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

Binhua Lin, Bianxiao Cui, Xinliang Xu, Ronen Zangi, Haim Diamant, Stuart A. Rice

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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 De(q), with the static structure factor S(q) and the self-diffusion coefficient of isolated particles D0: Hq≡DeqSq/D0. We find an apparent divergence of H(q) as q→0 with the form Hq q-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 De(q) does. This behavior is qualitatively different from that of the three-dimensional H(q) and De(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 De(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)PLEEE81539-375510.1103/PhysRevE.51.423], of the prediction by Bleibel, arXiv:1305.3715, that De(q) for a monolayer of colloid particles constrained to lie in the interface between two fluids diverges as q-1 as q→0.

Original languageEnglish
Article number022303
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume89
Issue number2
DOIs
StatePublished - 7 Feb 2014

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