Related papers: Analytical solution of Stokes flow inside an evapo…
Here, we trap and control the position of droplets to study their dynamics using hydrodynamic forces alone without an external field. The hydrodynamic trap is adapted from a previously implemented Stokes trap by incorporating a…
The Stokes equation describes the motion of fluids when inertial forces are negligible compared to viscous forces. In this article, we explore the consequence of parity-violating and non-dissipative (i.e. odd) viscosities on Stokes flows in…
The unsteady motion of a two-layer fluid induced by oscillatory motion of a flat plate along its length is mathematically analyzed. Two cases are considered: (i) the two-layer fluid is bounded only by the oscillating plate (Stokes' second…
Free surface, axially symmetric shallow flow is analysed in both the centrifugal and centripetal directions. Referring to the inviscid steady flow over a flat plate characterised by a unique value of specific energy, the analytical sub- and…
We analyze the stability and dynamics of toroidal liquid droplets. In addition to the Rayleigh instabilities akin to those of a cylindrical droplet there is a shrinking instability that is unique to the topology of the torus and dominates…
Fluid and solute transfer in X-junctions between straight channels is shown to depend critically on the junction angle in the Stokes flow regime. Experimentally, water and a water-dye solution are injected at equal flow rates in two facing…
Suspensions of anisotropic particles are commonly encountered in a wide spectrum of applications, including industrial and architectural coatings, targeted drug delivery and manufacturing of fiber-reinforced composites. A grand challenge in…
Stokes flow equations, used to model creeping flow, are a commonly used simplification of the Navier--Stokes equations. The simplification is valid for flows where the inertial forces are negligible compared to the viscous forces. In…
Various substances in the liquid state tend to form droplets. In this paper the shape of such droplets is investigated within the spherical model of a lattice gas. We show that in this case the droplet boundary is always diffusive, as…
Evaporating droplets of polymer or colloid solution may produce a glassy crust at the liquid-vapour interface, which subsequently deforms as an elastic shell. For sessile droplets, the known radial outward flow of solvent is expected to…
When a colloidal sessile droplet dries on a substrate, the particles suspended in it usually deposit in a ring-like pattern. This phenomenon is commonly referred to as the "coffee-ring" effect. One paradigm for why this occurs is as a…
In a companion study \cite{patterson2020computing2D}, we present a numerical method for simulating 2D viscous flow through an open compliant closed channel, drive by pressure gradient. We consider the highly viscous regime, where fluid…
This paper is concerned with self-similar solutions of the steady Navier-Stokes system in a two-dimensional sector with the no-slip boundary condition. We give necessary and sufficient conditions in terms of the angle of the sector and the…
We present a fully analytical solution for the natural oscillation of an inviscid sessile drop of arbitrary contact angle on a horizontal plate for the case for the case of low Bond number, when surface tension dominates gravity. The…
We study the problem of evaporating drops contracting to a point. Going back to Maxwell and Langmuir, the existence of a spherical solution for which evaporating drops collapse to a point in a self-similar manner is well established in the…
We show that in general, the specification of a contact angle condition at the contact line in inviscid fluid motions is incompatible with the classical field equations and boundary conditions generally applicable to them. The limited…
We investigate a possibility to regularize the hydrodynamic contact line singularity in the configuration of partial wetting (liquid wedge on a solid substrate) via evaporation-condensation, when an inert gas is present in the atmosphere…
The single droplet under shear is a foundational problem in fluid mechanics. In computational fluid dynamics, the two-dimensional (2D) formulation offers advantages in both computational efficiency and relevance, yet its theoretical…
We consider a coupled model for fluid flow and transport in a domain consisting of two bulk regions separated by a thin porous layer. The thickness of the layer is of order $\varepsilon$ and the microscopic structure of the layer is…
The asymptotic behavior of a class of stochastic reaction-diffusion-advection equations in the plane is studied. We show that as the divergence-free advection term becomes larger and larger, the solutions of such equations converge to the…