%0 Journal Article
%A Dhont, Jan K. G.
%A Briels, Willem
%A Park, Gun Woo
%T Motility-Induced Inter-Particle Correlations and Dynamics: a Microscopic Approach for Active Brownian Particles
%J Soft matter
%V 17
%@ 1744-6848
%C London
%I Royal Soc. of Chemistry
%M FZJ-2021-01848
%P 5613-5632
%D 2021
%X Amongst the theoretical approaches towards dynamics and phase behaviour of suspensions of active Brownian particles (ABPs), no attempt has been made to specify motility induced inter-particle correlations as quantified by the pair-correlation function. Here we derive expressions for the pair-correlation function for ABPs with very short-ranged direct interactions for small and large swimming velocities and low concentrations. The pair-correlation function is the solution of a differential equation that is obtained from the Fokker-Planck equation for the probability density function of the positions and orientations of the ABPs. For large swimming Peclet numbers lambda, the pair-correlation function is highly asymmetric. The pair-correlation function attains a large value ~lambda within a small region of spatial extent ~1/lambda near contact of the ABPs when the ABPs approach each other. The pair-correlation function is small within a large region of spatial extent ~lambda^1/3 when the ABPs move apart, with a contact value that is essentially zero. From the explicit expressions for the pair-correlation function, Fick's diffusion equation is generalized to include motility. It is shown that mass transport, in case of large swimming velocities, is dominated by a preferred swimming direction that is induced by concentration gradients. The expression for the pair-correlation function derived in this paper could serve as a starting point to obtain approximate results for high concentrations, which could then be employed in a first-principle analysis of the dynamics and phase behaviour of ABPs at higher concentrations.
%F PUB:(DE-HGF)16
%9 Journal Article
%$ 33998621
%U <Go to ISI:>//WOS:000651129400001
%R 10.1039/D1SM00426C
%U https://juser.fz-juelich.de/record/891971