Spatially two-dimensional mathematical model of the flow hydrodynamics in a spacer-filled channel - The effect of inertial forces

In the present work a spatially two-dimensional (2D) mathematical model of the flow hydrodynamics in a flat channel filled with a net-like spacer is presented, taking into account the fluid inertia in the momentum balance equation (laminar flow regime). The effect of the inertial term on flow uniformity in the system under study is analyzed. In accordance with expectations, in the range of low Reynolds numbers the impact of fluid inertia is negligible and the model results show characteristics of creeping flow, as presented in previous work. However, at higher values typical of industrial electrodialysis, the laminar flow model presented predicts significant non-uniform flow in critical regions. This is mainly due to the formation of jets at an inlet side that transport the fluid more deeply into the working volume of the electrodialysis chamber. The results obtained are discussed in relation to the range of applicability of a simplified model neglecting fluid inertia (creeping flow regime). Special attention is paid to the inlet and outlet regions characterized by sudden contraction or expansion of the flow cross-section area.