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We report the results of experimental studies of the short time-longwavelength behavior of collective particle displacements inquasi-one-dimensional and quasi-two-dimensional colloid suspensions. Ourresults are represented by the behavior of the hydrodynamic function H(q) thatrelates the effective collective diffusion coefficient, D_e(q) with the staticstructure factor S(q) and the self-diffusion coefficient of isolated particlesD_0: H(q)=D_e(q)S(q)/D_0. We find an apparent divergence of H(q) as q->0 withthe form H(q) proportional to q^-gamma, 1.7<gamma<1.9, for both q1D and q2Dcolloid suspensions. Given that S(q) does not diverge as q=>0 we infer thatD_e(q) does. We provide evidence that this divergence arises from the interplayof boundary conditions on the flow of the carrier liquid and many-bodyhydrodynamic interactions between colloid particles that affect the longwavelength behavior of the particle collective diffusion coefficient in thesuspension. We speculate that in the q1D and q2D systems studied the divergenceof H(q) might be associated with a q-dependent partial slip boundary condition,specifically an effective slip length that increases with decreasing q. We alsoverify, 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 interfacebetween two fluids diverges as 1/q as q->0. The verification of thatprediction, which is based on an analysis that allows two-dimensional colloidmotion embedded in three-dimensional suspending fluid motion, supports thecontention that the boundary conditions that define a q2D system play a veryimportant role in determining the long wavelength behavior of the collectivediffusion coefficient.

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