An acoustic rheometer is a device used to measure the rheological properties of

fluid In physics, a fluid is a liquid, gas, or other material that may continuously motion, move and Deformation (physics), deform (''flow'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are M ...

s, such as viscosity and elasticity, by utilizing

sound wave In physics, sound is a vibration that propagates as an acoustic wave through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...

s. It works by generating

acoustic wave Acoustic waves are types of waves that propagate through matter—such as gas, liquid, and/or solids—by causing the particles of the medium to compress and expand. These waves carry energy and are characterized by properties like acoustic pres ...

s in the fluid and analyzing the changes in the wave propagation caused by the fluid's rheological behavior. An acoustic rheometer uses a piezo-electric

crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...

to generate the acoustic waves, applying an oscillating extensional stress to the system. System response can be interpreted in terms of extensional rheology. :This interpretation is based on a link between shear rheology, extensional rheology and

acoustics Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician ...

. Relationship between these scientific disciplines was described in details by Litovitz and Davis in 1964. It is well known that properties of

viscoelastic In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both Viscosity, viscous and Elasticity (physics), elastic characteristics when undergoing deformation (engineering), deformation. Viscous mate ...

fluid are characterised in shear rheology with a

shear modulus In materials science, shear modulus or modulus of rigidity, denoted by ''G'', or sometimes ''S'' or ''μ'', is a measure of the Elasticity (physics), elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear s ...

''G'', which links

shear stress Shear stress (often denoted by , Greek alphabet, Greek: tau) is the component of stress (physics), stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross secti ...

''T_ij'' and

shear strain In mechanics, strain is defined as relative deformation, compared to a position configuration. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or the ...

''S_ij'' ::

There is similar linear relationship in extensional rheology between extensional stress ''P'', extensional strain ''S'' and extensional modulus ''K'': ::

Detail theoretical analysis indicates that propagation of

sound In physics, sound is a vibration that propagates as an acoustic wave through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the br ...

ultrasound Ultrasound is sound with frequency, frequencies greater than 20 Hertz, kilohertz. This frequency is the approximate upper audible hearing range, limit of human hearing in healthy young adults. The physical principles of acoustic waves apply ...

through a viscoelastic fluid depends on both shear modulus ''G'' and extensional modulus ''K''.Morse, P. M. and Ingard, K. U. "Theoretical Acoustics", Princeton University Press (1986)Dukhin, A.S. and Goetz, P.J
"Characterization of liquids, nano- and micro- particulates and porous bodies using Ultrasound"
Elsevier, 2017 It is convenient to introduce a combined longitudinal modulus ''M'': ::

M =M' + M''=K + \fracG

There are simple equations that express longitudinal modulus in terms of acoustic properties, sound speed ''V'' and

attenuation In physics, attenuation (in some contexts, extinction) is the gradual loss of flux intensity through a Transmission medium, medium. For instance, dark glasses attenuate sunlight, lead attenuates X-rays, and water and air attenuate both light and ...

α ::

M'= \rho \cdot V^2

M''= \frac

Acoustic rheometer measures sound speed and

for a set of

frequencies Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...

in the

megahertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose formal expression in terms of SI base ...

range. These measurable parameters can be converted into real and imaginary components of ''longitudinal modulus''. :Sound speed determines M', which is a measure of system elasticity. It can be converted into fluid

compressibility In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility or, if the temperature is held constant, the isothermal compressibility) is a measure of the instantaneous relative volume change of a f ...

. :Attenuation determines M", which is a measure of viscous properties, energy

dissipation In thermodynamics, dissipation is the result of an irreversible process that affects a thermodynamic system. In a dissipative process, energy ( internal, bulk flow kinetic, or system potential) transforms from an initial form to a final form, wh ...

. This parameter can be considered as extensional viscosity :In the case of Newtonian liquid attenuation yields information on the

volume viscosity Volume viscosity (also called bulk viscosity, or second viscosity or, dilatational viscosity) is a material property relevant for characterizing fluid flow. Common symbols are \zeta, \mu', \mu_\mathrm, \kappa or \xi. It has dimensions (mass / (leng ...

. Stokes' law (sound attenuation) provides relationship among

dynamic viscosity Viscosity is a measure of a fluid's rate-dependent resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for example, syrup h ...

and

of the Newtonian fluid. This type of rheometer works at much higher frequencies than others. It is suitable for studying effects with much shorter relaxation times than any other rheometer.

References

See also