Research On Mathematical Model And Optical Measurement Of Liquid Surface Shape With Wetting Effect

Wetting effect has an important application in our daily life.The contact angle and the surface tension of the liquid are two important parameters of wettability.The measurement of contact angel and liquid surface tension is an interesting topic in liquid domain,Optical measurement method,with the characteristics of high precision,non-destructive and non-contact,is suitable for the research of liquid surface shape measurement.In this dissertation,three math models of liquid surface shape were analyzed,and light scattering from the liquid surface were derived out.At last,the wetting effect of liquid surface shape were measured.First of all,mathematical model of the shape of the liquid surface was established when a plate was inserted into the liquid,and the characteristics of the reflected light field from this liquid surface was studied.The relation between the light field distribution,the surface tension of the liquid,the equilibrium contact angle,and the shape of the liquid surface is obtained.The liquid surface tension,equilibrium contact angle,and liquid surface shape can be measured simultaneously by this optical means,and the established mathematical model has been experimentally verified.Then,the mathematical model of the droplet on the horizontal plate is established,and the shape characteristics of the elongated droplet and the axisymmetric droplet are discussed respectively.The transmission and reflection light field distribution characteristics from the droplet are studied,and the transmission and reflection light field distribution functions are deduced mathematically.The theoretical results show that the light field distribution of the axisymmetric droplet on the plate is mainly regulated by the equilibrium contact angle.This method has a high accuracy in the study of the change of the equilibrium contact angle,so it has a potential application in the fields of thermal control and magnetic control of wettability.Finally,a three-dimensional mathematical model of the droplets on the inclined plate was established.The light field distribution characteristics from the droplets on the inclined plate are theoretically obtained based on our model.It is proposed that the parameters such as liquid surface tension,liquid refractive index,and liquid surface shape can be measured simultaneously.The dynamic contact angle and contact angle lag of the droplet can also be measured by this means.At last,the surface tension,liquid refractive index and liquid surface shape of water and ethylene glycol were measured experimentally.The experimental results show that the mathematical model and light diffraction distribution from the inclined plate droplets coincide with the experimental results.