Chemistry Reference
In-Depth Information
3
2
1
0
0
2
4
6
8
10
12
14
Time lag
τ (
s)
Figure 2 Ensemble-averaged MSD of 0.5
m
m particles as a function of time
t
in
Newtonian liquids:
'
, 60 wt.% aqueous glycerol solution;
&
, 88 wt.%
aqueous glycerol solution. The lines are theoretical values calculated from
Equation (2) using the known viscosities of glycerol solutions (0.0107 and
0.147 Pa s)
plots of MSD versus
t
calculated from the Stokes-Einstein equation (2) and the
known values of the viscosity of the solutions.
23
This excellent agreement with
the theory demonstrates the validity of the particle tracking technique for
determining the shear viscosity under these ideal conditions.
For the case of non-Newtonian media, it is convenient also to plot the MSD
as a function of time on a double logarithmic plot. The fitted slope
a
, which
corresponds to the exponent in the relationship
o
Dr
2
(
t
)>
B
t
a
,
(5)
lies somewhere between the purely viscous limit (
a
¼
1) and the elastic limit
(
a
¼
0). A value of
a
o
1 indicates that the motion is sub-diffusive, or hindered,
whereas a slope of
a
1 indicates that the motion can be regarded as entirely
diffusive (as in the glycerol solutions). Even for a purely Newtonian liquid, the
fitted value of
a
does not always work out to be exactly unity because of various
factors: image resolution errors (spatial and temporal), statistical fluctuations
and small uncorrected drifts. We make the practical assumption here that a
system that can be fitted with a value of
a
4 0.9 is effectively viscous on the
timescale of the experimental observation.
Before moving on to consider the microrheology of the emulsion systems, we
present data on their bulk rheological properties. Figure 3 shows apparent
viscosity as a function of shear rate for the caseinate-stabilized emulsions
(30 vol.% oil, 1.4 wt.% protein) with different xanthan concentrations in the
aqueous phase (0.03-0.07 wt.%). In agreement with previous work on emul-
sions of this type,
15,24
B
the curves show pronounced shear-thinning behaviour
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