**4. Conclusions**

162 Hydrodynamics – Advanced Topics

<sup>w</sup> **Particle tracking**

**10<sup>3</sup> 10<sup>4</sup> 10<sup>5</sup> 10<sup>6</sup>**

**M <sup>w</sup>**

0.2 0.4 0.6 0.8 1.0 1.2

)

Γ(mg/m <sup>2</sup>

Fig. 11. Surface shear viscosity of a monolayer of poly(t-butyl acrylate) (molecular weight 4.6 kDa) measured by particle tracking. Different microparticles where used: poly(styrene) of 1.6 and 5.7 µm (stabilized by sulfonate groups); poly(methylmethacrylate) stabilized by Coulombic repulsions (PMMA1), or by steric repulsions (PMMA2); Silica particles stabilized by Coulombic repulsions. Empty symbols: the viscosities were calculated using Fischer

(2003). This discrepancy between micro- and macrorheology in the study of monolayers seems to be a rather general situation (Schmidt et al., 2000; Khair & Brady, 2005; Oppong & de Bruyn, 2010; Lee et al., 2010) and no clear theoretical answer has been found so far.

PtBAc monolayer (4.6kDa)

<sup>η</sup>s ~M 0.21 w

Fig. 10. Surface shear viscosity for monolayers of poly(t-butyl acrylate) as a function of the molecular weight and for a surface pressure of 16 mN·m-1. The lower curve corresponds to data obtained from particle tracking. The upper curve was obtained from conventional

**Oscillating rheometer**

<sup>η</sup>s ~M 1.05 w

1.4 Particle/diamater (μm) *Fischer method.* PS(1.6) PMMA (2) PMMA (1) SiO2 (1) PS (5.7) *Weitz method* PS(1.6)

<sup>η</sup>s ~M 1.95 w

η∼Γ<sup>2</sup>

<sup>η</sup>s ~M 3.3

**10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 10<sup>0</sup> 10<sup>1</sup> 10<sup>2</sup>**

0.2

theory. Full symbols: calculated by the GSE equation.

0.4

109

·η, N·s/m

0.6

0.8

1.0

1.2

η**s (N s m-1**

oscillatory rheometers.

**)**

The set of microrheological techniques offer the possibility of studying the rheology of very small samples, of systems which are heterogeneous, and facilitate to measure the shear modulus over a broad frequency range. Particle tracking techniques are especially well suited for the study of the diffusion of microparticles either in the bulk or at fluid interfaces. Different types of mean squared displacements, MSD, (one-particle, two-particle) allow one to detect spatial heterogeneities in the samples. Even though good agreement has been found between micro- and macrorheology (at least when two-particle MSD is used) in bulk systems, the situation is still not clear for the case of fluid interfaces, where the shear surface microviscosity is much smaller than the one measured with conventional surface rheometers.
