# Microrheology

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Microrheology

Microrheology[1] 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

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).[2]

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 $G(\omega)=G'(\omega)+i G''(\omega)\,$ with G′(ω) dissipative part and G″(ω) the conservative part and ω=2πf the pulsation. The GSER is as follow:

$\tilde{G}(s)=\frac{k_{\mathrm{B}}T}{\pi a s \langle\Delta \tilde{r}^{2}(s)\rangle}$

with

$\tilde{G}(s)$: Laplace transform of G
kB: Boltzmann constant
T: temperature in kelvins
s: the Laplace frequency
a: the radius of the tracer
$\langle\Delta \tilde{r}^{2}(s)\rangle$: the Laplace transform of the mean square displacement

## Active microrheology

Active microrheology may use a magnetic field [3][4][5][6][7] or optical tweezers[8] to apply a force on the tracer and then find the stress/strain relation.

## References

1. ^ Mason Weitz (1995). Physical Review Letters 74: 7.
2. ^ European Physical Journal E 8: 431–436. 2002. Bibcode 2002EPJE....8..431B. doi:10.1140/epje/i2002-10026-0.
3. ^ A.R. Bausch et al. (1999). "Measurement of Local Viscoelasticity and Forces in Living Cells by Magnetic Tweezers". Biophysical Journal 76: 573. Bibcode 1999BpJ....76..573B. doi:10.1016/S0006-3495(99)77225-5. PMID 9876170.
4. ^ K.S. Zaner and P.A. Valberg (1989). "Viscoelasticity of F-actin measured with magnetic microparticles". Journal of Cell Biology 109: 2233. doi:10.1083/jcb.109.5.2233. PMID 2808527.
5. ^ F.Ziemann, J. Radler, and E. Sackmann (1994). "Local measurements of viscoelastic moduli of entangled actin networks using an oscillating magnetic bead micro-rheometer". Biophysical Journal 66: 2210. Bibcode 1994BpJ....66.2210Z. doi:10.1016/S0006-3495(94)81017-3. PMID 8075354.
6. ^ F.G. Schmidt, F. Ziemann, and E. Sackmann (1996). European Biophysics Journal 24: 348.
7. ^ F. Amblard et al. (1996). "Subdiffusion and Anomalous Local Viscoelasticity in Actin Networks". Physical Review Letters 77: 4470. Bibcode 1996PhRvL..77.4470A. doi:10.1103/PhysRevLett.77.4470. PMID 10062546.
8. ^ E. Helfer et al. (2000). "Microrheology of Biopolymer-Membrane Complexes". Physical Review Letters 85: 457. Bibcode 2000PhRvL..85..457H. doi:10.1103/PhysRevLett.85.457. PMID 10991307.

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### Look at other dictionaries:

• microrheology — noun a) A technique capable of measuring microviscosity b) The branch of rheology that deals with emulsions and heterogeneous mixtures …   Wiktionary

• David A. Weitz — Born October 3, 1951(1951 10 03) Ottawa, Ontario, Canada Residence U.S …   Wikipedia

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