9,803 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
An Energetic Variational Approach for ion transport
The transport and distribution of charged particles are crucial in the study
of many physical and biological problems. In this paper, we employ an Energy
Variational Approach to derive the coupled Poisson-Nernst-Planck-Navier-Stokes
system. All physics is included in the choices of corresponding energy law and
kinematic transport of particles. The variational derivations give the coupled
force balance equations in a unique and deterministic fashion. We also discuss
the situations with different types of boundary conditions. Finally, we show
that the Onsager's relation holds for the electrokinetics, near the initial
time of a step function applied field
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