Electroacoustic phenomena
Encyclopedia
Electroacoustic phenomena arise when ultrasound
propagates through a fluid
containing ions. The associated particle motion generates electric signals because ions have electric charge
. This coupling between ultrasound and electric field
is called electroacoustic phenomena. Fluid might be a simple Newtonian liquid, or complex heterogeneous dispersion
, emulsion
or even a porous body. There are several different electroacoustic effects depending on the nature of the fluid.
. This difference creates an alternating electric potential between various points in sound wave. This effect was extensively used in 1950’s and 1960’s for characterizing ion solvation. These works are mostly associated with names of Zana and Yaeger, who published a review of their studies in 1982.
can be regarded as behaving like a parallel plate capacitor with a compressible dielectric filling. When sound waves induce a local pressure variation, the spacing of the plates varies at the frequency of the excitation, generating an AC displacement current normal to the interface. For practical reasons this is most readily observed at a conducting surface. It is therefore possible to use an electrode immersed in a conducting electrolyte as a microphone, or indeed as a loudspeaker when the effect is applied in reverse.
Colloid Vibration Potential/Current was first reported by Hermans and then independently by Rutgers in 1938. It is widely used for characterizing the ζ-potential of various dispersions and emulsions. The effect, theory, experimental verification and multiple applications are discussed in the book by Dukhin and Goetz.
μd.
where
Dynamic electrophoretic mobility is similar to electrophoretic mobility that appears in electrophoresis
theory. They are identical at low frequencies and/or for sufficiently small particles.
There are several theories of the dynamic electrophoretic mobility. Their overview is given in the Ref.5. Two of them are the most important.
The first one corresponds to Smoluchowski limit. It yields following simple expression for CVI for sufficiently small particles with negligible CVI frequency dependence:
where:
This remarkably simple equation has same wide range of applicability as Smoluchowski equation for electrophoresis
. It is independent on shape of the particles, their concentration.
Validity of this equation is restricted with the following two requirements.
First of all it is valid only for thin Double Layer
, when Debye length
is much smaller than particles radius a:
Secondly, it neglect contribution of the surface conductivity
. This assumes small Dukhin number
:
Restriction of the thin Double Layer
limits applicability of this Smoluchwski type theory only to aqueous systems with sufficiently large particles and not very low ionic strength. This theory does not work well for nano-colloids, including proteins and polymers at low ionic strength. It is not valid for low- or non-polar fluids.
There is another theory that is applicable for other extreme case of thick Double Layer
, when
This theory takes into consideration overpap of Double Layer that inevitably occur for concentrated systems with thick Double Layer. This allows introduction of so-called "quasi-homogeneous" approach, when overlapped diffuse layers of particles cover complete inter particle space. Theory becomes much simplified in this extreme case, as shown by Shilov and oth. . Their derivation predict that surface charge density σ is better parameter than ζ-potential for characterizing electroscoustic phenomena in such systems. Expression for CVI simplified for small particles follows:
Ultrasound
Ultrasound is cyclic sound pressure with a frequency greater than the upper limit of human hearing. Ultrasound is thus not separated from "normal" sound based on differences in physical properties, only the fact that humans cannot hear it. Although this limit varies from person to person, it is...
propagates through a fluid
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....
containing ions. The associated particle motion generates electric signals because ions have electric charge
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...
. This coupling between ultrasound and electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
is called electroacoustic phenomena. Fluid might be a simple Newtonian liquid, or complex heterogeneous dispersion
Dispersion (chemistry)
A dispersion is a system in which particles are dispersed in a continuous phase of a different composition . See also emulsion. A dispersion is classified in a number of different ways, including how large the particles are in relation to the particles of the continuous phase, whether or not...
, emulsion
Emulsion
An emulsion is a mixture of two or more liquids that are normally immiscible . Emulsions are part of a more general class of two-phase systems of matter called colloids. Although the terms colloid and emulsion are sometimes used interchangeably, emulsion is used when both the dispersed and the...
or even a porous body. There are several different electroacoustic effects depending on the nature of the fluid.
- Ion Vibration Current/PotentialIon Vibration Current/PotentialIon Vibration Current/Potential is an electric signal that arises when an acoustic wave propagates through a homogeneous fluid.Historically, the IVI is the first known electroacoustic phenomena. It was predicted by Debye in 1933...
