The evaporation of a liquid drop on a solid substrate is a remarkably common phenomenon. Yet, the complexity of the underlying mechanisms has constrained previous studies to spherically symmetric configurations. Here we investigate well-defined, non-spherical evaporating drops of pure liquids and binary mixtures. We deduce a universal scaling law for the evaporation rate valid for any shape and demonstrate that more curved regions lead to preferential localized depositions in particle-laden drops. Furthermore, geometry induces well-defined flow structures within the drop that change according to the driving mechanism. In the case of binary mixtures, geometry dictates the spatial segregation of the more volatile component as it is depleted. Our results suggest that the drop geometry can be exploited to prescribe the particle deposition and evaporative dynamics of pure drops and the mixing characteristics of multicomponent drops, which may be of interest to a wide range of industrial and scientific applications.

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. *

The linear stability characteristics of pressure-driven two-layer channel flow are considered, wherein a Newtonian fluid layer overlies a layer of a Herschel-Bulkley fluid. A pair of coupled Orr-Sommerfeld eigenvalue equations are derived and solved using an efficient spectral collocation method for cases in which unyielded regions are absent. An asymptotic analysis is also carried out in the long-wave limit, the results of which are in excellent agreement with the numerical predictions. Our analytical and numerical results indicate that increasing the dimensionless yield stress, prior to the formation of unyielded plugs below the interface, is destabilizing. Increasing the shear-thinning tendency of the lower fluid is stabilizing.

The linear and nonlinear spatio-temporal stability of an interface separating two Newtonian fluids in pressure-driven channel flow at moderate Reynolds numbers is analysed both theoretically and numerically. A linear, Orr–Sommerfeld-type analysis shows that most of such systems are unstable. The transition to an absolutely unstable regime is investigated, and is shown to occur in an intermediate range of Reynolds numbers and ratios of the thicknesses of the two layers, for near-density matched fluids with a viscosity contrast. A critical Reynolds number is found for transition from convective to absolute instability of relatively thin films. Results obtained from direct numerical simulations (DNSs) of the Navier–Stokes equations for long channels using a diffuse-interface method elucidate that waves generated by random noise at the inlet show that, near the inlet, waves are formed and amplified strongly, leading to ligament formation. Successive waves coalesce with each other further downstream, resulting in longer larger-amplitude waves further downstream. In the linearly absolute regime, the characteristics of the spatially growing wave near the inlet agree with that of the saddle point as predicted by the linear theory. The transition point from a convective to an absolute regime predicted by linear theory is also in agreement with a sharp change in the value of a healing length obtained from the DNSs.

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