Lubrication Approximation with Prescribed Nonzero Contact Angle
نویسنده
چکیده
We prove long{time existence for a weak solution s(t; x) 0 of the lubrication approximation @ t s + @ x (s @ 3 x s) = 0 in fs > 0g with prescribed contact angle of, say, 4 (@ x s) 2 = 1 on @fs > 0g :
منابع مشابه
Darcy’s Flow with Prescribed Contact Angle – Well-posedness and Lubrication Approximation
We consider the spreading of a thin two-dimensional droplet on a solid substrate. We use a model for viscous fluids where the evolution is governed by Darcy’s Law. At the triple point where air and liquid meet the solid substrate, the liquid assumes a constant, non-zero contact angle (partial wetting). We show local and global well-posedness of this free boundary problem in the presence of the ...
متن کاملBiorthogonal wavelet-based full-approximation schemes for the numerical solution of elasto-hydrodynamic lubrication problems
Biorthogonal wavelet-based full-approximation schemes are introduced in this paper for the numerical solution of elasto-hydrodynamic lubrication line and point contact problems. The proposed methods give higher accuracy in terms of better convergence with low computational time, which have been demonstrated through the illustrative problems.
متن کاملSimulation of Droplet Motion on Low-Energy and Heterogeneous Surfaces
tact angle, for a static drop, will depend on the previous A method of calculation is introduced that allows the simulahistory of the drop motion, a phenomenon known as contact tion of the time-dependent three-dimensional motion of liquid angle hysteresis. Contact angle hysteresis is believed to be droplets on solid substrates for systems exhibiting finite equilibcaused by substrate heterogenie...
متن کاملNonlocal diffuse interface theory of thin films and the moving contact line.
A nonlocal diffuse interface model is explored using the "lubrication approximation" applicable to thin films. We show the inconsistency of the expansion leading to a nonlinear diffusion model, and solve an untruncated integro-differential mean field equation to compute the equilibrium density profile across the fluid-vapor interface. The disjoining potential and effect of interfacial curvature...
متن کاملHysteretic Effects in Droplet Motions on Heterogeneous Substrates: Direct Numerical Simulation
Amethodof calculation is introduced that allows the simulation of the time-dependent three-dimensional motion of liquid droplets on solid substrates for systems with finite equilibrium contact angles. The contact angle is a prescribed function of position on the substrate. An evolution equation is given, using the lubrication assumption, that includes viscous, capillary, and disjoining forces. ...
متن کامل