Three-dimensional streaming flow patterns in confinement

Steady streaming flow exited by oscillating bubbles is an intriguing tool for transport, mixing, sorting, or force actuation applications in microfluidics. Often the geometry of the set-up is intended to encourage two-dimensional (2D) flows, keeping the flow pattern across the channel depth uniform. This condition cannot always be ideally fulfilled, and three-dimensional (3D) streaming effects may be greatly beneficial, e.g., in mixing applications. We demonstrate that a weak 3D streaming component can be combined with existing 2D streaming theory, resulting in a systematic description of 3D streaming flow patterns. We show that these patterns can indeed be observed in bubble microstreaming, using 3D trajectory tracking by astigmatic particle tracking velocimetry