Volume viscosity

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Volume viscosity

Volume viscosity (also called bulk viscosity or second viscosity) appears in the Navier-Stokes equation if it is written for compressible fluid, as described in the most books on general hydrodynamics , , and acoustics ,.

where µ^v is the volume viscosity coefficient. Authors who use the alternative term bulk viscosity for the same parameter include , .

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Divergence

In vector calculus, the divergence is an operator that measures the magnitude of a vector field's source or sink at a given point; the divergence of a vector field is a scalar....
of the flow equals 0.

This viscosity parameter is additional to the usual dynamic viscosity µ. The volume viscosity becomes important only for such effects where fluid compressibility is essential. Examples would include shock wave

Shock wave

A shock wave is a type of propagating disturbance. Like an ordinary wave, it carries energy and can propagate through a medium or in some cases in the absence of a material medium, through a field such as the electromagnetic field....
s and sound

Sound

Sound is vibration transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a threshold of hearing to be heard, or the sensation stimulated in organs of hearing by such vibrations....
propagation. It appears in the Stokes' law (sound attenuation)

Stokes' law (sound attenuation)

Stokes derived law for attenuation of sound in Newtonian liquid.According to this law attenuation of sound a is proportional to the dynamic viscosity ?, square of the sound frequency ?, and reciprocally proportional to the liquid density ? and cubic power of sound speed V...
that describes propagation of sound in Newtonian liquid.

The volume viscosity of many fluids is inaccurately known, despite its fundamental role for fluid dynamics

Fluid dynamics

In physics, fluid dynamics is the sub-discipline of fluid mechanics dealing with fluid flow — the natural science of fluids in motion....
at high frequencies. The only values for the volume viscosity of simple Newtonian liquids known to us come from the old Litovitz and Davis review, see References. They report the volume viscosity of water at 15 °C is 3.09 centipoise

Modern Acoustic rheometer

Acoustic rheometer

Acoustic rheometer employes piezo-electric crystal that can easily launch a successive wave of extensions and contractions into the fluid. It applies an oscillating extensional stress to the system....
s are able to measure this parameter, see External links.

Volume viscosity

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