(IVI), an electric signal that arises when an acoustic waveAcoustic waveAcoustic waves are a type of longitudinal waves that propagate by means of adiabatic compression and decompression. Longitudinal waves are waves that have the same direction of vibration as their direction of travel. Important quantities for describing acoustic waves are sound pressure, particle...
propagates through a homogeneousHomogeneous (chemistry)A substance that is uniform in composition is a definition of homogeneous. This is in contrast to a substance that is heterogeneous.The definition of homogeneous strongly depends on the context used. In Chemistry, a homogeneous suspension of material means that when dividing the volume in half, the...
fluid. - Streaming Vibration Current/PotentialStreaming Vibration Current/PotentialStreaming vibration current/potential is an electric signal that arises when an acoustic wave propagates through a porous body in which the pores are filled with fluid....
(SVI), an electric signal that arises when an acoustic wave propagates through a porous body in which the pores are filled with fluid. - Colloid Vibration CurrentColloid vibration currentColloid vibration current is an electroacoustic phenomenon that arises when ultrasound propagates through a fluid that contains ions and either solid particles or emulsion droplets ....
/Potential (CVI), an electric signal that arises when ultrasound propagates through a heterogeneous fluid, such as a dispersionDispersion (chemistry)A dispersion is a system in which particles are dispersed in a continuous phase of a different composition . See also emulsion. A dispersion is classified in a number of different ways, including how large the particles are in relation to the particles of the continuous phase, whether or not...
or emulsionEmulsionAn emulsion is a mixture of two or more liquids that are normally immiscible . Emulsions are part of a more general class of two-phase systems of matter called colloids. Although the terms colloid and emulsion are sometimes used interchangeably, emulsion is used when both the dispersed and the...
. - Electric Sonic AmplitudeElectric sonic amplitudeElectric sonic amplitude is an electroacoustic phenomenon that is the reverse to colloid vibration current. It occurs in colloids, emulsions and other heterogeneous fluids under the influence of an oscillating electric field...
(ESA), the inverse of CVI effect, in which an acoustic field arises when an electric fieldElectric fieldIn physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
propagates through a heterogeneous fluids.
Ion Vibration Current
Historically, the IVI is the first known electroacoustic effect. It was predicted by Debye in 1933. He pointed out that the difference in the effective mass or friction coefficient between anion and cation would result in different displacement amplitudes in a longitudinal waveLongitudinal wave
Longitudinal waves, as known as "l-waves", are waves that have the same direction of vibration as their direction of travel, which means that the movement of the medium is in the same direction as or the opposite direction to the motion of the wave. Mechanical longitudinal waves have been also...
. This difference creates an alternating electric potential between various points in sound wave. This effect was extensively used in 1950’s and 1960’s for characterizing ion solvation. These works are mostly associated with names of Zana and Yaeger, who published a review of their studies in 1982.
Streaming Vibration Current
Streaming Vibration Current was experimentally observed in 1948 by Williams . A theoretical model was developed some 30 years later by Dukhin and others. This effect opens another possibility for characterizing the electric properties of the surfaces in porous bodies. A similar effect can be observed at a non-porous surface, when sound is bounced off at an oblique angle. The incident and reflected waves superimpose to cause oscillatory fluid motion in the plane of the interface, thereby generating an AC streaming current at the frequency of the sound waves.Double Layer Compression
The electrical double layerDouble layer
Double layer may refer to:* Double layer , a structure in a plasma and consists of two parallel layers with opposite electrical charge* Double layer , a structure that appears on the surface of an object when it is placed into a liquid...
can be regarded as behaving like a parallel plate capacitor with a compressible dielectric filling. When sound waves induce a local pressure variation, the spacing of the plates varies at the frequency of the excitation, generating an AC displacement current normal to the interface. For practical reasons this is most readily observed at a conducting surface. It is therefore possible to use an electrode immersed in a conducting electrolyte as a microphone, or indeed as a loudspeaker when the effect is applied in reverse.
Colloid Vibration Potential / Current
Colloid vibration potential measures the AC potential difference generated between two identical relaxed electrodes, placed in the dispersion, if the latter is subjected to an ultrasonic field. When a sound wave travels through a colloidal suspension of particles whose density differs from that of the surrounding medium, inertial forces induced by the vibration of the suspension give rise to a motion of the charged particles relative to the liquid, causing an alternating electromotive force. The manifestations of this electromotive force may be measured, depending on the relation between the impedance of the suspension and that of the measuring instrument, either as colloid vibration potential or as colloid vibration current.Colloid Vibration Potential/Current was first reported by Hermans and then independently by Rutgers in 1938. It is widely used for characterizing the ζ-potential of various dispersions and emulsions. The effect, theory, experimental verification and multiple applications are discussed in the book by Dukhin and Goetz.
