Acoustic streaming in second-order fluids

In this article, inner acoustic streaming for second-order fluids has been studied analytically by employing asymptotic expansions for a thin Stokes layer and low acoustic Mach number. In addition, a multiple-timescale approach has been adopted to separate the primary oscillatory flow and the steady acoustic streaming. The study considers two sample cases: (i) motionless boundary and (ii) vibrating boundary and compares the characteristics associated with their streaming. It is observed that both the primary oscillatory flow and acoustic streaming flow fields are suppressed in second-order fluids due to the extra stress components present in the fluids. This study considers both compressible and incompressible Stokes layers to bring out the acoustic streaming characteristics associated with fluid compressibility. For the compressible Stokes layer, stronger acoustic streaming flow results for the motionless boundary, leveraging the deeper interaction between the primary oscillatory pressure field and the steady streaming. In the case of a vibrating boundary, the primary oscillatory pressure field is independent of the Stokes layer compressibility, and hence, the acoustic streaming flow remains unaltered. The extra stresses in second-order fluids reduce the acoustic body force density, and the maximum reduction has been observed for the vibrating boundary. In order to understand Lagrangian streaming, Stokes drift has also been calculated and compared for all the scenarios. The theoretical analysis and fundamental insights derived from this study have potential for applications in diverse fields such as particle manipulation, biosensing, cell sorting, and removal of loosely bound material such as non-specifically bound proteins.