Residual Force Determines Surface Tension in Active Systems

Abstract

The mechanical tension at the interface of motility-induced phase separating active Brownian particles (ABPs) remains an open question. Here, we determine the surface tension by analyzing the spatial distribution of forces at the molecular level in a slab-confined system of ABPs exhibiting high and low density regions separated by a one-dimensional active interface. Unlike previous approaches that evaluate active and interaction stresses independently - often producing near-zero or negative surface tension - we show that on average, interaction forces act antagonistically to active propulsion, reducing the net force experienced by particles. By evaluating the work required to bring a particle to the interface using this total-force framework, we find a positive and physically consistent surface tension. These results reframe the mechanical interpretation of local stresses and provide a generalizable method for connecting microscopic force distributions to emergent interfacial properties in nonequilibrium systems.

Figures (5)

• Figure 1: Steady state snapshot for a system of $100172$ ABPs confined in a box of size $800\times200$ showing active interface in the steady state ($t=250$) at a large activity value ($Pe=125$). Orientation of particles is depicted in colour. Higher concentration of violet in the upper region and orange in the lower region shows preferential sorting of particle orientations by the confining walls.
• Figure 2: Total force per unit length along the $y$-direction for different thickness $\Delta y$ of the coarse-graining strip for $Pe=125$. Total force per unit length in the region of interface increases as $\Delta y$ increase from $0$ to $\sigma/2$ because a larger $\Delta y$ implies more particles contribute to the sum of forces. Beyond $\Delta y > \sigma/2$, though even larger number of particles contribute to the sum of forces, $F_y^{Tot}(y)$ is found to decrease due to the onset of bulk effects.
• Figure 3: For a system of confined ABPs with $Pe=125$, (a) average packing fraction as a function of the $y$-coordinate. (b) Average active and interaction force per unit length parallel to interface ($x$-axis). (c) Total force per unit length in the direction parallel to the interface. (d) Average active and interaction force per unit length in the direction normal to the interface ($y$-axis). (e) Total force per unit length in the direction normal to the interface. (f) Total force per unit length in the direction normal to the interface zoomed in on the interfacial region with blue vertical line representing the average position of the interface. Data points are joined with lines.
• Figure 4: Surface tension of the active interface obtained by evaluating the amount or work required to bring a particle from bulk region to the interface plotted as a function of $Pe-Pe_{crit}$ where $Pe_{crit} \approx 32$ is the critical value of swim force.
• Figure 5: (a) The density bifurcation diagram obtained using nonlinear least square fitting of the packing fraction. The region between $25<Pe<40$ has no points as the fitting become unreliable in this region. (b) Binder cumulant for varying sub box size $L$ is found to exhibit $L$ independence and crossover at $Pe=32$. Data points are joined by line segments which serve as a guide to the eye.