Microrheology
Encyclopedia
Microrheology is a technique to measure the rheological properties
of a medium, such as microviscosity
, via the measurement of the trajectory of a flow tracer
(a micrometre-size particle). It is a new way of doing rheology
, traditionally done using a rheometer
. The size of the tracer is around a micrometre. There are two types of microrheology: passive microrheology and active microrheology. Passive microrheology uses inherent thermal energy
to move the tracers, whereas active microrheology uses externally applied forces, such as from a magnetic field
or an optical tweezer, to do so. Microrheology can be further differentiated into 1- and 2-particle methods
.
(DWS). From the mean square displacement with respect to time (noted MSD or <Δr2> ), one can calculate the visco-elastic moduli G′(ω) and G″(ω) using the generalized Stokes–Einstein relation (GSER). Here is a view of the trajectory of a particle of micrometer size.
Observing the MSD for a wide range of time scales gives information on the microstructure of the medium where are diffusing the tracers. If the tracers are having a free diffusion, on can deduce that the medium is purely viscous. If the tracers are having a sub-diffusive mean trajectory, it indicates that the medium presents some viscoelastic properties. For example, in a polymer network, the tracer may be trapped. The excursion δ of the tracer is related to the elastic modulus G′ with the relation G′ = kBT/(6πaδ2).
Microrheology is another way to do linear rheology. Since the force involved is very weak (order of 10−15 N), microrheology is guaranteed to be in the so-called linear region of the strain/stress relationship. It is also able to measure very small volumes (biological cell).
Given the complex viscoelastic modulus
with G′(ω) dissipative part and G″(ω) the conservative part and ω=2πf the pulsation. The GSER is as follow:
with
: Laplace transform of G
A related method of passive microrheology involves the tracking positions of a particle at a high frequency, often with a quadrant photodiode. From the position,
, the power spectrum, 
can be found, and then related to the real and imaginary parts of the response function, 
. The response function leads directly to a calculation of the complex shear modulus, 
via:
or optical tweezers to apply a force on the tracer and then find the stress/strain relation.
Rheology
Rheology is the study of the flow of matter, primarily in the liquid 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 applied force....
of a medium, such as microviscosity
Microviscosity
Microviscosity, also known as microscopic viscosity, is the friction experienced by a single particle undergoing diffusion because of its interaction with its environment at the micrometer length scale. The concept of microviscosity is intimately related to the concept of single particle diffusion...
, via the measurement of the trajectory of a flow tracer
Flow tracer
thumb|right|300px|On May 2, [[2001]], the Moderate-resolution Imaging Spectroradiometer obtained this spectacular image of the [[Atlantic Ocean]]'s [[Gulf Stream]]. The [[false color]]s in the image represent "[[brightness temperature]]" observed at the top of the [[atmosphere]]...
(a micrometre-size particle). It is a new way of doing rheology
Rheology
Rheology is the study of the flow of matter, primarily in the liquid 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 applied force....
, traditionally done using a rheometer
Rheometer
A rheometer is a laboratory device used to measure the way in which a liquid, suspension or slurry flows in response to applied forces. It is used for those fluids which cannot be defined by a single value of viscosity and therefore require more parameters to be set and measured than is the case...
. The size of the tracer is around a micrometre. There are two types of microrheology: passive microrheology and active microrheology. Passive microrheology uses inherent thermal energy
Thermal energy
Thermal energy is the part of the total internal energy of a thermodynamic system or sample of matter that results in the system's temperature....
to move the tracers, whereas active microrheology uses externally applied forces, such as from a magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
or an optical tweezer, to do so. Microrheology can be further differentiated into 1- and 2-particle methods
.
Passive microrheology
Passive microrheology uses the thermal energy (kT) to move the tracers. The trajectories of the tracers are measured optically either by microscopy or by diffusing-wave spectroscopyDiffusing-wave spectroscopy
Diffusing-wave spectroscopy is an optical technique derived from dynamic light scattering that studies the dynamics of scattered light in the limit of strong multiple scattering. It has been widely used in the past to study colloidal suspensions, emulsions, foams, gels, biological media and other...
(DWS). From the mean square displacement with respect to time (noted MSD or <Δr2> ), one can calculate the visco-elastic moduli G′(ω) and G″(ω) using the generalized Stokes–Einstein relation (GSER). Here is a view of the trajectory of a particle of micrometer size.
Observing the MSD for a wide range of time scales gives information on the microstructure of the medium where are diffusing the tracers. If the tracers are having a free diffusion, on can deduce that the medium is purely viscous. If the tracers are having a sub-diffusive mean trajectory, it indicates that the medium presents some viscoelastic properties. For example, in a polymer network, the tracer may be trapped. The excursion δ of the tracer is related to the elastic modulus G′ with the relation G′ = kBT/(6πaδ2).
Microrheology is another way to do linear rheology. Since the force involved is very weak (order of 10−15 N), microrheology is guaranteed to be in the so-called linear region of the strain/stress relationship. It is also able to measure very small volumes (biological cell).
Given the complex viscoelastic modulus
with G′(ω) dissipative part and G″(ω) the conservative part and ω=2πf the pulsation. The GSER is as follow:with
: Laplace transform of G
- kB: Boltzmann constant
- T: temperature in kelvins
- s: the Laplace frequency
- a: the radius of the tracer
: the Laplace transform of the mean square displacement
A related method of passive microrheology involves the tracking positions of a particle at a high frequency, often with a quadrant photodiode. From the position,
, the power spectrum, can be found, and then related to the real and imaginary parts of the response function, . The response function leads directly to a calculation of the complex shear modulus, via:Active microrheology
Active microrheology may use a magnetic fieldor optical tweezers to apply a force on the tracer and then find the stress/strain relation.