An acoustic rheometer employs a

piezo-electric Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied mechanical stress. The word '' ...

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, macr ...

that can easily launch a successive

wave In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (r ...

of extensions and contractions into the

fluid In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shea ...

. It applies an

oscillating Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...

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 Rheology (; ) is the study of the flow of matter, primarily in a fluid (liquid or gas) state, but also as "soft solids" or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an applie ...

, extensional rheology and acoustics. 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 viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linear ...

fluid are characterised in

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 elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain: :G \ \stack ...

''G'', which links

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

''T_ij'' and shear strain ''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 ...

ultrasound Ultrasound is sound waves with frequencies higher than the upper audible limit of human hearing. Ultrasound is not different from "normal" (audible) sound in its physical properties, except that humans cannot hear it. This limit varies fr ...

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 medium. For instance, dark glasses attenuate sunlight, lead attenuates X-rays, and water and air attenuate both light and sound at variable ...

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. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from '' angular frequency''. Frequency is measured in hertz (Hz) which is e ...

in the megahertz 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 ...

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

dissipation In thermodynamics, dissipation is the result of an irreversible process that takes place in homogeneous thermodynamic systems. In a dissipative process, energy (internal, bulk flow kinetic, or system potential) transforms from an initial form ...

. This parameter can be considered as extensional viscosity :In the case of

Newtonian liquid A Newtonian fluid is a fluid in which the viscous stresses arising from its flow are at every point linearly correlated to the local strain rate — the rate of change of its deformation over time. Stresses are proportional to the rate of chang ...

attenuation yields information on the

volume viscosity Volume viscosity (also called bulk 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 / (length × time)), and the ...

. Stokes' law (sound attenuation) provides relationship among

dynamic viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...

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