Fluctuation-induced forces in driven systems with a diffusivity anomaly

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Fluctuation-induced forces in driven systems with a diffusivity anomaly

Mauro Sellitto

Phys. Rev. E 102, 050101(R) – Published 16 November 2020

Abstract

We show that Casimir-like forces in boundary-driven systems with a bulk diffusivity anomaly are enhanced by cooperative dynamical effects and can be made locally attractive or repulsive depending on the boundary densities. Theoretical predictions based on mean-field arguments and the explicit evaluation of the Casimir force in the fluctuating hydrodynamics framework are supported by Monte Carlo simulation of a two-dimensional ( $2 D$ ) exclusion process with selective kinetic constraints. Consistent with the entropic interpretation of the Casimir effect, we find that local repulsive forces do appear whenever finite-size transverse density fluctuations exceed their infinite-size value. Our results suggest that the bulk diffusivity anomaly is a crucial ingredient in the small-scale design of driven soft-matter systems with tunable fluctuation-induced forces.

Received 14 September 2020
Accepted 26 October 2020

DOI:https://doi.org/10.1103/PhysRevE.102.050101

Physics Subject Headings (PhySH)

Classical statistical mechanics Dissipative dynamics

Statistical Physics & Thermodynamics

Authors & Affiliations

Mauro Sellitto

Dipartimento di Ingegneria, Università degli Studi della Campania “Luigi Vanvitelli,” Via Roma 29, 81031 Aversa, Italy and Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy

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Issue

Vol. 102, Iss. 5 — November 2020

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Images

Figure 1
The setup considered in Monte Carlo simulations consists of a square lattice of size $ℓ \times L$ connected to two reservoirs at $x = 0$ and $x = L$ , with densities $ρ (0, y) = ρ_{0}$ and $ρ (L, y) = ρ_{1} > ρ_{0}$ , respectively. There are periodic boundary conditions in the direction transverse to the particle flux $J$ . The bulk dynamics is governed by a selective kinetic constraint obeying the detailed balance condition: A particle can hop to a nearby empty site only if it is not surrounded by two nearest neighboring particles before and after the move. Red bonds show forbidden hoppings due to the selective kinetic constraint on a specific configuration of particles. (Hoppings forbidden by the pure hard-core exclusion are not shown.)
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Figure 2
Normalized profiles, $\tilde{ρ} (x) = [ρ (x) - ρ_{0}] / (ρ_{1} - ρ_{0})$ , in the cooperative exclusion process with selective kinetic constraints on a square lattice of size $L \times ℓ$ . The system edges at $x = 0$ and $x = L$ are in contact with a particle reservoir at density $ρ_{0}$ and $ρ_{1}$ , respectively. There are periodic boundary conditions in the direction transverse to the particle current. For comparison, the density profile for the simple exclusion process is shown as a dotted straight line.
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Figure 3
Main paper results: Rescaled fluctuation-induced pressure $\tilde{Π} (x) = ℓ L Π (x)$ in a cooperative exclusion process with selective kinetic constraint on a square lattice. Dashed lines are the predictions based on the no-correlation approximation (NCA) of bulk diffusion. Full lines are the predictions of fluctuating hydrodynamics theory (FHT) obtained from estimating density profiles with a fifth- or sixth-order polynomial. Data points refer to the direct measurement of pressure by Monte Carlo (MC) simulations of $10^{8}$ MC sweeps (average over 10 independent realizations): multiple ghost sites with volume $Δ V = 2 ℓ$ , $λ \in [0, 1]$ discretized into 24 values equally spaced over three contiguous subintervals ([0.01,0.04], [0.04,0.2], and [0.2,1], with a cutoff $λ_{\min} = 0.001$ ). Panel parameters for system sizes and boundary densities as in Fig. 2. Statistical errors on data points are only visible in panel (a) because of the lower signal-to-noise ratio.
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Figure 4
Rescaled excess of transverse density fluctuations $\tilde{Δ} (x) = 100 Δ (x) {(ℓ \times L)}^{1 / 4}$ for the cooperative exclusion process with selective kinetic constraint on a square lattice. The factor 100 is included for sake of a better comparison with Fig. 3. Panel parameters as in Fig. 2.
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