Microfluidic Mixing by Rigid and Flexible Flaps

Professor R. H. Rangel
Ruth A. Lambert, Ph.D. Student

This study explores a method of enhancing the rates of macromolecular transport through a microchannel by introducing an oscillating mechanical flap in the fluidic system. A theoretical model is developed to determine the enhancement of macromolecular transport to a reaction site located along the channel surface. A numerical analysis is performed by considering a hinged flap located on the top or bottom walls of the channel. An order of magnitude analysis is conducted to estimate the reaction time which is bounded by the diffusion and the flow residence time. The period of oscillation is chosen to match the surface reaction time. The values of the characteristic flow variables adopted in this study, are representative of typical biomolecular transport processes confined to microscale geometries. With background flow, the results of the numerical analysis show that the mechanical actuator behaves like a miniature pump that drives a
favorable gradient of macromolecules towards the surface reaction sites within an initial lapse of time. In a stagnant fluid, the results show that the moving flap behaves like a stirring agent bringing fluid with a higher concentration in contact with the reaction site
and enhancing the surface concentration. In the latter case, the effect of the moving flap increases as the reaction progresses. The moving flap has the largest beneficial effect on surface concentration in the presence of a background flow when the position of the moving flap is along the top wall above the reaction site.

We explore the capacity of a flexible flaps 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.

Publications

Lambert, R. A., Das, S., Madou, M. J., Chakraborty, S., Rangel, R. H. (2008). Rapid Macromolecular Synthesis in Microfluidic Channels with Oscillating Flaps. Int. J. Heat Mass Transfer, 51(17-19), 4367-4378.

Lambert, R. A., Rangel, R. H. (2010). The role of elastic flap deformation on fluid mixing in a microchannel. Physics of Fluids, 22(5), 96-111.

Lambert, R. A., Rangel, R. H. (2011). Micro-Mixing and the Role of Multiple Rotating and Bending Flaps. Int J. Trans Phenomena, 12(1-2), 133-145.