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We present an effective thermoviscous theory of acoustofluidics includingpressure acoustics, thermoviscous boundary layers, and streaming for fluidsembedded in elastic cavities. By including thermal fields, we thus extend theeffective viscous theory by Bach and Bruus, J. Acoust. Soc. Am. 144, 766(2018). The acoustic temperature field and the thermoviscous boundary layersare incorporated analytically as effective boundary conditions andtime-averaged body forces on the thermoacoustic bulk fields. Because it avoidsresolving the thin boundary layers, the effective model allows for numericalsimulation of both thermoviscous acoustic and time-averaged fields in 3D modelsof acoustofluidic systems. We show how the acoustic streaming depends stronglyon steady and oscillating thermal fields through the temperature dependency ofthe material parameters, in particular the viscosity and the compressibility,affecting both the boundary conditions and spawning additional body forces inthe bulk. We also show how even small steady temperature gradients (1 K/mm)induce gradients in compressibility and density that may result in very highstreaming velocities (1 mm/s) for moderate acoustic energy densities (100J/m^3).

Theory of pressure acoustics with thermoviscous boundary layers and streaming in elastic cavities