Tracer-diffusion in colloidal mixtures: A mode-coupling scheme with hydrodynamic interactions

1998 ◽  
Vol 108 (22) ◽  
pp. 9566-9576 ◽  
Author(s):  
Gerhard Nägele ◽  
Jan K. G. Dhont
Keyword(s):  
Mode Coupling ◽  
Tracer Diffusion ◽  
Hydrodynamic Interactions ◽  
Coupling Scheme

MODE-COUPLING THEORY, DYNAMIC SCALING, AND TWO-DIMENSIONAL TURBULENCE

1995 ◽  
Vol 09 (09) ◽  
pp. 1081-1097 ◽  
Author(s):  
MALAY K. NANDY ◽  
JAYANTA K. BHATTACHARJEE
Keyword(s):  
Perturbation Theory ◽  
Mode Coupling ◽  
Direct Interaction ◽  
External Parameter ◽  
Coupling Scheme ◽  
Dynamic Scaling ◽  
Logarithmic Correction ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Self Consistent

A self-consistent mode-coupling scheme, along with dynamic scaling ideas, is used to obtain a renormalized perturbation theory in the Eulerian framework from Wyld’s perturbation theory of the forced Navier-Stokes equation. For the force-correlation behaving as k−(d−4+y), the Kolmogorov and Kraichnan-Batchelor scaling spectra of two-dimensional turbulence for the inverse energy cascade, [Formula: see text] and the direct entropy cascade, [Formula: see text], are obtained for y=4 and y=6 respectively, including the logarithmic correction for the latter. Unlike the usual Eulerian formulations (e.g. the direct-interaction approximation), the theory is finite in the energy regime, while it becomes marginal in the enstrophy regime, leading to the logarithmic correction. Calculations yield C=6.447 and C′=1.923 at one-loop order, which are in exact agreement with those of field-theoretic renormalization group calculations [P. Olla, Phys. Rev. Lett. 67, 2465 (1991)]. However, a self-consistent treatment of the logarithmic scalings in E(k) and the inverse response-time yields a different value: C′=2.201. The theory is free of any external parameter; the choice of y(=4 or 6) is dictated by the condition of conserved transfer of energy or enstrophy.

scholarly journals Tracer diffusion in colloidal suspensions under dilute and crowded conditions with hydrodynamic interactions

2012 ◽  
Vol 137 (1) ◽  
pp. 014503 ◽  
Author(s):  
A. Tomilov ◽  
A. Videcoq ◽  
T. Chartier ◽  
T. Ala-Nissilä ◽  
I. Vattulainen
Keyword(s):  
Colloidal Suspensions ◽  
Tracer Diffusion ◽  
Hydrodynamic Interactions
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