In contrast, there has been very little work on the understanding of such flow in an expansion–contraction microchannel with a confined cavity. We investigate the flow of five types of non-Newtonian fluids with distinct rheological properties and water through a planar single-cavity microchannel. All fluids are tested in a similarly wide range of flow rates, from which the observed flow regimes and vortex development are summarized in the same dimensionless parameter spaces for a unified understanding of the effects of fluid inertia, shear thinning, and elasticity as well as confinement. Our results indicate that fluid inertia is responsible for developing vortices in the expansion flow, which is trivially affected by the confinement. Fluid shear thinning causes flow separations on the contraction walls, and the interplay between the effects of shear thinning and inertia is dictated by the confinement. Fluid elasticity introduces instability and asymmetry to the contraction flow of polymers with long chains while suppressing the fluid inertia-induced expansion flow vortices. However, the formation and fluctuation of such elasto-inertial fluid vortices exhibit strong digressions from the unconfined flow pattern in a contraction–expansion microchannel of similar dimensions.

Vortex evolution patterns for flow of dilute polymer solutions in confined microfluidic cavities

“…To quantify the evolution of the vortex in a confined cavity, we define X r as the length between the first corner point of the expansion wall and the reattachment point of the vortex along the cavity wall and then calculate the normalized vortex size X * = X r /∑ X i , as introduced in ref. 15 [Fig. 3(b)].…”

“…The vortex size for the Newtonian fluids in cavity flow shows a monotonically increasing trend [Fig. 3(c)], which can be fitted by a logistic function: 15 where k is the curve steepness and a is the value of the sigmoid's midpoint.…”

“…In contrast to the purely viscous fluids, the stretching and re-orientation of PVP chains lead to the accumulation of elastic stresses in cavity flow of PVP solution, accelerating and enhancing the vortex formation along curved flow streamlines. 11,15,44…”

“…11–13 It is therefore critical to understand the key factors and how they affect the vortex evolution in confined cavities. 14–17…”

“…Factors such as inertia, shear-thinning, and elasticity are found to affect vortex formation under different conditions. 15,39 On the expansion wall, vortex formation is dominated by fluid inertia, 39–41 whereas on the contraction wall, the fluid shear-thinning leads to flow separation and the fluid elasticity facilitates instability and asymmetry while suppressing the fluid inertia-induced vortices. 38,42,43…”