Numerical solution of a cavity problem under surface tension effect

A three-dimensional numerical simulation of flow in patterned microchannel with alternate layers of hydrophilic and hydrophobic surfaces at the bottom wall is studied here. Surface characteristics of the microchannel are accounted by specifying the contact angle and the surface tension of the fluid. Meniscus profiles with varying amplitude and shapes are obtained under the different specified surface conditions. Flow instability increases as the fluid at the bottom wall traverses alternately from hydrophilic region to hydrophobic region. To understand the surface tension effect of the side walls, a two-dimensional numerical study has also been carried out for the microchannel and the results are compared with three-dimensional simulation. The surface tension effect of the side walls enhances the capillary effect for three-dimensional case.

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Cavity Detachment from a Wedge with Rounded Edges and the Surface Tension Effect

Journal of Marine Science and Engineering ◽

10.3390/jmse9111253 ◽

2021 ◽

Vol 9 (11) ◽

pp. 1253

Author(s):

Yuriy N. Savchenko ◽

Georgiy Y. Savchenko ◽

Yuriy A. Semenov

Keyword(s):

Surface Tension ◽

Weber Number ◽

Solution Process ◽

Cavity Flow ◽

Surface Tension Effect ◽

Force Coefficient ◽

Hodograph Method ◽

Wide Range ◽

Critical Weber Number ◽

Cavity Boundary

Cavity flow around a wedge with rounded edges was studied, taking into account the surface tension effect and the Brillouin–Villat criterion of cavity detachment. The liquid compressibility and viscosity were ignored. An analytical solution was obtained in parametric form by applying the integral hodograph method. This method gives the possibility of deriving analytical expressions for complex velocity and for potential, both defined in a parameter plane. An expression for the curvature of the cavity boundary was obtained analytically. By using the dynamic boundary condition on the cavity boundary, an integral equation in the velocity modulus was derived. The particular case of zero surface tension is a special case of the solution. The surface tension effect was computed over a wide range of the Weber number for various degrees of cavitation development. Numerical results are presented for the flow configuration, the drag force coefficient, and the position of cavity detachment. It was found that for each radius of the edges, there exists a critical Weber number, below which the iterative solution process fails to converge, so a steady flow solution cannot be computed. This critical Weber number increases as the radius of the edge decreases. As the edge radius tends to zero, the critical Weber number tends to infinity, or a steady cavity flow cannot be computed at any finite Weber number in the case of sharp wedge edges. This shows some limitations of the model based on the Brillouin–Villat criterion of cavity detachment.

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Computer Modeling of Ceramics Sintering: Effects of Inhomogeneity on Sintering Kinetics

Solid State Phenomena ◽

10.4028/www.scientific.net/ssp.281.918 ◽

2018 ◽

Vol 281 ◽

pp. 918-933

Author(s):

Wen Dong Luo ◽

Hai Peng Qiu ◽

Jing Zhe Pan

Keyword(s):

Surface Tension ◽

Grain Size ◽

Grain Boundary ◽

Computational Model ◽

Numerical Solution ◽

Surface Diffusion ◽

Triple Junction ◽

Diffusion Mechanism ◽

Sintering Kinetics ◽

Effect Of Surface

In the sintering of ceramics, cracks are inevitably encountered after sintering. But very few studies have been presented in the literature for qualifying and quantifying effects of inhomogeneity on sintering kinetics. Therefore, a series of detailed sintering variables such as grain size, surface tension and diffusivity are chosen to study the effects of their inhomogeneity on sintering kinetics through a computational model calculated by computer.Furthermore, there are two main achievements in this computational model that first one is providing a numerical solution for the curvature at triple junction (pore tip) of microscopic particles, and second one is considering the effect of surface diffusion on first-stage sintering where diffusion mechanism is coupled by grain-boundary and surface diffusion.

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