This paper introduces two numerical approaches to model the capillary forces under two different initial conditions: given volume of the liquid and under the capillary condensation. The paper thoroughly analyzes the solutions of both numerical methods. Due to multiple numerical solutions may exist for a given set of parameters, criteria based on the derivative and the second derivative of the solution are proposed to determine the existence and stability of those numerical solutions. The features of those numerical solutions are also carefully discussed. Moreover, the results of two numerical methods are compared in different system parameters for several configurations, including two plates with different volume of liquid between them, a plate and a cone of different incline angle, and a plate and spheres of different radius. Suggestions of the applicability of both methods are given based on the results. To allow calculation of capillary forces between arbitrary shaped objects, the paper proposes an early approach to calculate the capillary forces for discretized surfaces.

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