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.
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 spectroscopy (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 garanty 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:
- : 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
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