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We study the geometric flow of a planar curve driven by its curvature and the normal derivative of its capacity potential. Under a convexity condition that is natural to our problem, we establish long term existence and large time…
We propose coupled evolution equations for the thickness of a liquid film and the density of an adsorbate layer on a partially wetting solid substrate. Therein, running droplets are studied assuming a chemical reaction underneath the…
The influence of an underlying carrier flow on the terminal velocity of sedimenting particles is investigated both analytically and numerically. Our theoretical framework works for a general class of (laminar or turbulent) velocity fields…
Many biological examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen and the intracellular trafficking of vesicles into dendritic spines, involve the near-contact of…
We develop the theory of hydrodynamic charge and heat transport in strongly interacting quasi-relativistic systems on manifolds with inhomogeneous spatial curvature. In solid-state physics, this is analogous to strain disorder in the…
In this work we will study the dynamics of a thin layer of a viscous fluid which is embedded in the interior of another viscous fluid. The resulting flow can be approximated by means of the solutions of a free boundary problem for the…
Understanding the complex patterns in space-time exhibited by active systems has been the subject of much interest in recent times. Complementing this forward problem is the inverse problem of controlling active matter. Here we use optimal…
We consider the governing equations for the motion of the viscous fluids in two moving domains and an evolving surface from both energetic and thermodynamic points of view. We make mathematical models for multiphase flow with surface flow…
Flow of dissipative particles driven by peristaltic motion of a tube is numerically studied. A transition from slow unjammed flow to fast jammed flow is found through the observation of the mass flux if the minimum width of the peristaltic…
We introduce a system of shallow water-type equations to model laboratory experiments of particle-laden flows. We explore homogeneous liquid-solid suspensions of fine, non-cohesive, monodisperse glass beads which propagate as an equivalent…
We combine experiments, theory and numerical simulation to investigate the dynamics of a binary suspension of paramagnetic colloidal particles dispersed in water and transported above a stripe patterned magnetic garnet film. The substrate…
Thin liquid films are nanoscopic elements of foams, emulsions and suspensions, and form a paradigm for nanochannel transport that eventually test the limits of hydrodynamic descriptions. Here we use classical dynamical systems…
Non Newtonian flows are typically governed by intrinsic bulk rheology, which imposes strong constraints on transport through confined geometries. Here, we show that stable boundary lubrication can fundamentally alter this behavior by…
Suspensions of finite-size solid particles in a turbulent pipe flow are found in many industrial and technical flows. Due to the ample parameter space consisting of particle size, concentration, density and Reynolds number, a complete…
We discuss the motion of colloidal particles relative to a two component fluid consisting of solvent and solute. Particle motion can result from (i) net body forces on the particle due to external fields such as gravity; (ii) slip…
We highlight the differing roles of vorticity and strain in the transport of coarse-grained scalars at length-scales larger than $\ell$ by smaller scale (subscale) turbulence. %subscale flux/stress which appear in the evolution of…
The motion of charged particles in weakly varying electromagnetic fields is described using a perturbation method. This provides a systematic and physically transparent description of the particle motion on fast and slow spatio-temporal…
A wide range of natural and engineered fluid flows exhibit spatial or temporal viscosity variations, spanning scales from microbial locomotion to planetary mantle convection. These variations introduce qualitatively new physical mechanisms…
In recent years, our knowledge of photospheric magnetic fields went through a thorough transformation--nearly unnoticed by dynamo theorists. It is now practically certain that the overwhelming majority of the unsigned magnetic flux crossing…
Turbulent viscosity is frequently used in accretion disk theory to replace the microphysical viscosity in order to accomodate the observational need for in- stabilities in disks that lead to enhanced transport. However, simply replacing the…