Deep Neural Network for Oscillation Dynamics of Capillary Rise (Advances in Applied Mathematics and Mechanics, 2024)
The phenomenon of capillary rise in a tube is mainly affected by the inertia,capillary force, gravitational force, and viscous force of fluids. It has been observed thatcertain fluid properties and tube geometries can cause the liquid column to oscillate. Inthis paper, we first present a general second-order ordinary differential equation thatcan be used to describe the dynamic process of oscillation in terms of the tube length,tube radius, and contact angle. However, it is difficult to obtain its finding an analyticalsolution owing to the existence of nonlinear terms. Thus, we adopt a deep neuralnetwork (DNN) method to solve this equation for its distinct feature in function-fittingability. Simulations are conducted to test the performance of the DNN method, and theresults are found to be in good agreement with data reported in the literature. Based ona suitably designed and trained DNN, we further perform a comprehensive analysisof the rising height and moving velocity of the fluid during the oscillatory process fordifferent combinations of tube length, tube radius, and contact angle. The results showthat the DNN method provides an effective tool for studying the oscillation dynamicsof capillary rise.