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In the first part of the paper we provide a new classification of incompressible fluids characterized by a continuous monotone relation between the velocity gradient and the Cauchy stress. The considered class includes Euler fluids,…
We investigate the behavior of the slip length in Newtonian liquids subject to planar shear bounded by substrates with mixed boundary conditions. The upper wall, consisting of a homogenous surface of finite or vanishing slip, moves at a…
The molecular mechanism of slip at the interface between polymer melts and weakly attractive smooth surfaces is investigated using molecular dynamics simulations. In agreement with our previous studies on slip flow of shear-thinning fluids,…
The complicated dynamics of the contact line of a moving droplet on a solid substrate often hamper the efficient modeling of microfluidic systems. In particular, the selection of the effective boundary conditions, specifying the contact…
The aim of this work is to show the local null controllability of a fluid-solid interaction system by using a distributed control located in the fluid. The fluid is modeled by the incompressible Navier-Stokes system with Navier slip…
Consider the dynamics of a layer of viscous incompressible fluid under the influence of gravity. The upper boundary is a free boundary with the effect of surface tension taken into account, and the lower boundary is a fixed boundary on…
In this work, we study the motion of a rigid body in a bounded domain which is filled with a compressible isentropic fluid. We consider the Navier-slip boundary condition at the interface as well as at the boundary of the domain. This is…
In this work, we investigate the small-time global exact controllability of the Navier-Stokes equation, both towards the null equilibrium state and towards weak trajectories. We consider a viscous incompressible fluid evolving within a…
This work is dedicated to providing a detailed account of the flow dynamics in the closure region of an internal ship air cavity. A geometrically simple multiwave test cavity is considered, and a simulation of the flow is conducted using…
When a droplet spreads on a solid substrate, it is unclear what are the correct boundary conditions to impose at the moving contact line. The classical no-slip condition is generally acknowledged to lead to a non-integrable singularity at…
We discuss a methodology that could be gainfully exploited using easily measurable experimental quantities to ascertain if the ``no-slip" boundary condition is appropriate for the flows of fluids past a solid boundary.
In this paper we consider the effect of surface heterogeneity on the slippage of fluid, using two complementary approaches. First, MD simulations of a corrugated hydrophobic surface have been performed. A dewetting transition, leading to a…
Understanding what happens inside the rippling and dancing surface of a liquid remains one of the great challenges of fluid dynamics. Using molecular dynamics (MD) we can pick apart the interface structure and understand surface tension. In…
The hydrodynamic slippage at a solid-liquid interface is currently at the center of our understanding of fluid mechanics. For hundreds of years this science has relied upon no-slip boundary conditions at the solid-liquid interface that has…
A comprehensive review of current analytical models, experimental techniques, and influencing factors is carried out to highlight the current challenges in this area. The study of fluid-solid boundary conditions has been ongoing for more…
The conventional no-slip boundary condition leads to a non-integrable stress singularity at a moving contact line. This makes numerical simulations challenging, especially when capillary effects are essential for the dynamics of the flow.…
In this paper, we present a novel approach to model the fluid/solid interaction forces in a direct solver of the Navier-Stokes equations based on the volume of fluid interface tracking method. The key ingredient of the model is the explicit…
The chemical step is an elementary pattern in chemically heterogeneous substrates, featuring two regions of different wettability separated by a sharp border. Within the framework of lubrication theory, we investigate droplet motion and the…
We consider a nonlinear, moving boundary, fluid-structure interaction problem between a time dependent incompressible, viscous fluid flow, and an elastic structure composed of a cylindrical shell supported by a mesh of elastic rods. The…
We prove the existence of martingale solutions to a stochastic fluid-structure interaction problem involving a viscous, incompressible fluid flow, modeled by the Navier-Stokes equations, through a deformable elastic tube modeled by…