Acoustic streaming and shape evolution of viscous droplets in ultrasonic fields

The droplet–microfluidic system under acoustic-field actuation represents a classical multiphase flow problem with broad relevance to engineering and biomedical applications. When an acoustic wave interacts with a viscous droplet suspended in another liquid, it induces acoustic streaming both inside and outside the droplet and exerts acoustic radiation stresses that deform its shape. In this work, we present a comprehensive analytical and numerical framework to investigate the coupled dynamics of droplet shape evolution, acoustic fields and acoustic streaming. The study considers droplets stably positioned within a standing wave at either a pressure node or a velocity node, undergoing deformations analogous to the classical Taylor regime. Our analytical model, supported by numerical simulations, reveals that the acoustic field is predominantly governed by low-order modes, up to the quadrupole. Furthermore, the acoustic-streaming pattern is dictated by the density contrast between the droplet and the surrounding fluid, whereas both density and compressibility contrasts control the droplet deformation. We also demonstrate that impedance mismatch is not the fundamental criterion for acoustic scattering. Instead, mismatches in density, or compressibility, or both, serve as the primary mechanisms. In addition, we develop a phase diagram illustrating droplet shape-deformation and streaming-pattern regimes as functions of the material properties (density ratio and compressibility ratio). These results provide deep mechanistic insights for the design and control of efficient droplet–acoustofluidic platforms and lay the groundwork for next-generation ultrasound-driven strategies for precise droplet manipulation in soft-matter and microfluidic applications.