Direct simulation of 3D emulsion flow in microchannels using the boundary element method

Olga Abramova, Yulia Itkulova, Nail Gumerov


Application of boundary element method to study of flow microstructure and to solve wide range of problems on emulsion flows in micro- and nanoscales

Simulation results for dynamics of emulsion droplets in shear flow (a part of computational domain is shown)

The boundary element method (BEM) is a numerical method for solving partial differential equations, which can be represented in the boundary integral form. The BEM in application to a numerical solution of micro- and nanoscale dynamics of dispersed systems problems is more effective then others methods. It is due to the fact that this method enables to reduce the problem dimensionality by one as only the domain boundaries and interfaces are discretized.


Direct numerical simulation of 3D flow of two-phase Newton liquid with droplet microstructure in unbounded domain at low Reynolds number. BEM acceleration is achieved using of both advanced scalable algorithm (Fast multipole method, FMM) and heterogeneous computational structures on the base graphics processors (Graphics Processing Unit, GPU).


For the first time this approach enables direct calculation of dynamic interaction of 10934 deformable droplets under imposed shear flow. And the run time for this case was about 5 hours for 100 time steps on the one workstation.


Flow of emulsion droplets in a cross-section of 3D cylindrical channel
Triangulation of a axisymmetric channel with variable cross section

Problems about flow of one-phase liquid and two-phase emulsion in microchannels with variable cross-section are considered. To improve the accuracy of numerical calculations the BEM was modified on the base of perturbation method. Comparison of obtained numerical results with analytical solution for fluid motion with small droplet concentration shows high accuracy and efficiency of the modified BEM. 


The developed method can be used to establish the closing relations for simulation of two-phase liquid-liquid flow based on the continuum approach in macroscales