Research On The Spreading And Migration Of Droplets On The Surface Of An Immiscible Liquid With High Viscosity Ratio

The dynamics at the liquid-liquid interface of the two-layer immiscible liquid films have a wide range of applications,such as the development of liquid lenses to replace traditional solid lenses,the cleanup and recovery of oil spilled on the surface of seawater,and the application of oil drop to diagnose diseases,etc.It is undoubted that further studies on the dynamic of two-layer immiscible liquid films have a significant practical value.Most related research is experimental and theoretical under the condition of total wetting,and there are only a few academic studies on the spreading and migration characteristics of droplets on the surface of an immiscible liquid under the condition of partial wetting.Therefore,in this paper,we establish a mathematical model for the dynamic process of droplets on the surface of an immiscible liquid and explore the spreading and migration of droplets with high viscosity ratios.The main contents are as follows:(1)For the spreading of droplets on the surface of an immiscible liquid with high viscosity ratios,the evolution equations of two-layer liquid films are established based on the lubrication approximation,the influence of high viscosity ratios and interfacial tension ratios on evolution and equilibrium state of droplets is investigated,and the variation in crucial parameters including the droplet thickness and spreading radius are analyzed.The results show that the deformation of the liquid-liquid interface near the contact line is affected by the viscosity ratio and the interfacial tension ratio;the increase of the viscosity ratio reduces the spreading rate and the time constant,thereby prolonging the spreading evolution,but does not affect the final stable shape of droplets;the composition of the repulsive and attractive forces in the disjoining pressure can affect the spreading time and the final equilibrium shape of the droplet;in the case of the high viscosity ratio,the relationship between the droplet spreading radius and time satisfies the logarithmic relationship.Compared with the case of the low viscosity ratio,the inertial oscillation phenomenon does not appear at the final stage of droplet spreading.(2)Based on the above model,considering the energy equation and the relationship between interfacial tension and temperature,a thermocapillary migration model of droplets on the surface of an immiscible liquid with high viscosity ratio was established.The effects of characteristic parameters such as temperature gradient,heat transfer parameters and interfacial tension coefficient on the migration process of droplets are explored.The results show that the temperature gradient is proportional to the migration velocity;the movement direction of droplets is determined by the positive and negative of the interfacial tension coefficient;as the absolute value of the interfacial tension coefficient increases,the droplet migration velocity also increases;the droplet migration process is closely related to the interface heat transfer parameters.The increase of the Biot number of the gas-liquid interface can slow down the migration velocity of the droplet,and the addition of thermal conductivity ratio at the liquid-liquid interface also reduces the migration velocity of the lens but to an insignificant degree;with the increase of viscosity ratio and initial interfacial tension ratio,it needs to overcome a greater resistance,and the migration velocity decreases in a negative correlation;the droplet migration velocity can be guaranteed only when the height of liquid substrate is appropriate,and the droplet migration velocity can be reduced if the height of liquid substrate is too high or too low.Under the same temperature gradient,the separation velocity or polymerization velocity of two droplets on the surface of a liquid substrate is much less than that of a single droplet.