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This review highlights the profound and unexpected ways in which viscosity varying in space and time can affect flow. The most striking manifestations are through alterations of flow stability, as established in model shear flows and industrial applications. Future studies are needed to address the important effect of viscosity stratification in such diverse environments as Earth's core, the Sun, blood vessels, and the re-entry of spacecraft.

The stability of miscible two-fluid flow in a horizontal channel is examined. The flow dynamics are governed by the continuity and Navier-Stokes equations coupled to a convective-diffusion equation for the concentration of the more viscous fluid through a concentration-dependent viscosity.Our analysis of the flow in the linear regime delineates the presence of convective and absolute instabilities and identifies the vertical gradients of viscosity perturbations as the main destabilizing influence in agreement with previous work. Our transient numerical simulations demonstrate the development of complex dynamics in the nonlinear regime, characterized by roll-up phenomena and intense convective mixing; these become pronounced with increasing flow rate and viscosity ratio, as well as weak diffusion. *

We consider the flow dynamics of a thin evaporating droplet in the presence of an insoluble surfactant and non-interacting particles in the bulk. Based on lubrication theory, we derive a set of evolution equations for the film height, the interfacial surfactant and bulk particle concentrations, taking into account the dependence of the liquid viscosity on the local particle concentration. An important ingredient of our model is that it takes into account the fact that the surfactant adsorbed at the interface hinders evaporation. We perform a parametric study to investigate how the presence of surfactants affects the evaporation process as well as the flow dynamics with and without the presence of particles in the bulk. Our numerical calculations show that the droplet life-time is affected significantly by the balance between the ability of surfactant to * To whom correspondence should be addressed † Department of Chemical Engineering, University of Patras, Patras 26500, Greece ‡ Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Sangareddy 502 285, Telangana, India ¶ Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK 1 enhance spreading suppressing the effect of thermal Marangoni stresses-induced motion and to hinder the evaporation flux through the reduction of effective interfacial are of evaporation, which tend to accelerate and decelerate the evaporation process, respectively. For particle-laden droplets and in the case of dilute solutions, the droplet life-time is found to be weakly-dependent on the initial particle concentration. We also show that the particle deposition patterns are influenced strongly by the direct effect of surfactant on the evaporative flux; in certain cases, the "coffee stain" effect is enhanced significantly. A discussion of the delicate interplay between the effects of capillary pressure, solutal and thermal Marangoni stresses, which drive the liquid flow inside the evaporating droplet giving rise to the observed results is provided herein.

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