Formation of vortices in long microcavities at low Reynolds number

Abstract

Microcavities are a central feature of many microflow systems ranging from sprouting capillaries during angiogenesis to various microfluidic devices. Recently, the flow and transport phenomena in microcavities have been subject of a number of studies, yet a physical picture of the flow properties at low Reynolds number, which is the relevant regime in many biological applications, has not been fully brought out. We have therefore systematically investigated, experimentally and by modeling, the flow in a long microcavity and found that the flow properties depend decisively on the depth/width ratio of the cavity. Notably, if this cavity aspect ratio is higher than approximately 0.51, counter-flow vortices emerge in the cavity even at vanishing Reynolds number. The distance of the first vortex from the cavity entrance decreases with an increasing aspect ratio as an inverse power law. In the vortex-free regime below the threshold aspect ratio, the flow velocity decays exponentially away from the cavity entrance, with a decay length that scales with the width of the cavity and depends also on the aspect ratio of its cross section. The results of our numerical simulations are supported by a theoretical analysis and are in good agreement with experimental data, acquired by optical velocimetry with optical tweezers.