Parametric Form Analytical Solution For The Young-Laplace Equation

In this paper,we study the meridional profile of the axisymmetric liquid bridge between two diffexent size spheres.According to the principle of minimum potential energy and the necessary condition for the existence of extreme values in functional analysis,we can derive the Young-Laplace equation under axisymmetric model,however,most of the literatures on the liquid bridge under the axisymmetric model directly use this equation without systematic derivation.After using the boundary conditions,we calculate the general parameters form analytical solution of Young-Laplacc equation,The phase diagram of the equation is drawn according to the region divided by parameters.And when the Integral constant is zero,we obtain the geometric shape of the liquid bridge under this special condition and the relationship between some physical parameters.Finally,compared with other models,the relationship is verified again.In the first chapter,the development history of capillary mechanics,the establishoent of Young-Laplace equation,the influence af the liquid bridge and the research status are briefly introduced.In the second chapter,starting with the total free energy of the liquid-bridge system,the Young-Laplace equation under the axisymmetric model is derived by using the principle of minimum potential energy and the necessary conditions for the existence of the extreme valties in functional analysis.In the third chapter,the process of calculating the parametric form analytic solution of Young-Laplace equation i5 described in detail,and the corresponding phase diagram is drawn according to the region divided by parameters.And when the integral constant is zero,then the form of the solution in this particular case is analyzed,and the shape of the liquid bridge in this case is obtgtined,and then compared with other models.In the fourth chapter,we summarize the article,draw a conclusion,and look forward to the development prospect an the basis of the obtained results.