The effect of the contact line on droplet spreading. (English) Zbl 0719.76071
Summary: The motion of the free surface of a viscous droplet is investigated. By using lubrication theory a model is developed for the motion of the free surface which includes both the effect of slip and the dependence of the contact angle on the slip velocity. We solve the resulting nonlinear partial differential equation in several ways. First we investigate the initial motion of the drop at a nonequilibrium contact angle using the method of matched asymptotics. Then we develop a pseudo-spectral method to numerically solve the full nonlinear system. The dependence of the spreading rate of the drop on the various physical parameters and for different slip models is determined.
MSC:
| 76T99 | Multiphase and multicomponent flows |
| 76D08 | Lubrication theory |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
Keywords:
free surface of a viscous droplet; lubrication theory; nonlinear partial differential equation; nonequilibrium contact angle; method of matched asymptoticsReferences:
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