Numerical Investigation on the Deformation of the Free Interface During Water Entry and Exit of a Circular Cylinder by Using the Immersed Boundary-Multiphase Lattice Boltzmann Flux Solver

In this work,the deformation of free interface during water entry and exit of a circular cylinder is investigated numerically by using the two-dimensional(2D)immersed boundary-multiphase lattice Boltzmann flux solver(IB-MLBFS).The fluid domain is discretized by finite volume discretization,and the flux on the grid interface is evaluated by lattice Boltzmann equations.Both the implicit velocity correction and the surface flux correction are implemented by using the immersed boundary-method to consider the fluid-structure interaction and the contact interface between the multiphase fluids and the structure.First,the water entry of a circular cylinder is simulated and the results are compared with the experiment,which considered the length-diameter ratio of the circular cylinder.The reliability of 2D simulation is verified and the deformation of the free interface is well investigated.Afterward,the water exit of a circular cylinder with constant velocity is simulated,which is less researched.In addition,the results show the advantage of present IB-MLBFS to some extent.Finally,the water exit and re-entry of a circular cylinder are presented,and the results present the complex deformation of the free interface and the dynamic response of the moving structure.Based on the numerical results,the free interface of the multiphase fluids is well captured,and the contact interface on the boundary of the moving structure is accurately presented by the IB-MLBFS.

Theoretical analysis of droplet transition from Cassie to Wenzel state

Whether droplets transit from the Cassie to the Wenzel state （C-W） on a textured surface is the touchstone that the superhydrophobicity of the surface is still maintained. However, the C-W transition mechanism, especially the spontaneous transition of small droplets, is still not very clear to date. The interface free energy gradient of a small droplet is firstly proposed and derived as the driving force for its C-W evolution in this study based on the energy and gradient analysis. Then the physical and mathematical model of the C-W transition is found after the C-W driving force or transition pressure, the resistance, and the parameters of the meniscus beneath the droplet are formulated. The results show that the micro/nano structural parameters significantly affect the C-W driving force and resistance, The smaller the pillar diameter and pitch, the minor the C-W transition pressure, and the larger the resistance. Consequently, the C-W transition is difficult to be completed for the droplets on nano-textured surfaces. Meanwhile if the posts are too short, the front of the curved liquid-air interface below the droplet will touch the structural substrate easily even though the three phase contact line （TPCL） has not depinned. When the posts are high enough, the TPCL beneath the drop must move firstly before the meniscus can reach the substrate. As a result, the droplet on a textured surface with short pillars is easy to complete its C-W evolution. On the other hand, the smaller the droplet, the easier the C-W shift, since the transition pressure becomes larger, which well explains why an evaporating drop will collapse spontaneously from composite to Wenzel state. Besides, both intrinsic and advancing contact angles affect the C-W transition as well. The greater the two angles, the harder the C-W transition. In the end, the C-W transition parameters and the critical conditions measured in literatures are calculated and compared, and the calculations accord well with the experimental results.

Analysis of meniscus beneath metastable droplets and wetting transition on micro/nano textured surfaces

Tile expressions of interface flee energy （IFE） of composite droplets with meniscal liquid-air interlhce in metastable state on nlicro/nano textured snrfaces were formulated. Then tile parameters to describe the meniscus were determined based on the principle of minimtun 1FE. Furthermore, the IFE barriers and the necessary and sufficient conditions of drop wetting transition fl＇om Cassie to Wenzel were analyzed and the corresponding criteria were lk^rmulated. The results show that the liquid-air interface below a composite droplet is fiat when the post pitches are relatively small, but in a shape of curved meniscus when the piteches are comparatively large and the curvature depends on structural parameters. The angle between meniscus and pillar wall is just equal to the supplementary angle of intrinsic contact angle of post material. The calculations also illustrate that Cassie droplets will transform to Wenzel state when post pitch is large enough or when drop volume is sufficiently small. The opposite transition from Wenzel to Cassie state, however, is unable to take place spontaneously because the energy barrier is always positive. Finally, the calculation results of this model are well consistent with tile experimental obserwttions in literatures for the wetting transition of droplets from Cassie to Wenzel state.

Simulation of Thermocapillary Convection in a TwoLayer Immiscible Fluid System Using a Boundary Element Method

A boundary element method for simulating thermocapillary convection in a two-layer immiscible fluid system with flat and free interface has been developed.The divergence theorem is applied to the non-linear convective volume integral of the boundary element formulation with the pressure penalty function.Consequently,velocity gradients are eliminated and the complete formulation is written in terms of velocity.This avoids the difficulty of convective discretizations and provides considerable reductions in storage and computational requirements while improving accuracy.In this paper,we give the influence of different parameters(Marangoni number, Reynolds number)on thermocapillary convection in cavity with two-layer immiscible fluids.As shown by the numerical results,when the physical parameters between liquid encapsulant and melt are chosen appropriately, the detrimental flow in the bottom melt layer can be greatly suppressed.The influence of the free interface on thermocapillary convection is also shown.

Asymptotic Analysis in a Gas-Solid Combustion Model with Pattern Formation

The authors consider a free interface problem which stems from a gas-solid model in combustion with pattern formation. A third-order, fully nonlinear, self-consistent equation for the flame front is derived. Asymptotic methods reveal that the interface approaches a solution to the Kuramoto-Sivashinsky equation. Numerical results which illustrate the dynamics are presented.

Robust a Simulation for Shallow Flows with Friction on Rough Topography

In this paper,we propose a robust finite volume scheme to numerically solve the shallow water equations on complex rough topography.The major difficulty of this problem is introduced by the stiff friction force term and the wet/dry interface tracking.An analytical integration method is presented for the friction force term to remove the stiffness.In the vicinity of wet/dry interface,the numerical stability can be attained by introducing an empirical parameter,the water depth tolerance,as extensively adopted in literatures.We propose a problem independent formulation for this parameter,which provides a stable scheme and preserves the overall truncation error of δ(Δx^(3)).The method is applied to solve problems with complex rough topography,coupled with h-adaptive mesh techniques to demonstrate its robustness and efficiency.