Abstract
While acoustic streaming patterns in microfluidic channels with rectangular cross-sections have been widely shown in the literature, boundary-driven streaming fields in non-rectangular channels have not been well studied. In this paper, a two-dimensional numerical model was developed to simulate the boundary-driven streaming fields on cross-sections of cylindrical fluid channels. Firstly, the linear acoustic pressure fields at the resonant frequencies were solved from the Helmholtz equation. Subsequently, the outer boundary-driven streaming fields in the bulk of fluid were modelled while using Nyborg’s limiting velocity method, of which the limiting velocity equations were extended to be applicable for cylindrical surfaces in this work. In particular, acoustic streaming fields in the primary (1, 0) mode were presented. The results are expected to be valuable to the study of basic physical aspects of microparticle acoustophoresis in microfluidic channels with circular cross-sections and the design of acoustofluidic devices for micromanipulation.
Highlights
Ultrasonic particle manipulation (UMP) is a contactless method that is well-suited for micromanipulation in microfluidic systems
When a standing wave field is established in a microfluidic channel, the movements of particles suspended in the fluid medium are determined by two main forces, i.e., the acoustic radiation force (ARF) and the acoustic streaming (AS) induced drag force, which scale with the volume and diameter of the particle, respectively
In most UPM devices, ARF is the main engine for particle manipulation, while the AS effects are mostly regarded as disturbances as they usually place a lower limit on the particle size that can be manipulated by the ARFs [11]
Summary
Ultrasonic particle manipulation (UMP) is a contactless method that is well-suited for micromanipulation in microfluidic systems. The AS field in a microfluidic channel of particular interest is generally dominated by boundary-driven streaming, which arises from the absorption of acoustic momentum flux in the viscous boundary layer [16]. New boundary-driven streaming patterns that cannot be explained by Rayleigh’s theory have been observed in the bulk of fluid in addition to the classical Rayleigh streaming whose orientations are generally perpendicular to the driving boundaries and the transducer radiating surfaces in experimental UPM devices. In thin-layer UPM devices with high aspect-ratio rectangular fluid channels, AS vortices with orientations parallel to the driving boundaries and the transducer radiating surfaces, called ‘transducer-plane streaming’, have been experimentally observed [24,25,26]. Nyborg’s LV equations have been extended for predicting outer streaming fields in cylindrical fluid channels
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