STIRRING FREE SURFACE FLOWS DUE TO HORIZONTAL CIRCULATORY OSCILLATION OF A PARTIALLY FILLED CONTAINER

Abstract

Mixing in a partially filled beaker or conical flask using oscillator shaker tables is routinely used for cultivation of biological cells. The present study seeks to gain a better understanding of fluid flow inside a beaker on a shaker table and the fluid motion influence on the mixing of cells within the fluid medium used for their cultivation. The imposed oscillatory motion on the beaker induces free surface deformations, which may cause laminar and low shear flow environments thus uniformly mixing the fluid medium. The low shear and uniformly mixed cell culture medium are requirements necessary for optimum cellular growth. In this study, fluid flow due to periodic and horizontal circulatory oscillations at a beaker boundary has been analyzed both numerically and experimentally. A partially filled beaker was modeled as a circular cylinder, and the cell culture medium was modeled as an incompressible fluid with a free and deformable liquid interface. The three-dimensional numerical model that can resolve the free surface deformation was based on finite difference scheme based on the oMarker-and-Cello method. The method was used to determine the free surface deformation, its coupling to the flow dynamics within the beaker, and the resulting stirring effects. To verify the numerical model and validate the results, a simple flow visualization experiment was performed using an ion laser sheet to optically section flow chamber and reveal the flow pattern. The flow patterns obtained using numerical simulations were similar to those obtained experimentally through flow visualization. This study provides useful information that can be used to optimize the operation of a shaker table necessary to mix uniformly the cell culture, ensuring cell growth. In addition, this model can be extended to study the mixing processes in any chemical reactions within a partially filled container subjected to oscillatory forces.