Related papers: An effective slip boundary for micro-structured su…
We study a model describing the motion of the fluid in a lake, assuming inflow-outflow effects across the bottom, the porous coast and the inflows and outflows of rivers. We prove the global in time existence result for this model. The…
Zhu & Granick [Phys. Rev. Lett. 87, 096105 (2001)] have recently experimentally established existence of a boundary slip in a Newtonian liquid. They reported typical values of the slip length of the order of few micro-meters. In this light,…
This article is devoted to the study of an incompressible viscous flow of a fluid partly enclosed in a cylindrical container with an open top surface and driven by the constant rotation of the bottom wall. Such type of flows belongs to a…
We consider two-phase Navier--Stokes flow with a Boussinesq--Scriven surface fluid. In such a fluid the rheological behaviour at the interface includes surface viscosity effects, in addition to the classical surface tension effects. We…
We consider a coupled system of partial differential equations describing the interactions between a closed free interface and two viscous incompressible fluids. The fluids are assumed to satisfy the incompressible Navier-Stokes equations…
We analyze the two-dimensional incompressible Navier-Stokes equations on a smooth, bounded domain with Navier boundary conditions. Starting from an initial vorticity in $L^p$ with $p>2$, we show strong convergence of the vorticity in the…
Experiments on fluid systems in micro-/nano-scale solid conveyors have shown a violation of the no-slip assumption that have been adopted by the classical fluid mechanics. To correct this mechanics for the fluid slip, various approaches…
In this paper we analyze a 2D free-boundary viscoelastic fluid model of Oldroyd-B type at infinite Weissenberg number. Our main goal is to show the existence of the so-called splash singularities, namely points where the boundary remains…
The classical fluid dynamics boundary condition of no-slip suggests that variation in the wettability of a solid should not affect the flow of an adjacent liquid. However experiments and molecular dynamics simulations indicate that this is…
The classical theorems of inviscid stability have been extended for compressible flows past compliant surfaces. We consider normal modes imposed on a plane parallel compressible flow past compliant walls modelled as spring-backed plates and…
The rigid-lid approximation is a commonly used simplification in the study of density-stratified fluids in oceanography. Roughly speaking, one assumes that the displacements of the surface are negligible compared with interface…
In this paper, we first investigate necessary optimality conditions for problems governed by systems describing the flow of an incompressible second grade fluid. Next, we study the asymptotic behavior of the optimal solution when the…
We describe a tensorial generalization of the Navier slip boundary condition and illustrate its use in solving for flows around anisotropic textured surfaces. Tensorial slip can be derived from molecular or microstructural theories or…
Secondary flows are ubiquitous in channel flows, where small velocity components perpendicular to the main velocity appear due to the complexity of the channel geometry and/or that of the flow itself such as from inertial or non-Newtonian…
We study a three-dimensional fluid-structure interaction problem describing the motion of an incompressible, viscous fluid coupled with a deformable elastic shell of Koiter type that forms part of the fluid boundary. The fluid motion is…
In this paper, a novel immersed boundary method is developed, validated, and applied. Through devising a second-order three-step flow reconstruction scheme, the proposed method is able to enforce the Dirichlet, Neumann, Robin, and Cauchy…
Transport of material across liquid interfaces is ubiquitous for living cells and is also a crucial step in drug delivery and in many industrial processes. The fluids that are present on either side of the interfaces will usually have…
In this Letter, the 2-dimensional dense flow of polygonal particles on an incline with a flat frictional inferior boundary is analyzed by means of contact dynamics discrete element simulations, in order to develop boundary conditions for…
This paper is concerned with the incompressible limit problem for strong solutions of compressible two-phase flow models under periodic boundary conditions, where the Navier-Stokes equations are nonlinearly coupled with either Cahn-Hilliard…
We report results of investigations of a high-speed drainage of thin aqueous films squeezed between randomly nanorough surfaces. A significant decrease in hydrodynamic resistance force as compared with predicted by Taylor's equation is…