Hydrochemical interactions in dilute phoretic suspensions: From individual particle properties to collective organization

Abstract

Janus phoretic colloids (JPs) self-propel as a result of self-generated chemical gradients and exhibit spontaneous nontrivial dynamics within phoretic suspensions, on length scales much larger than the microscopic swimmer size. Such collective dynamics arise from the competition of (i) the self-propulsion velocity of the particles, (ii) the attractive/repulsive chemically mediated interactions between particles, and (iii) the flow disturbance they introduce in the surrounding medium. These three ingredients are directly determined by the shape and physicochemical properties of the colloids' surface. Owing to such link, we adapt a recent and popular kinetic model for dilute suspensions of chemically active JPs where the particle's far-field hydrodynamic and chemical signatures are intrinsically linked and explicitly determined by the design properties. Using linear stability analysis, we show that self-propulsion can induce a wave-selective mechanism for certain particles' configurations consistent with experimental observations. Numerical simulations of the complete kinetic model are further performed to analyze the relative importance of chemical and hydrodynamic interactions in the nonlinear dynamics. Our results show that regular patterns in the particle density are promoted by chemical signaling but prevented by the strong fluid flows generated collectively by the polarized particles, regardless of their chemotactic or antichemotactic nature, i.e., for both puller and pusher swimmers.

Hydrochemical interactions of phoretic particles: a regularized multipole framework

“…Ibrahim & Liverpool 2016;Thutupalli et al 2018;Kanso & Michelin 2019;). An alternative mean-field approach describes the particles' motion in the ambient chemical and hydrodynamic fields generated by the superposition of their individual far-field signatures (Liebchen et al 2015;Traverso & Michelin 2020).…”

Collective dynamics and rheology of confined phoretic suspensions

“…In addition, we consider in the following repulsive chemically-induced drift (ξ t = −0.5) in order to isolate the effect of reorientation as chemical attraction. Setting ξ r /ρ and ξ t of similar magnitudes as u 0 results in the particles' passive drifts in a O(1) chemical gradient to be of the same order as their intrinsic propulsion speed; this reflects the theoretical expectation that collective dynamics develop when the motion due to inter-particle interactions is comparable with that due to self-propulsion [50]. These values correspond to dilute suspensions (O(10 −2 ) volume fraction) of JPs of colloidal size (R ∼ 10 −6 m), and small solute molecules (D c ∼ 10 −9 m 2 s −1 ).…”

“…As a result, a fixed degree of confinement is considered throughout the analysis, F = 1. A detailed analysis of the effect of F is beyond the scope of the present study; nevertheless, preliminary results (unreported here) show that reducing the degree of confinement (F > 1) progressively weakens the wave-guide effects of the walls and is associated with a gradual transition towards bulk-like dynamics, F 1, where particle aggregates emerge far from the walls in the form of circular asters [50].…”

“…To this end, the kinetic model recently used by Ref. [50] to model autophoretic suspensions in a bulk environment is adapted here to include the effect of rigid no-slip walls and of an external flow.…”

Hydrochemical interactions of phoretic particles: a regularized multipole framework

“…[58][59][60][61]. An alternative mean-field approach describes the particles' motion in the ambient chemical and hydrodynamic fields generated by the superposition of their individual far-field signatures [62,63].…”