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Three-dimensional streaming around an obstacle in a Hele-Shaw cell
- Publication Year :
- 2022
-
Abstract
- The application of oscillatory flow around an obstacle drives a steady ``streaming'' due to inertial rectification, which has been used in a host of microfluidic applications. While theory has focused largely on two-dimensional (2D) flows, streaming in many practical microfluidic devices is three-dimensional (3D) due to confinement. We develop a three-dimensional streaming theory around an obstacle in a microchannel with a Hele-Shaw like geometry, where one dimension (depth) is much shorter than the other two dimensions. Utilizing inertial lubrication theory, we demonstrate that the time-averaged streaming flow has a three-dimensional structure. Notably, the flow changes direction across the depth of the channel, which is a feature not observed in less confined streaming setups. This feature is confirmed by our experiments of streaming around a cylinder sandwiched in a microchannel. Our theory also predicts that the streaming velocity decays as the inverse cube of the distance from the cylinder, faster than that expected from previous two-dimensional approaches. We verify this decay rate quantitatively using particle tracking measurements from experiments of streaming around cylinders with different aspect ratios at different driving frequencies.
- Subjects :
- Physics - Fluid Dynamics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2211.08335
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1017/jfm.2023.276