A reply to the comments of Cichocki and Felderhof concerning my paper on the rheological behavior of concentrated colloidal dispersions [J. Chem. Phys. 99, 567 (1993)] is given. Differences exist between my scaling predictions as maximum packing is approached for the reduced dynamic viscosity and the dilute analysis of Cichocki and Felderhof

Brady, John F.

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Caltech Authors - Main

Response to “Comment on ‘The rheological behavior of concentrated 
colloidal dispersions’ ” [J. Chem. Phys. 101, 1757 (1994)] 
John F. Brady 
Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, 
California 91125 
(Received 15 March 1994; accepted 7 April 1994) 
Cichocki and Felderhof are correct that a factor of 2 was 
dropped (not from a failure to recognize something, how- 
ever, but from a simple mistake) and my variable p should 
be modified accordingly. A copying error was also made in 
the numerator of Eq. (57), although the plotted curves are 
correct; the correct numerator should read: 
1+2@+2@+$@+$@+$,@. Equation (56) is correct 
from which (57) and (58) can be obtained afresh by an in- 
terested reader. The overlooked factor of 2 does shift the 
curves to the right as Cichocki and Felderhof suggest. The 
agreement with experiment might now be considered less 
than “excellent,” although the raw experimental data were 
not known and therefore it is possible a constant factor is 
needed to scale time to properly compare. In any case, the 
adjective “excellent” was meant to imply the collapsed scal- 
ing when a*/Di( I$) is used, not the quantitative agreement. 
I was aware of these oversights, as any careful reader would 
discover, and have made note of them in my forthcoming 
paper’ on the long-time self-diffusivity in concentrated col- 
loidal dispersions. 
About these issues I agree with Cichocki and Felderhof. 
As to whether the scaled dynamic viscosity is a universal 
function of a2/Dfj(+), my theory is a scaling theory as 
maximum packing is approached and decidedly includes hy- 
drodynamic interactions. (Just because my final approximate 
equations after scaling resemble those in the absence of hy- 
drodynamic interactions, does not in any way imply that hy- 
drodynamics are unimportant or neglected in my develop- 
ment.) Conjectures made and analyses carried out without 
hydrodynamics, as Cichocki and Felderhof have done, may 
lead to a different conclusion. Any attempt to infer from a 
dilute or semidilute analysis the behavior near maximum 
packing is not something I would undertake lightly. The ex- 
perimental data, viewed in total, do seem to conform to this 
universal scaling, and remarkably well for a wide range of 
concentrations, not just near maximum packing. Deviations 
from this universal behavior for small volume fractions are 
to be expected, however, as should be clear from my paper 
where I note the additional, subdominant, contributions to 
the stress, and this may explain why the analysis of Cichocki 
and Felderhof suggests otherwise. 
I am pleased to see that Cichocki and Felderhof only 
question the functional form for the reduced dynamic viscos- 
ity. The much more important aspects of my paper, such as 
the scaling prediction that the viscosity diverges at close 
packing with an exponent of -2, the influence of interpar- 
title forces on rheology, etc., are uncommented upon, and 
therefore I infer accepted. I also wish to add that I am, and 
was, aware of their work on this subject, but as it deals with 
dilute systems, its relevance to concentrated dispersions is 
questionable. 
‘J. E Brady, J. Fluid Mech. (in press). 
1758 J. Chem. Phys. 101 (2), 15 July 1994 0021-9606/94/l 01(2)/l 758lli$6.00 0 1994 American Institute of Physics Downloaded 13 Jan 2006 to 131.215.225.172. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp


Response to "Comment on 'The rheological behavior of concentrated colloidal dispersions'"

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Response to "Comment on 'The rheological behavior of concentrated colloidal dispersions'"

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