Liquid drops sliding on surfaces are ubiquitous both in the natural and industrial world. The prediction of such drop motions has far-reaching implications in many fields of application, including microfluidics, phase change heat transfer, or coating technology. We present a numerical model based on the particle finite element method for the prediction of the sliding motion of liquid drops. The model includes the effect of a retention force which acts in the vicinity of the drop's contact line. This effect is found to be essential to obtain realistic spatiotemporal evolution of the drop. Thus far limited to two-dimensional simulations, the proposed model is validated by using experimental data found in the published literature, covering a wide range of drop size and physical properties. The numerical results are found to be mesh-independent and in good agreement with the experiments.
A particle finite element method (PFEM) based model is proposed to analyze droplet dynamics problems, particularly droplet spreading on solid substrates (wetting). The model uses an updated Lagrangian framework to formulate the governing equations of the liquid. Curvature of the liquid surface is tracked accurately using a deforming boundary mesh. In order to predict the spreading rate of the droplet on the solid substrate and track the corresponding contact angle evolution, dissipative forces at the contact line are included in the formulation in addition to the Navier-slip boundary conditions at the solid-liquid interface. The inclusion of these boundary conditions makes it possible to account for the induced Young's stress at the contact line and for the viscous dissipation along the solid-liquid interfacial region. These are found to be essential to obtain a mesh-independent physical solution. The temporal evolution of the contact angle and contact line velocity of the proposed model are compared with spreading droplets and micro sessiledroplet injection experiments, and are shown to be in good agreement.
Analysis of drop spreading and sliding on solid substrates is critical for many industrial applications, such as microfluidic devices, cooling towers, and fuel cells. A new three-dimensional model is proposed for droplet dynamics. Its numerical solution is obtained by the particle finite element method, based on an updated Lagrangian framework to accurately track the deformation of the droplet. The model hinges on boundary conditions at the solid-liquid interface to account for viscous dissipation and retention forces. These conditions are essential to obtain mesh-independent solutions and a realistic spatio-temporal evolution of the droplet deformation. Several numerical simulations are performed to assess the performance of the model for spreading and sliding drops, and results are compared to experimental data found in the literature. Good agreement is obtained with the available data. Simulations performed in two dimensions show striking discrepancies with the experimental data, thus demonstrating the need for three-dimensional simulations.
This paper proposes a numerical model for simulating an immiscible compressible two-phase flow in a periodic heterogeneous porous media with application to a coal-bed methane extraction system. Methane flow in a coal sample submerged in water is simulated using the multiscale homogenization method and the averaged macroscopic approach. A weak formulation is used to discretize the governing equations coupled with the boundary conditions using the finite element method and solved using the open-source code Freefem++. It was observed that the general behavior of both methods was in good agreement with actual gas saturation evolution. However, the multiscale approach provided more information regarding the global pressure evolution behavior of the mitigating gas.
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