Eckart Streaming Analysis Generated by Weakly Focused Gaussian Beam

When a viscous fluid is subjected to intense ultrasonic waves, it can cause the stationary fluid to move, a phenomenon known as acoustic streaming which has been applied in many fields such as cell aggregation, particle transportation, and enhanced heat transfer. Among them, the acoustic streaming motion with a scale much larger than the acoustic wavelength is called Eckart flow. This paper conducts theoretical and simulation studies on the characteristics of Eckart flow. Based on the N-S momentum equation and the continuity equation, the acoustic streaming control equation is obtained by using the small perturbation theory, and the control equation is approximately solved. Meanwhile, numerical simulation analysis is carried out based on the COMSOL software to explore the formation mechanism of the flow field. The results show that the axial flow velocity of the Eckart flow caused by weakly focused ultrasound always presents a trend of first increasing and then decreasing, and reaches the maximum value near the focal length of the transducer. The main mechanism for the formation of Eckart flow lies in the fact that, affected by the viscosity of the liquid, the acoustic energy will attenuate along the propagation path, resulting in an acoustic radiation pressure difference along this path,