The steady streaming (SS) phenomenon is gaining increased attention in the microfluidics community, because it can generate net mass flow from zero-mean vibration. We developed numerical simulation and experimental measurement tools to analyze this vibration-induced flow, which has been challenging due to its unsteady nature. The validity of these analysis methods is confirmed by comparing the three-dimensional (3D) flow field and the resulting particle trajectories induced around a cylindrical micro-pillar under circular vibration. In the numerical modeling, we directly solved the flow in the Lagrangian frame so that the substrate with a micro-pillar becomes stationary, and the results were converted to a stationary Eulerian frame to compare with the experimental results. The present approach enables us to avoid the introduction of a moving boundary or infinitesimal perturbation approximation. The flow field obtained by the micron-resolution particle image velocimetry (micro-PIV) measurement supported the three-dimensionality observed in the numerical results, which could be important for controlling the mass transport and manipulating particulate objects in microfluidic systems.

The vibration-induced flow (VIF), in which a mean flow is induced by the interaction between the system vibration and micro-structures, has been studied as a fluid/particle micro-manipulation method that does not require an external pump. While the use of VIF with a wide variety of vibrations is expected to realize sophisticated fluid manipulation, numerical tools to predict these unsteady flows remain difficult. In this study, we have performed a numerical simulation of VIF with different vibrations and micropillar cross-sections. A proposed numerical model, which directly solves the continuity and Navier-Stokes equations in the coordinate system moving with the vibrating micropillar, enables us to avoid the introduction of a moving boundary, and therefore has significant advantage in numerical stability and accuracy. The immersed boundary technique allows us to embed arbitrary complex micro-structures in the Cartesian computational domain without requiring boundary-fitted meshes for each geometry. The dependencies of characteristics of flow on vibration parameters, such as vibration frequency, amplitude, direction, and the shape of micro-structures, were investigated and compared with the experimental results obtained by the particle image velocimetry (PIV) measurement. Excellent agreement between the numerical and experimental results validates that the present numerical approach can be a powerful tool to design functional VIF systems, such as mixing, particle/cell transport, trapping, and separation.

The steady streaming (SS) phenomenon is gaining increased attention in the microfluidics community, because it can generate net mass flow from the zero-mean vibration. We developed numerical simulation and experimental measurement tools to analyze this vibration induced flow, which has been challenging due to its unsteady nature. Validity of these analysis methods is confirmed by comparing the three-dimensional (3D) flow field induced around a cylindrical micropillar under circular vibration. In the numerical modeling, we directly solved the flow in the Lagrangian frame so that the substrate with a micropillar becomes stationary, and the result was converted to the Eulerian frame to compare them with the experimental results. The present approach enables to avoid the introduction of moving boundary or small perturbation approximation. The flow field obtained by the micro particle image velocimetry (PIV) measurement supported the three-dimensionality observed in the numerical results, which could be important for controlling the mass transport and manipulating particulate objects in the microfluidic systems.

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