  When an acoustic wave travels in a lossy medium such as a liquid, it
progressively transfers its pseudo-momentum to the fluid, which results in a
steady acoustic streaming. Remarkably, the phenomenon involves a balance
between sound attenuation and shear, such that viscosity vanishes in the final
expression of the velocity field. For this reason, the effect of viscosity has
long been ignored in acoustic streaming experiments. Here, we show
experimentally that the viscosity plays a major role in cavities such as the
streaming induced by surface acoustic waves in sessile droplets. We develop a
numerical model based on the spatial filtering of the streaming source term to
compute the induced flow motion with dramatically reduced computational
requirements. We evidence that acoustic fields in droplets are a superposition
of a chaotic field and a few powerful caustics. It appears that the caustics
drive the flow, which allows a qualitative prediction of the flow structure.
Finally, we reduce the problem to two dimensionless numbers related to the
surface and bulk waves attenuation and simulate hemispherical sessile droplets
resting on a lithium niobate substrate for a range of parameters. Even in such
a baseline configuration, we observe at least four distinct flow regimes. For
each of them, we establish a correlation of the average streaming speed in the
droplet, which is increasingly dependent on the bulk wave attenuation as the
viscosity increases. These correlations extend our results to a wide range of
fluids and actuation frequencies.
