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On the basis of theoretical considerations (mechanistic model), an equation was determined that allowed to calculate the free energy (Helmholtz) of a spherical droplet deposited on a flat surface in a system without external forces. Assuming isochoric and isothermal transformation of the system and a very fast conversion of mechanical energy into heat, the obtained equation allows to determine the trajectory of thermodynamic transformation consisting of the spreading of the droplet on the surface of the substrate. The similarities and differences in the behaviour of spherical droplets described by the mechanistic model and Young's model, together with its improvements, were discussed. The trajectories of free energy changes during the spreading of droplets in a system in which the adhesive force acting perpendicular to the wetted surface was considered as well. [ABSTRACT FROM AUTHOR]

In the currently existing physical models of wetting a solid substrate by a liquid drop, the contact angle is determined on the basis of the equilibrium of forces acting tangentially to the wetted surface at any point in the perimeter of the wetted area, ignoring the forces (or their components) acting perpendicular to this area. In the solution shown in the paper, the equilibrium state of forces acting on a droplet was determined based on the minimum mechanical energy that the droplet achieves in the state of equilibrium. This approach allows one to take into account in the model, in addition to the forces tangential to the wetted surface, also forces perpendicular to it (also the force of adhesion), moreover, these may be dispersed forces acting on the entire interface, not on a single point. The correctness of this approach is confirmed by the derived equations concerning the forces acting on the liquid both tangentially and perpendicularly to the wetted surface. The paper also identifies the areas of solutions in which the obtained equilibrium of forces is stable and areas of unstable equilibrium of forces. The solution is formulated both for isothermal and isochoric system. Based on the experimental data accessible in the literature, the condition that has to be met by the droplets (and their surroundings) during measurements performed under gravity conditions was formulated. [ABSTRACT FROM AUTHOR]

On the basis of the principles of non-equilibrium thermodynamics, the following condition was determined: necessary and sufficient for the occurrence of a minimum free energy of a liquid droplet deposited on a solid substrate in a gaseous environment in an isothermal and isochoric system. Only for positive values of the energy of three-phase tension line (shrinking the wetting circumference) for small and large contact angles can the system not reach this minimum. Without exceeding a certain free energy limit, it is not possible for the drop to spontaneously spread over the surface. For zero and negative energy of three-phase tension line (stretching the wetting circumference), the system can always reach a minimum of free energy. The developed equations allow determining the change of free energy occurring between any two stationary states when the droplet volume and physicochemical parameters characterizing energies at the interfaces are known. For a known set of such parameters, the equations allow determining the trajectory of free energy changes in the system as a function of the contact angle from the moment the drop comes into contact with the substrate. The application of the principles of non-equilibrium thermodynamics makes it possible to treat a real system as one in which the drops do not evaporate. However, the system has to be isothermal. [ABSTRACT FROM AUTHOR]