Equilibrium profile of extended isothermal meniscus with gravity inclination effect

The effect of substrate inclination on equilibrium profile of a wetting liquid near the contact line is predicted theoretically. The model is based on the augmented Young–Laplace equation, which dictates balance of hydrostatic, capillary and retarded van der Waals dispersion forces. In order to solve this model numerically, a high-order (up to the ninth-order) perturbation method, in terms of the Bond number, is developed. The decoupled equations obtained are solved recursively from lower to higher orders. The solution sequence is shown to be convergent for a wide range of operating parameters. Confrontation between theoretical predictions and experimental results shows excellent agreement. Predictions indicate that, although for small Bond numbers, the profile of menisci inside capillary experiences significant sensitivity to inclination angle. The study shows that the effect of gravity becomes more pronounced as the inclination angle increases till 90°. The study provides also a validity criterion of neglecting solid substrate inclination. It is shown that, for a tolerance of 10%, the threshold angle equals approximately 10°. The model may be extended to take into consideration non-retarded van der Waals force in a straightforward manner.