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We are interested in rationalizing the phenomenon of like-charge attraction between charged bodies, such as a pair of colloids, in the strong coupling regime. The two colloids are modelled as uniformly charged parallel plates, neutralized by mobile counterions. In an earlier work [Palaia et al., J. Phys. Chem. B 126, 3143 (2022)], we developed an effective-field theory for symmetric plates, stemming from the ground-state description that holds at infinite couplings. Here, we generalize the approach to the asymmetric case, where the plates bear charges of the same sign, but of different values. In the symmetric situation, the mobile ions, which are localized in the vicinity of the two plates, share equally between both of them. Here, the sharing is non-trivial, depending both on the coupling parameter and the distance between the plates. We thus introduce a counterion occupation parameter, that is determined variationally to ensure minimum of the free energy. The resulting analytical results for the pressure as a function of the plate-plate distance $d$ agree well with our Monte Carlo data, in a large interval of strong and intermediate coupling constants $\Xi$. We show in particular that within this description, there exists a range of large distances at which the attractive pressure features a $1/d^2$ behavior., Comment: 16 pages, 6 figures

We study thermal equilibrium of classical pointlike counterions confined between symmetrically charged walls at distance $d$. At very large couplings when the counterion system is in its crystal phase, a harmonic expansion of particle deviations is made around the bilayer positions, with a free lattice parameter determined from a variational approach. For each of the two walls, the harmonic expansion implies an effective one-body potential at the root of all observables of interest in our Wigner Strong-Coupling expansion. Analytical results for the particle density profile and the pressure are in good agreement with numerical Monte Carlo data, for small as well as intermediate values of $d$ comparable with the Wigner lattice spacing. While the strong-coupling theory is extended to the fluid regime by using the concept of a correlation hole, the Wigner calculations appear trustworthy for all electrostatic couplings investigated. Our results significantly extend the range of accuracy of analytical equations of state for strongly interacting charged planar interfaces.

We study a classical system of identically charged counter-ions near a planar wall carrying a uniform surface charge density. The equilibrium statistical mechanics of the system depends on a single dimensionless coupling parameter. A new self-consistent theory of the correlation-hole type is proposed which leads to a modified Poisson-Boltzmann integral equation for the density profile, convenient for analytical progress and straightforward to solve numerically. The exact density profiles are recovered in the limits of weak and strong couplings. In contrast to previous theoretical attempts of the test-charge family, the density profiles fulfill the contact-value theorem at all values of the coupling constant, and exhibit the mean-field decay at asymptotically large distances from the wall, as expected. We furthermore show that the density corrections at large couplings exhibit the proper dependence on coupling parameter and distance to the charged wall. The numerical results for intermediate values of the coupling provide accurate density profiles which are in good agreement with those obtained by Monte-Carlo simulations. The crossover to mean-field behavior at large distance is studied in detail.

We study how a neutralising cloud of counterions screens the electric field of a uniformly charged planar membrane plate, when the counterions are characterised by a distribution of charges (or valence), $n(q)$. We work out analytically the one-plate and two-plate cases, at the level of non-linear Poisson-Boltzmann theory. The (essentially asymptotic) predictions are successfully compared to numerical solutions of the full Poisson-Boltzmann theory, but also to Monte Carlo simulations. The counterions with smallest valence control the long-distance features of interactions, and may qualitatively change the results pertaining to the classic monodisperse case where all counterions have the same charge. Emphasis is put on continuous distributions $n(q)$, for which new power-laws can be evidenced, be it for the ionic density or the pressure, in the one- and two-plates situations respectively. We show that for discrete distributions, more relevant for experiments, these scaling laws persist in an intermediate but yet observable range. Furthermore, it appears that from a practical point of view, hallmarks of the continuous $n(q)$ behaviour is already featured by discrete mixtures with a relatively small number of constituents., Comment: 23 pages, 10 figures

The screening of plate-plate interactions by counterions is an age-old problem. We revisit this classic question when counterions exhibit a distribution of charges. While it is expected that the long-distance regime of interactions is universal, the behaviour of the inter-plate pressure at smaller distances should a priori depend rather severely on the nature of the ionic mixture screening the plate charges. We show that is not the case, and that for comparable Coulombic couplings, different systems exhibit a quasi-universal equation of state., Comment: 5 pages, 3 figures

We use numerical simulations to study the effect of particle friction on suspension flows of non-Brownian hard particles. By systematically varying the microscopic friction coefficient $\mu_p$ and the viscous number $J$, we build a phase diagram that identifies three regimes of flow: Frictionless, Frictional Sliding, and Rolling. Using energy balance in flow, we predict relations between kinetic observables, confirmed by numerical simulations. For realistic friction coefficient and small viscous numbers (below $J\sim 10^{-3}$) we show that the dominating dissipative mechanism is sliding of frictional contacts, and we characterize asymptotic behaviors as jamming is approached. Outside this regime, our observations support that flow belongs to the universality class of frictionless particles. We discuss recent experiments in the context of our phase diagram., Comment: 8 pages

The rheology of dense Brownian suspensions of hard spheres is investigated numerically beyond the low shear rate Newtonian regime. We analyze an athermal analogue of these suspensions, with an effective logarithmic repulsive potential representing the vibrational entropic forces. We show that both systems present the same rheology without adjustable parameters. Moreover, all rheological responses display similar Herschel-Bulkley relations once the shear stress and the shear rate are respectively rescaled by a characteristic stress scale and by a microscopic reorganization time-scale, both related to the normal confining pressure. This pressure-controlled approach, originally developed for granular flows, reveals a striking physical analogy between the colloidal glass transition and granular jamming., Comment: 6 figures, 6 pages

The dynamical mechanism at the origin of the non-local rheology of dense granular flows is investigated trough discrete element simulations. We show that the influence of a shear band on the mechanical behavior of a distant zone is contained in the spatial variations observed in the network of granular contacts. Using a micro-rheology technique, we establish that the exponential responses hence obtained, do not proof the validity of a mechanical activation process as previously suggested, but stem from the spatial relaxation of the shear rate as a direct consequence of a macroscopic non-local constitutive relation. Finally, by direct visualization of the local relaxation processes, we dismiss the kinetic elasto-plastic picture, where a flow is conceived as a quasi-static sequence of localized plastic events interacting through the stress field. We therefore conclude in favor of the jamming scenario, where geometrical constrains lead to coherent non-affine displacements along floppy modes, inherently non-local., Comment: Manuscript submitted to Phys. Rev. Lett. + Supplementary Material: 7 pages, 7 figures

We compare weak and strong coupling theory of counterion-mediated electrostatic interactions between two asymmetrically charged plates with extensive Monte-Carlo simulations. Analytical results in both weak and strong coupling limits compare excellently with simulations in their respective regimes of validity. The system shows a surprisingly rich structure in terms of interactions between the surfaces as well as fundamental qualitative differences in behavior in the weak and the strong coupling limits., Comment: 15 pages, 8 figures