A Constrained Level Set Method for Simulating the Formation of Liquid Bridges (Communications in Computational Physics, 2020)
In this paper, we investigate the dynamic process of liquid bridge formation between two parallel hydrophobic plates with hydrophilic patches, previouslystudied in [1]. We propose a dynamic Hele-Shaw model to take advantage of thesmall aspect ratio between the gap width and the plate size. A constrained level setmethod is applied to solve the model equations numerically, where a global constraintis imposed in the evolution [2] stage together with local constraints in the reinitialization [3] stage of level set function in order to limit numerical mass loss. In contrastto the finite element method used in [2], we use a finite difference method with a5th order HJWENO scheme for spatial discretization. To illustrate the effectivenessof the constrained method, we have compared the results obtained by the standardlevel set method with those from the constrained version. Our results show that theconstrained level set method produces physically reasonable results while that of thestandard method is less reliable. Our numerical results also show that the dynamicnature of the flow plays an important role in the process of liquid bridge formationand criteria based on static energy minimization approach has limited applicability.