Mathematical modeling of drop mixing in a slit-type microchannel

Fast solute mixing can be achieved in a microchannel by rapid unidirectional displacement of a discrete liquid drop. The recirculation streamlines created within the liquid during the drop’s motion cause the solute to interlayer across the channel depth, provided the interlayer diffusion of the solute is small. Uniform interlayering appears when the drop is displaced by more than three drop lengths in a slit-type microchannel, thereby reducing the solute diffusion distances to a fraction of the channel depth. By fabricating the microchannel to a depth of less than 50 μm even large molecules with a low diffusivity (D < 10−8 cm2 s−1) can be mixed in seconds. The above strategy is shown by modeling the mixing of solutes present in a drop moving in a slit-type microchannel.