11,973 research outputs found
Molecular hydrodynamics of the moving contact line in two-phase immiscible flows
The ``no-slip'' boundary condition, i.e., zero fluid velocity relative to the
solid at the fluid-solid interface, has been very successful in describing many
macroscopic flows. A problem of principle arises when the no-slip boundary
condition is used to model the hydrodynamics of immiscible-fluid displacement
in the vicinity of the moving contact line, where the interface separating two
immiscible fluids intersects the solid wall. Decades ago it was already known
that the moving contact line is incompatible with the no-slip boundary
condition, since the latter would imply infinite dissipation due to a
non-integrable singularity in the stress near the contact line. In this paper
we first present an introductory review of the problem. We then present a
detailed review of our recent results on the contact-line motion in immiscible
two-phase flow, from MD simulations to continuum hydrodynamics calculations.
Through extensive MD studies and detailed analysis, we have uncovered the slip
boundary condition governing the moving contact line, denoted the generalized
Navier boundary condition. We have used this discovery to formulate a continuum
hydrodynamic model whose predictions are in remarkable quantitative agreement
with the MD simulation results at the molecular level. These results serve to
affirm the validity of the generalized Navier boundary condition, as well as to
open up the possibility of continuum hydrodynamic calculations of immiscible
flows that are physically meaningful at the molecular level.Comment: 36 pages with 33 figure
Instability of standing waves of the Schrödinger equation with inhomogeneous nonlinearity
This paper is concerned with the inhomogeneous nonlinear Shrödinger equation (INLS-equation)iu_t + Δu + V(Єx)│u│^pu = 0, x Є R^N. In the critical and supercritical cases p ≥ 4/N, with N ≥ 2, it is shown here that standing-wave solutions of (INLS-equation) on H^1(R^N) perturbation are nonlinearly unstable or unstable by blow-up under certain conditions on the potential term V with a small Є > 0
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