Equilibrium And Stability Of Floating And Exotic Capillary Systems

With the rapid development of space technology and microfluidics,people are confronted with more and more capillary phenomena under microgravity and small-scale conditions.Capillary fluid statics mainly studies the equilibrium and stability involved in capillary phenomena,which can make reasonable explanation and accurate prediction for various capillary phenomena,and guide people's life and industry,such as mineral flotation,anti fog lens and design of water walking robots.In this paper,based on the capillary statics,a series of theoretical studies have been carried out on several typical capillary floating phenomena and exotic capillary phenomena,and the effects of various physical and geometric parameters on the stability of floating objects and the meniscius stability,including wettability,the morphology of solid,the magnitude and direction of gravity,the scale,etc.,have been analyzed.In addition,based on the bifurcation theory,this paper also studies the "multi equilibrium" problem in the above phenomena.The main research results of the present paper are organized as follows:(1)A three-plate system is proposed as a simplified model to study the capillary action between multiple floating particles,and the lateral capillary force between the three plates and the equilibrium and stability of the middle plate are studied.The expression of lateral capillary force between three plates is determined,and five different types of forcedisplacement curves are obtained.Based on the bifurcation theory,the effect of the distance between the plates on two sides on the equilibrium and stability of the middle plate is studied,and eight types of bifurcation diagrams are obtained to predict the final equilibrium position of the middle plate.(2)Based on the variational principle,a mathematical model to calculate the resultant force and moment of resultant force of a two-dimensional floating body with an arbitrary convex and piecewise smooth cross-section is established.The validity and accuracy of the model are verified by three typical configurations,and the effects of surface tension on the vertical and rotational stability are studied by changing the physical and geometric parameters(e.g.,the radius of curvature of the solid surface at the contact line and the size of the floating body).Generally,the smaller the radius of curvature of the solid surface,the stronger the vertical and rotational stability of the two-dimensional floating body.(3)The floating phenomenon of a two-dimensional cylinder with a concave crosssection is studied.Different from the convex cylinder,there may be multiple possible menisci around the concave cylinder.Based on the bifurcation theory,the "multi equilibrium" problem of meniscus is studied by selecting the height of floating body as the bifurcation parameter,and the corresponding saddle-node bifurcation is obtained to predict the change of the number and stability of meniscus with height.Through a typical example,it is found that there is a hysteresis loop in the force displacement curve of the concave cylinder,which indicates that the force acting on the concave cylinder is related to its historical position.(4)Three kinds of exotic capillary cylinders classified by their cross-section curvature are proposed,and the influence of different physical and geometric parameters on the shapes of exotic capillary cylinders is studied.According to the exotic properties of the exotic capillary cylinder,it is found that the minimum eigenvalue corresponding to any meniscus on the exotic capillary cylinder is equal to zero,which is verified by serveral numerical examples.According to the above conclusion,a new method to determine the critical value directly is proposed for determining the meniscus stability.(5)The concept of generalized exotic capillary tube under positive/negative gravity is proposed,and the mathematical model to determine the shape of generalized exotic capillary tube is established.Eight types of the generalized exotic capillary tubes are obtained under different conditions.Based on the exotic property,a new method to determine the critical value is developed without solving the corresponding Jacobian equation.