Shear-thinning viscoelastic (STVE) flows exhibit intriguing phenomena owing to their complex rheology and the coupling of various forces involved. Here, we present an understanding of the cross-stream migration of droplets in a confined STVE flow and unravel the role of a shear-thinning induced lift force (FSM) in their dynamical behavior. We perform experiments with popular STVE liquids of different molecular weights and concentrations (c) for Reynolds numbers Re < 1 and Weissenberg numbers Wi = 0.01–7.4. Our results reveal larger droplets (of drop-to-channel ratio β ≥ 0.28) that follow their original streamlines, whereas smaller droplets (β ≤ 0.2) exhibit center ward migration and the migration rates depend upon the drop-to-medium viscosity (k) and elasticity (ξ) ratios. The lateral displacement of droplets is tracked using high-speed imaging that is used to estimate the relevant forces using suitable correlations. We find that the migration dynamics of droplets is underpinned by the non-inertial lift (FNIL), viscoelastic lift (FVM, FVD), and shear-thinning induced lift (FSM) forces. We provide experimental evidence of the proposed FSM and, from analytical scaling and empirical modeling, develop an expression for FSM ∼ (with R2 = 0.95) for an object at a distance h from the wall and with a drop in viscosity Δμ and strain rate across its diameter D. Our study sheds light on the underlying dynamics on droplets in an STVE medium and opens up avenues for sorting and focusing of drops in an STVE medium at low Re.
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