Lyes Kahouadji

A hybrid interface tracking – level set technique for multiphase flow with soluble surfactant

Abstract A formulation for soluble surfactant transport in multiphase flows recently presented by Muradoglu and Tryggvason (JCP 274 (2014) 737–757) [17] is adapted to the context of the Level Contour Reconstruction Method, LCRM, (Shin et al. IJNMF 60 (2009) 753–778, [8] ) which is a hybrid method that combines the advantages of the Front-tracking and Level Set methods. Particularly close attention is paid to the formulation and numerical implementation of the surface gradients of surfactant concentration and surface tension. Various benchmark tests are performed to demonstrate the accuracy of different elements of the algorithm. To verify surfactant mass conservation, values for surfactant diffusion along the interface are compared with the exact solution for the problem of uniform expansion of a sphere. The numerical implementation of the discontinuous boundary condition for the source term in the bulk concentration is compared with the approximate solution. Surface tension forces are tested for Marangoni drop translation. Our numerical results for drop deformation in simple shear are compared with experiments and results from previous simulations. All benchmarking tests compare well with existing data thus providing confidence that the adapted LCRM formulation for surfactant advection and diffusion is accurate and effective in three-dimensional multiphase flows with a structured mesh. We also demonstrate that this approach applies easily to massively parallel simulations.

Simulation of immiscible liquid–liquid flows in complex microchannel geometries using a front-tracking scheme

The three-dimensional two-phase flow dynamics inside a microfluidic device of complex geometry is simulated using a parallel, hybrid front-tracking/level-set solver. The numerical framework employed circumvents numerous meshing issues normally associated with constructing complex geometries within typical computational fluid dynamics packages. The device considered in the present work is constructed via a module that defines solid objects by means of a static distance function. The construction combines primitive objects, such as a cylinder, a plane, and a torus, for instance, using simple geometrical operations. The numerical solutions predicted encompass dripping and jetting, and transitions in flow patterns are observed featuring the formation of drops, ‘pancakes’, plugs, and jets, over a wide range of flow rate ratios. We demonstrate the fact that vortex formation accompanies the development of certain flow patterns, and elucidate its role in their underlying mechanisms. Experimental visualisation with a high-speed imaging are also carried out. The numerical predictions are in excellent agreement with the experimental data.