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

We report the results of experimental studies of the short time-long wavelength behavior of collective particle displacements in q1D and q2D colloid suspensions. Our results are reported via the $q$-\textgreater 0 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 $D_{o}$: $H(q) D_{e}(q) S(q)$/$ D_{o}$. We find an apparent divergence of $H(q)$ as $q$-\textgreater 0 with the form H(q)q$^{-}$(1.7 \textless $\gamma $\textless 1.9), for both q1D and q2D colloid suspensions. Given that $S(q)$ does not diverge as we infer that $D_{e}(q)$ does. This behavior is qualitatively different from that of the three-dimensional $H(q)$ and $D_{e}(q)$ as $q$-\textgreater 0, and the divergence is of a different functional form from that predicted for the diffusion coefficient in one component 1D and 2D fluids not subject to boundary conditions that define the dimensionality of the system.