ElectricSonic Amplitude
Electric Sonic Amplitude was experimentally discovered by Cannon with co-authors in early 1980’s. It is also widely used for characterizing ζ-potential in dispersions and emulsions. There is review of this effect theory, experimental verification and multiple applications published by Hunter.Theory of CVI and ESA
With regard to the theory of CVI and ESA, there was an important observation made by O’Brien, who linked these measured parameters with dynamic electrophoretic mobilityDynamic electrophoretic mobility
Dynamic electrophoretic mobility is a parameter that determines intensity of electroacoustic phenomena, such as Colloid Vibration Current and Electric Sonic Amplitude in colloids. It is similar to electrophoretic mobility, but at high frequency, on a scale of megahertz...
μd.
where
- A is calibration constant, depending on frequency, but not particles properties;
- ρp is particle density,
- ρm density of the fluid,
- φ is volume fraction of dispersed phase,
Dynamic electrophoretic mobility is similar to electrophoretic mobility that appears in electrophoresis
Electrophoresis
Electrophoresis, also called cataphoresis, is the motion of dispersed particles relative to a fluid under the influence of a spatially uniform electric field. This electrokinetic phenomenon was observed for the first time in 1807 by Reuss , who noticed that the application of a constant electric...
theory. They are identical at low frequencies and/or for sufficiently small particles.
There are several theories of the dynamic electrophoretic mobility. Their overview is given in the Ref.5. Two of them are the most important.
The first one corresponds to Smoluchowski limit. It yields following simple expression for CVI for sufficiently small particles with negligible CVI frequency dependence:
where:
- ε0 is vacuum dielectric permittivity,
- εm is fluid dielectric permittivity,
- ζ is electrokinetic potential
- η is dynamic viscosity of the fluid,
- Ks is conductivity of the system,
- Km is conductivity of the fluid,
- ρs is density of the system.
This remarkably simple equation has same wide range of applicability as Smoluchowski equation for electrophoresis
Electrophoresis
Electrophoresis, also called cataphoresis, is the motion of dispersed particles relative to a fluid under the influence of a spatially uniform electric field. This electrokinetic phenomenon was observed for the first time in 1807 by Reuss , who noticed that the application of a constant electric...
. It is independent on shape of the particles, their concentration.
Validity of this equation is restricted with the following two requirements.
First of all it is valid only for thin Double Layer
Double layer
Double layer may refer to:* Double layer , a structure in a plasma and consists of two parallel layers with opposite electrical charge* Double layer , a structure that appears on the surface of an object when it is placed into a liquid...
, when Debye length
Debye length
In plasma physics, the Debye length , named after the Dutch physicist and physical chemist Peter Debye, is the scale over which mobile charge carriers screen out electric fields in plasmas and other conductors. In other words, the Debye length is the distance over which significant charge...
is much smaller than particles radius a:
Secondly, it neglect contribution of the surface conductivity
Surface conductivity
Surface conductivity is an additional conductivity of an electrolyte in the vicinity of charged surfaces. Close to charged surfaces a layer of counter ions of opposite polarity exists which is attracted by the surface charges. This layer of higher ionic concentration is a part of the interfacial ...
. This assumes small Dukhin number
Dukhin number
Dukhin number is a dimensionless quantity that characterizes the contribution of the surface conductivity to various electrokinetic and electroacoustic effects, as well as to electrical conductivity and permittivity of fluid heterogeneous systems....
:
Restriction of the thin Double Layer
Double layer
Double layer may refer to:* Double layer , a structure in a plasma and consists of two parallel layers with opposite electrical charge* Double layer , a structure that appears on the surface of an object when it is placed into a liquid...
limits applicability of this Smoluchwski type theory only to aqueous systems with sufficiently large particles and not very low ionic strength. This theory does not work well for nano-colloids, including proteins and polymers at low ionic strength. It is not valid for low- or non-polar fluids.
There is another theory that is applicable for other extreme case of thick Double Layer
Double layer
Double layer may refer to:* Double layer , a structure in a plasma and consists of two parallel layers with opposite electrical charge* Double layer , a structure that appears on the surface of an object when it is placed into a liquid...
, when
This theory takes into consideration overpap of Double Layer that inevitably occur for concentrated systems with thick Double Layer. This allows introduction of so-called "quasi-homogeneous" approach, when overlapped diffuse layers of particles cover complete inter particle space. Theory becomes much simplified in this extreme case, as shown by Shilov and oth. . Their derivation predict that surface charge density σ is better parameter than ζ-potential for characterizing electroscoustic phenomena in such systems. Expression for CVI simplified for small particles follows: