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.

Electric field effects on the dynamics of bubble detachment from an inclined surface

“…It seems that the electric field is pulling the bubble downwards, preventing asymmetries in bubble growth. The same behaviour has been assessed also for droplets immersed in an external electric field [13]. Concerning the vertical direction, the case without electric field ( Figure 9) reveals a lower error with respect to the balance in tangential direction, around 30% in the worst case.…”

“…the overall energy balance. It has been presented and ( [13]) validated ( [14] and [15]) for spreading droplets and has been adapted to study bubble evolution. The phenomena and their contribution to the change in the energy of the bubble are listed below.…”

Determination of Wetting Behavior, Spread Activation Energy, and Quench Severity of Bioquenchants

“…Equation [6] shows that the preciseness of the heattransfer coefficient estimated depends on the accuracy of the cooling rate obtained from the cooling curve data. In the present work, experiments were repeated at least twice and the ANOVA technique was adopted to compare the cooling curves obtained with the same quench medium.…”

“…[1,2,3] The spreading of a liquid drop on a solid can be studied with the knowledge of contact angle measurement and material properties. [4,5,6] The spreading of a liquid drop on a horizontal solid surface can be divided into high speed impact spreading, which is inertia dominated or forced spreading and low speed impact spreading dominated by surface tension. Spontaneous spreading occurs when the impact speed is equal to zero.…”

Evaporation Model of Micro-Menisci for Thermoelectric Drop Sensor

“…The final diameter of a meniscus after settling on the surface can be evaluated with help of overall energy balance approach (OEB) [5].…”