Non-equilibrium pair interactions in colloidal dispersions

Abstract

We study non-equilibrium pair interactions between microscopic particles moving through a model shear-thinning fluid. Prior efforts to model pair interactions in non-Newtonian fluids have largely focused on constitutive models derived from polymer-chain kinetic theories focusing on conformational degrees of freedom, but neglecting the details of microstructural evolution beyond a single polymer length scale. To elucidate the role of strong structural distortion in mediating pair interactions in Brownian suspensions, we formulate and solve a Smoluchowski equation describing the detailed evolution of the particle configuration between and around a pair of microscopic probes driven at fixed velocity by an external force through a colloidal dispersion. To facilitate analysis, we choose a model system of Brownian hard spheres that do not interact hydrodynamically; while simple, this ‘freely draining’ model permits insight into connections between microstructure and rheology. The flow induces a non-equilibrium particle density gradient that gives rise to both viscous drag and an interactive force between the probes. The drag force acts to slow the centre-of-mass velocity of the pair, while the interactive force arising from osmotic pressure gradients can lead to attraction or repulsion, as well as deterministic reorientation of the probes relative to the external force. The degree to which the microstructure is distorted, and the shape of that distortion, depend on the arrangement of the probes relative to one another and their orientation to the driving force. It also depends on the magnitude of probe velocity relative to the Brownian velocity of the suspension. When only thermal fluctuations set probe velocity, the equilibrium depletion attraction is recovered. For weak forcing, long-ranged interactions mediated via the bath-particle flux give rise to entropic forces on the probes. The linear response is a viscous drag that slows forward motion; only the weakly nonlinear response can produce relative motion–attraction, repulsion or reorientation of the probes. We derive entropic coupling tensors, similar in ethos to pair hydrodynamic tensors, to describe this behaviour. The structural symmetry that permits this analogy is lost when forcing becomes strong, revealing instabilities in system behaviour. Far from equilibrium, the interactive force depends explicitly on the initial probe separation, orientation and strength of forcing; widely spaced probes interact through the distorted microstructure, whereas the behaviour of closely spaced probes is largely set by excluded-volume effects. In this regime, a pair of closely spaced probes sedimenting side-by-side tend to attract and reorient to permit alignment of their line-of-centres with the flow, while widely spaced probes fall without reorienting. Our results show qualitative agreement with experimental observations and provide a potential connection to the observed column instability in shear-thinning fluids.

Stress relaxation of dense spongy-particle systems

“…Many-particle hydrodynamic interactions are dominant when these radii are of the same order. According to Brady and coworkers, the viscosity of the solvent can be considered unaffected by the flow around the particles for [43,44]. This ratio is rather common for the particles of interest, see for instance, the size of the core, R h , vs. the thickness of the shell, R th − R h , in the core-shell particles in [45,46].…”

Tracer diffusion in crowded narrow channels

“…When several TPs are present, each of them will perturb the distribution of the environment particles in its vicinity and in order to minimise the micro-structural changes in the environment and to reduce the dissipation, they will start to move collectively. Stochastic pairing of two biased TPs has been observed in simulations in a model of a two-dimensional lattice gas [176], in experiments in colloidal suspensions [177,178], and also theoretically predicted for the relative motion of two TPs in a nearly-critical fluid mixture, due to emerging critical Casimir forces [179]. Formation of string-like clusters of TPs, or "trains" of TPs, which reveals an emerging effective attraction between them has been evidenced for situations with a small concentration of TPs [180][181][182].…”

Dynamic interfaces for contact-time control of colloidal interactions

“…Assuming semidilute polymers, the interparticle potential V = V brush + V HS is a sum of the entropic penalty of chain stretching and hard-core repulsion between monomers (see ESI † for functional forms). Normally, the translational motion of the colloids would also produce an advective particle flux contribution, vre x , which scales with the approach velocity, v. [19][20][21][22] Because our model aims to capture the transient relaxation after colloidal motion has ceased (v = 0 for t Z 0), we choose to set an initial, nonequilibrated concentration field to represent the state of monomers at t = 0 (see ESI †). Eqn (1) is numerically evaluated using the finite element software package FreeFEM++ 23 for an arbitrarily-large 3-dimensional volume which includes both colloidal particles and the two polymer brush domains.…”