Simulation Of Two-fluid Flows Research Articles

Simulation of two-fluid flows using a finite element/level set method. Application to bubbles and vesicle dynamics

A new framework for two-fluid flows using a finite element/level set method is presented and verified through the simulation of the rising of a bubble in a viscous fluid. This model is then enriched to deal with vesicles (which mimic red blood cells’ mechanical behavior) by introducing a Lagrange multiplier to constrain the inextensibility of the membrane. Moreover, high order polynomial approximation is used to increase the accuracy of the simulations. A validation of this model is finally presented on known behaviors of vesicles under flow such as “tank treading” and tumbling motions.

Wetting condition in diffuse interface simulations of contact line motion

We investigate the wetting condition for diffuse-interface methods in the simulation of two-fluid flows with moving contact lines. A current method, which uses a surface-energy approach, is shown not to result in a slope of the interface that is consistent with the prescribed value of the contact angle. A geometric formulation is proposed that does result in the prescribed contact angle. Test results are presented for the axisymmetric droplet spreading due to the capillary force and the motion of a droplet on a solid substrate in a shear flow.

Simulation of two-fluid flows by the least-squares finite element method using a continuum surface tension model

In this paper a numerical procedure for simulating two-fluid flows is presented. This procedure is based on the Volume of Fluid (VOF) method proposed by Hirt and Nichols and the Continuum Surface Force (CSF) model developed by Brackbill et al.. In the VOF method fluids of different properties are identified through the use of a continuous field variable (colour function). The colour function assigns a unique constant (colour) to each fluid. The interfaces between different fluids are distinct due to sharp gradients of the colour function. The evolution of the interfaces is captured by solving the convective equation of the colour function. The CSF model is used as a means to treat surface tension effect at the interfaces. Here a modified version of the CSF model, proposed by Jacqmin, is used to calculate the tension force. In the modified version, the force term is obtained by calculating the divergence of a stress tensor defined by the gradient of the colour function. In its analytical form, this stress formulation is equivalent to the original CSF model. Numerically, however, the use of the stress formulation has some advantages over the original CSF model, as it bypasses the difficulty in approximating the curvatures of the interfaces. The least-squares finite element method (LSFEM) is used to discretize the governing equation systems. The LSFEM has proven to be effective in solving incompressible Navier–Stokes equations and pure convection equations, making it an ideal candidate for the present applications. The LSFEM handles all the equations in a unified manner without any additional special treatment such as upwinding or artificial dissipation. Various bench mark tests have been carried out for both two-dimensional planar and axisymmetric flows, including a dam breaking, oscillating and stationary bubbles and a conical liquid sheet in a pressure swirl atomizer. © 1998 John Wiley & Sons, Ltd.