Equilibrium, stability and dynamics of microdrops

The stability of the contact line region as affected by the disjoining pressure has been analyzed. Disjoining pressure represents the extra potential in thin films that always exists in the contact angle region where a liquid drop or a wedge thins to meet the solid substrate. The disjoining pressure in turn affects the contact angle as well as the film profile. It is shown here that the integration of the augmented Young-Laplace equation to yield specific types of drop profiles under the action of disjoining pressure leads to the usual conditions of equilibrium as well as the condition of stability in the same analysis. The fact that stability condition has to coexist with the condition of equilibrium is pursued to show in one case that the stability modifies at least half of the predicted outcomes in the drop shapes. For the first time, the stability condition is extended to include besides the disjoining pressure, the effects of surface tension and curvature. The last effect turns out to be very important. Multiple solutions (five) for the drop profiles for the same type of disjoining pressures show that only one or two of these can be stable. Kinetics of wetting under disjoining pressure is studied by solving the equations governing the fluid mechanics of spreading numerically. For Hamaker forces driven flow and surface tension driven flow, the numerical results are in keeping with the theoretical analysis. We also numerically studied the spreading of polymer solution and got the dynamic profiles of the thin film near the contact line. It is seen that the manner in which experimental data are taken will show that the contact lines in some cases will show abrupt equilibration and in others may not show any equilibration when the accuracy of measurements is a lot higher than usual.