Domain Growth in the Active Model B: Critical and Off-critical Composition

ABSTRACT

We study the ordering kinetics of an assembly of active Brownian particles (ABPs) on a two-dimensional substrate. We use a coarse-grained equation for the composition order parameter $\psi (\mathbf{r},t)$,where$\mathbf{r}$ and $t$ denote space and time, respectively. The model is similar to the Cahn-Hilliard equation orModel B (MB) for a conserved order parameter with an additional activity term of strength $\lambda$. This model has been introduced by Wittkowski et al., Nature Comm. 5, 4351 (2014), and is termed Active Model B (AMB). We study domain growth kinetics and dynamical scaling of the correlation function for the AMB with critical and off-critical compositions. The quantity $P=\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}(\lambda \times {\psi }_0)$ governs the asymptotic growth kinetics for the off-critical AMB, where ${\psi }_0$ denotes the average order parameter. For negative $P$,the domain growth law is the usual Lifshitz-Slyozov growth law with $L(t,\lambda )\sim t^{1/3}$. For positive $P$,the growth law shows a crossover to a novel growth law $L(t,\lambda )\sim t^{1/4}$. Further, the correlation function shows good dynamical scaling for the off-critical AMB but the scaling function has a dependency on ${\psi }_0$ and $\lambda$. We also study the effects of both additive and multiplicative noise on the AMB.

KEYWORDS:

• Phase separation
• Colloids
• Complex Fluids

Acknowledgments

We are grateful to the TUE computational facility at S.N. Bose National Centre for Basic Sciences, Kolkata. S. Mishra thanks SERB (India) for financial support via project ECR/2017/000659. S. Pattanayak and S. Mishra would like to thank the Department of Physics, Indian Institute of Technology (BHU), Varanasi and S.N. Bose National Centre for Basic Sciences, Kolkata for their kind hospitality. S. Puri is grateful to the Department of Science and Technology, India for support via a J.C. Bose fellowship”.

Additional information

Funding

This work was supported by the Department of Science and Technology, India.