Microscopic steady streaming eddies created around short cylinders in a channel: Flow visualization and Stokes layer scaling

Abstract

Microscale steady streaming eddies created using low-intensity fluid oscillations offer appealing options for controlling fluids in microfluidic systems. We describe the three-dimensional (3D) steady streaming flow formed in a small channel containing single fixed cylinders when the channel fluid is oscillated at low intensity. Experiments include three cylinder sizes (length 1.5mm; radii a=125, 250, and 500μm) within identical channels (height 2h=1.5mm; width 4mm) over a range of oscillation frequencies (40⩽ω⩽1000Hz). The size of key flow features is measured from steady particle pathline images recorded within three flow symmetry planes. The resulting 3D streaming exhibits two distinct recirculating flows that are governed by the Stokes layer thickness δAC and geometric length scales. Four symmetric recirculating eddies are created adjacent to the cylinder far from channel walls, and their size is governed by δAC∕a as described by steady streaming theory for a 2D geometry. The cylinder/wall boundary layer junction drives a 3D recirculating flow with size that is directly proportional to δAC∕h and is not affected by a threefold variation of the cylinder radius. The flow images and scaling describe an organized 3D steady streaming flow that may be tuned to control fluid and its contents in microfluidic devices.