Exact Phoretic Interaction of Two Chemically Active Particles

Abstract

We study the nonequilibrium interaction of two isotropic chemically active particles taking into account the exact near-field chemical interactions as well as hydrodynamic interactions. We identify regions in the parameter space wherein the dynamical system describing the two particles can have a fixed point-a phenomenon that cannot be captured under the far-field approximation. We find that, due to near-field effects, the particles may reach a stable equilibrium at a nonzero gap size or make a complex that can dissociate in the presence of sufficiently strong noise. We explicitly show that the near-field effects originate from a self-generated neighbor-reflected chemical gradient, similar to interactions of a selfpropelling phoretic particle and a flat substrate.

Exact axisymmetric interaction of phoretically active Janus particles

“…Also, since there is no difference between the two compartments of each particle, we can group the geometrical functions together and define as the net neighbour-induced interaction, and as the net neighbour-reflected contribution. By setting , the relative speed given in (3.9) takes the simple form where As we discussed in our previous work (Nasouri & Golestanian 2020), and are both positive scalers that decay monotonically with the gap size, but so does their ratio; see figure 2( b ). Thus, the system of two isotropic particles can indeed have at most one fixed point.…”

“…2016; Sharifi-Mood et al. 2016; Michelin & Lauga 2017; Nasouri & Golestanian 2020). In what follows we show how this method can be adapted to obtain the geometrical functions.…”

“…Surprisingly, we find that allowing the mobilities to be non-uniform across the surface of the particles does not increase the number of fixed points in the dynamical system. This may be due to the fact that unlike the chemical activities that alter the chemical field directly, any discontinuity in the mobilities can only directly affect the hydrodynamic field which has proven to be less important in terms of determining the fixed points in the dynamical system (Nasouri & Golestanian 2020). Thus, we can then conclude that a pair of Janus particles can only have up to three fixed points in their relative motion.…”

Scalar Active Mixtures: The Nonreciprocal Cahn-Hilliard Model

“…Here, activity manifests itself only through the nature of the effective interactions between different particle species. Indeed, active particles that are spherically symmetric-for example, a fully coated catalytic colloid [4,20,21]-will not self-propel when in isolation and only exhibit anomalous fluctuations [22]. However, when two particles are present, this symmetry is broken, and effective interactions between them can arise.…”

“…Crucially, however, if the two particles are different, the effective active interactions are no longer constrained by Newton's third law, and the responses of each particle to the presence of the other need not be reciprocal. This behavior is easily seen in catalytic particles, where the phoretic response of a particle of species A to the chemical produced by a particle of species B is generically different from the phoretic response of B to the chemical produced by A [4,20,21,23]. These nonreciprocal interactions can result in substantial departures from equilibrium behavior, such as the formation of self-propelling small molecules [20] or cometlike macroscopic clusters [4].…”