Acoustic rheometer employes piezo-electric
crystalA crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is crystallography...
that can easily launch a successive
waveA wave is a disturbance that propagates through space and time, usually with transference of energy. A mechanical wave is a wave that propagates or travels through a medium due to the restoring forces it produces upon deformation. There also exist waves capable of traveling through a vacuum,...
of extensions and contractions into the
fluidA fluid is a substance that continually deforms under an applied shear stress. All gases are fluids, but not all liquids are fluids. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....
. It applies 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 the interdisciplinary science that deals with the study of sound, ultrasound and infrasound . A scientist who works in the field of acoustics is an acoustician. The application of acoustics in technology is called acoustical engineering...
. Relationship between these scietific disciplines was described in details by Litovitz and Davis in 1964 .
It is well known that properties of viscoelastic fluid are characterised in shear rheology with a
shear modulusIn materials science, shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is defined as the ratio of shear stress to the shear strain:...
G, which links
shear stressA shear stress, denoted , is defined as a stress which is applied parallel or tangential to a face of a material, as opposed to a normal stress which is applied perpendicularly.-General shear stress:...
Tij and
shear strainShear strain is a strain that acts parallel to the surface of a material that it is acting on. Normal strain, in contrast, acts perpendicular to the surface. There are two ways to interpret shear strain: the average shear strain and the engineering shear strain .Consider an infinitesimal...
Sij
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
soundSound is a travelling wave which is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.- Perception of sound...
or
ultrasoundUltrasound is cyclic sound pressure with a frequency greater than the upper limit of human hearing. Although this limit varies from person to person, it is approximately 20 kilohertz in healthy, young adults and thus, 20 kHz serves as a useful lower limit in describing ultrasound...
through a viscoelastic fluid depends on both shear modulus
G and extensional modulus
K, .
Acoustic rheometer employes piezo-electric
crystalA crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is crystallography...
that can easily launch a successive
waveA wave is a disturbance that propagates through space and time, usually with transference of energy. A mechanical wave is a wave that propagates or travels through a medium due to the restoring forces it produces upon deformation. There also exist waves capable of traveling through a vacuum,...
of extensions and contractions into the
fluidA fluid is a substance that continually deforms under an applied shear stress. All gases are fluids, but not all liquids are fluids. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....
. It applies 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 the interdisciplinary science that deals with the study of sound, ultrasound and infrasound . A scientist who works in the field of acoustics is an acoustician. The application of acoustics in technology is called acoustical engineering...
. Relationship between these scietific disciplines was described in details by Litovitz and Davis in 1964 .
It is well known that properties of viscoelastic fluid are characterised in shear rheology with a
shear modulusIn materials science, shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is defined as the ratio of shear stress to the shear strain:...
G, which links
shear stressA shear stress, denoted , is defined as a stress which is applied parallel or tangential to a face of a material, as opposed to a normal stress which is applied perpendicularly.-General shear stress:...
Tij and
shear strainShear strain is a strain that acts parallel to the surface of a material that it is acting on. Normal strain, in contrast, acts perpendicular to the surface. There are two ways to interpret shear strain: the average shear strain and the engineering shear strain .Consider an infinitesimal...
Sij
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
soundSound is a travelling wave which is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.- Perception of sound...
or
ultrasoundUltrasound is cyclic sound pressure with a frequency greater than the upper limit of human hearing. Although this limit varies from person to person, it is approximately 20 kilohertz in healthy, young adults and thus, 20 kHz serves as a useful lower limit in describing ultrasound...
through a viscoelastic fluid depends on both shear modulus
G and extensional modulus
K, . It is convenient to introduce a combined longitudinal modulus
M:
There are simple equations that express longitudinal modulus in terms of acoustic properties, sound speed
V and
attenuationIn physics, attenuation is the gradual loss in intensity of any kind of flux through a medium. For instance, sunlight is attenuated by dark glasses, and X-rays are attenuated by lead....
α
Acoustic rheometer measures sound speed and
attenuationIn physics, attenuation is the gradual loss in intensity of any kind of flux through a medium. For instance, sunlight is attenuated by dark glasses, and X-rays are attenuated by lead....
of
ultrasoundUltrasound is cyclic sound pressure with a frequency greater than the upper limit of human hearing. Although this limit varies from person to person, it is approximately 20 kilohertz in healthy, young adults and thus, 20 kHz serves as a useful lower limit in describing ultrasound...
for a set of frequencies in 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
Elasticity may refer to:*Elasticity , continuum mechanics of bodies which deform reversibly under stressVarious uses are derived from this physical sense of the term, especially in economics:...
. It can be converted into fluid compressibilityIn thermodynamics and fluid mechanics, compressibility is a measure of the relative volume change of a fluid or solid as a response to a pressure change.where V is volume and p is pressure...
.
- Attenuation determines M", which is a measure of viscous properties, energy dissipation
In physics, dissipation embodies the concept of a dynamical system where important mechanical modes, such as waves or oscillations, lose energy over time, typically due to the action of friction or turbulence. The lost energy is converted into heat, raising the temperature of the system...
. This parameter can be considered as extensional viscosityExtensional viscosity is a viscosity coefficient when applied stress is extensional stress. .Extensional viscosity can be measured using rheometers that apply extensional stress...
- In the case of Newtonian liquid attenuation yields information on the volume viscosity
Volume 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 ,....
. Stokes' law (sound attenuation)Stokes derived a law for the attenuation of sound in a Newtonian fluid.According to this law attenuation of sound α is proportional to the dynamic viscosity η, square of the sound frequency ω, and reciprocally proportional to the fluid density ρ and cubic power of sound speed VAttenuation is...
provides relatuionship between attenuationIn physics, attenuation is the gradual loss in intensity of any kind of flux through a medium. For instance, sunlight is attenuated by dark glasses, and X-rays are attenuated by lead....
, dynamic viscosity and volume viscosityVolume 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 ,....
of the Newtonian fluid.
This type of rheometers works at much higher frequencies than others. It is suitable for studying effects with much shorter
relaxation timeRelaxation time is a general concept in physics for the characteristic time in which a system changes to an equilibrium condition from a non-equilibrium condition...
s than any other rheometer.