Divergence of the long-wavelength collective diffusion coefficient in quasi-one- and quasi-two-dimensional colloidal suspensions

Abstract

We report the results of experimental studies of the short-time–long-wavelength behavior of collective particle displacements in quasi-one-dimensional (q1D) and quasi-two-dimensional (q2D) colloid suspensions. Our results are reported via the q → 0 behavior of the hydrodynamic function H(q) that relates the effective collective diffusion coefficient D[subscript e](q), with the static structure factor S(q) and the self-diffusion coefficient of isolated particles D[subscript 0]: H(q) ≡ D[subscript e](q)S(q)/D[subscript 0]. We find an apparent divergence of H(q) as q → 0 with the form H(q)∝q[superscript −γ] (1.7 < γ < 1.9) for both q1D and q2D colloid suspensions. Given that S(q) does not diverge as q → 0 we infer that D[subscript e](q) does. This behavior is qualitatively different from that of the three-dimensional H(q) and D[subscript e](q) as q → 0, and the divergence is of a different functional form from that predicted for the diffusion coefficient in one-component one-dimensional and two-dimensional fluids not subject to boundary conditions that define the dimensionality of the system. We provide support for the contention that the boundary conditions that define a confined system play a very important role in determining the long-wavelength behavior of the collective diffusion coefficient from two sources: (i) the results of simulations of H(q) and D[subscript e](q) in quasi-1D and quasi-2D systems and (ii) verification, using data from the work of Lin, Rice and Weitz [Phys. Rev. E 51, 423 (1995)], of the prediction by Bleibel et al., arXiv:1305.3715, that D[subscript e](q) for a monolayer of colloid particles constrained to lie in the interface between two fluids diverges as q[superscript −1] as q → 0.