An energy balance approach to modeling the hydrodynamically driven spreading of a liquid drop

Abstract

This paper extends the overall energy balance (OEB) approach to the modeling of liquid drop spreading to cases where the primary motive force is hydrodynamic in nature. In such cases the mass, and therefore total energy, of the system varies with time thus invalidating previous OEB models. By relating the change in internal energy of the drop with the energy entering the system, changes in potential energy and work done by the system, a non-linear first-order ordinary differential equation has been developed which describes the drop spreading process for the case of a spherical cap of constant dynamic contact angle and constant mass flow rate. To provide validation data for the model, an experimental study has also been undertaken. In these experiments the Axisymmetric Drop Shape Analysis technique has been used to monitor the changing contact angle and contact radius of the drop as it advances across a solid surface. The solution of the ODE is shown to be in very good agreement with the experimental results, until such time as the drop grows to beyond the range where the spherical cap approximation is valid. A comparison of the magnitude of the energetic terms has revealed that the major deterrent to drop spreading is the work required to increase the surface area of the drop. In the case of slow speed spreading, it is shown that the viscous dissipation at the three-phase line is negligible, leading to a model completely free of any empirically determined curve fitting factors.