Problems with unilateral constraints for NavierStokes equations and the dynamic contact angle problem
Abstract
A new approach is proposed for the analysis of some model problems in viscous fluid dynamics involving moving points of contact between a free boundary and a solid wall. The analysis is limited by twodimensional (plane and axisymmetrical) stationary problems. The free boundary of the fluid is determined approximately based on the capillary equilibrium condition, and the problem is reduced to that of solving NavierStokes equations with mixed boundary conditions. A modified version of the problem is proposed whereby an integral equality is replaced by a variational inequality. The solvability of the inequality is proved, and the uniqueness of the solution is demonstrated for the case of linearized NavierStokes equations.
 Publication:

PMTF Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki
 Pub Date:
 April 1990
 Bibcode:
 1990PMTF........27B
 Keywords:

 Capillary Flow;
 Computational Fluid Dynamics;
 NavierStokes Equation;
 Viscous Fluids;
 Asymptotic Methods;
 Free Boundaries;
 Hilbert Space;
 Rotating Bodies;
 Wall Flow;
 Fluid Mechanics and Heat Transfer