The role of elastic flap deformation on fluid mixing in a microchannel

Abstract

We explore the capacity of a flexible flap to increase mixing in a microchannel for a flap Reynolds number Ref ranging from 0.3–80. The fictitious-domain (DLM) method is used to model the fluid and solid interactions. The momentum equations for the fluid and solid are solved individually using the finite-volume and finite-difference methods. The equations are coupled using distributed Lagrange multipliers. The stress in the solid is derived from the nonlinear beam equations. Fluid mixing is quantified by solving the mass transport equation for a solute with low molecular diffusivity and calculating a global mixing fraction M. The flap is actuated using a distributed follower force along the length of the flap. The results show that mixing is enhanced for larger flap displacements and for dimensionless frequencies Sl between 1 and 2. Optimal mixing occurs when the flap length is 2/3 the microchannel height. The influence of the hydrodynamic force on the beam bending motion enhances the mixing process. Under optimal conditions the flap behaves as a rapid mixing device where 80% of the long time mixing fraction is reached during an initial time interval of 3.8 s.