The crossover from single file to Fickian diffusion

J. Sané; J. T. Padding; A. A. Louis

doi:10.1039/b905378f

paper

The crossover from single file to Fickian diffusion

arXiv:0905.1293 · doi:10.1039/b905378f

Abstract

The crossover from single-file diffusion, where the mean-square displacement scales as <x^2> ~t^(1/2), to normal Fickian diffusion, where <x^2>~t $, i ss t u d i e d a s a f u n c t i o n o f c hann e l w i d t h f or co l l o i d a l p a r t i c l es . B y co m p a r in g B r o w nian d y nami cs t o ah y b r i d m o l ec u l a r d y nami cs an d m esosco p i cs im u l a t i o n t ec hni q u e, w ec an s t u d y t h ee f f ec t o f h y d r o d y nami c in t er a c t i o n so n t h es in g l e f i l e m o bi l i t y an d o n t h ecr osso v er t o F i c k ian d i f f u s i o n f or w i d er c hann e l w i d t h s . F or d i sc - l ik e p a r t i c l es w i t ha s t ee p in t er p a r t i c l er e p u l s i o n, t h es in g l e f i l e m o bi l i t i es f or d i f f er e n tp a r t i c l e d e n s i t i es a r e w e l l d escr ib e d b y t h ee x a c tl y so l v ab l e ha r d - r o d m o d e l . T hi s h o l d s b o t h f or s im u l a t i o n s t ha t in c l u d e h y d r o d y nami cs, a s w e l l a s f or t h ose t ha t d o n^{'} t . W h e n t h es in g l e f i l eco n s t r ain t i s l i f t e d, t h e n f or p a r t i c l eso f d iam e t er σ an d p i p eo f w i d t h$ L$ such that (L- 2 σ)/σ= δ_c << 1 the particles can be described as hopping past one-another in an average time t_{hop}. For shorter times t << t_{hop} the particles still exhibit sub-diffusive behaviour, but at longer times t > t_{hop}, normal Fickian diffusion sets in with an effective diffusion constant D_{hop} ~ t_{hop}^(1/2). For the Brownian particles, t_{hop} ~ 1/δ_c^(2) when δ<< 1, but when hydrodynamic interactions are included, we find a stronger dependence than δ_c^{-2}. We attribute this difference to short-range lubrication forces that make it more difficult for particles to hop past each other in very narrow channels.

The crossover from single file to Fickian diffusion

Abstract

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