Divergence of the Long Wavelength Collective Diffusion Coefficient in Quasi-one and Quasi-two Dimensional Colloid Suspensions

TL;DR

This study experimentally investigates the divergence of the collective diffusion coefficient at long wavelengths in quasi-one and two-dimensional colloid suspensions, revealing a q-dependent divergence linked to boundary conditions and hydrodynamic interactions.

Contribution

It provides experimental evidence of the divergence of the hydrodynamic function H(q) in quasi-1D and 2D colloid systems and links this behavior to boundary conditions and hydrodynamic interactions.

Findings

H(q) diverges as q approaches 0 with a power-law form q^-gamma

D_e(q) also diverges as q approaches 0, despite S(q) remaining finite

Boundary conditions, such as partial slip, influence the long wavelength diffusion behavior

Abstract

We report the results of experimental studies of the short time-long wavelength behavior of collective particle displacements in quasi-one-dimensional and quasi-two-dimensional colloid suspensions. Our results are represented by the behavior of the hydrodynamic function H(q) that relates the effective collective diffusion coefficient, D_e(q) with the static structure factor S(q) and the self-diffusion coefficient of isolated particles D_0: H(q)=D_e(q)S(q)/D_0. We find an apparent divergence of H(q) as q->0 with the form H(q) proportional to q^-gamma, 1.7<gamma<1.9, for both q1D and q2D colloid suspensions. Given that S(q) does not diverge as q=>0 we infer that D_e(q) does. We provide evidence that this divergence arises from the interplay of boundary conditions on the flow of the carrier liquid and many-body hydrodynamic interactions between colloid particles that affect the long wavelength behavior of the particle collective diffusion coefficient in the suspension. We speculate that in the q1D and q2D systems studied the divergence of H(q) might be associated with a q-dependent partial slip boundary condition, specifically an effective slip length that increases with decreasing q. We also verify, using data from the work of Lin, Rice and Weitz (J. Chem. Phys. 99, 9585 (1993)), the prediction by Bleibel et al (arXiv:1305.3715), that D_e(q) for a monolayer of colloid particles constrained to lie in the interface between two fluids diverges as 1/q as q->0. The verification of that prediction, which is based on an analysis that allows two-dimensional colloid motion embedded in three-dimensional suspending fluid motion, supports the contention that the boundary conditions that define a q2D system play a very important role in determining the long wavelength behavior of the collective diffusion coefficient.