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 ''p ...

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 ...

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 (res ...

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 shear ...

. 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 In continuum mechanics, stress is a physical quantity. It is a quantity that describes the magnitude of forces that cause deformation. Stress is defined as ''force per unit area''. When an object is pulled apart by a force it will cause elonga ...

to the system. System response can be interpreted in terms of

extensional 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 appl ...

. :This interpretation is based on a link between shear 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 viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly wi ...

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

''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 the ot ...

''T_ij'' and

shear strain In physics, deformation is the continuum mechanics transformation of a body from a ''reference'' configuration to a ''current'' configuration. A configuration is a set containing the positions of all particles of the body. A deformation can ...

''S_ij'' ::

There is similar linear relationship in

between

''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 ...

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

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 The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as wel ...

''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 att ...

α ::

M'= \rho \cdot V^2

M''= \frac

Acoustic rheometer measures

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 eq ...

in the

megahertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or Cycle per second, cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, me ...

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 takes place in homogeneous thermodynamic systems. In a dissipative process, energy (internal, bulk flow kinetic, or system potential) transforms from an initial form to a ...

. This parameter can be considered as

extensional viscosity Extensional viscosity (also known as elongational viscosity) is a viscosity coefficient when applied stress is extensional stress. It is often used for characterizing polymer solutions. Extensional viscosity can be measured using rheometers tha ...

:In the case of Newtonian liquid 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) Stokes's law of sound attenuation is a formula for the attenuation of sound in a Newtonian fluid, such as water or air, due to the fluid's viscosity. It states that the amplitude of a plane wave decreases exponentially with distance traveled, at a ...

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 inter ...

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 time In the physical sciences, relaxation usually means the return of a perturbed system into equilibrium. Each relaxation process can be categorized by a relaxation time τ. The simplest theoretical description of relaxation as function of time ' ...

s than any other rheometer.

References

See also