Geometry Challenges Entropy: Regime-DependentRectification in Nanofluidic Cascades

Abstract

Can geometry alone reshape equilibrium? Cascaded nanofluidic chambers show complex accumulation patterns, traditionally attributed to geometric diode effects. We use 3D molecular dynamics to decouple funnel rectification from boundary reflection. Simulations with argon parameters (r = 0.19 nm) reveal a striking "reverse" rectification in a 2-chamber setup: the narrow side accumulates over 5x more particles (N_1/N_0 = 5.37 +/- 0.01, p < 0.0001). In a 10-chamber argon cascade, this effect drives massive downstream accumulation. A symmetric control (w_L = w_R) eliminates the gradient, confirming that funnel asymmetry - not boundary/edge effects - is the primary driver in the ballistic regime. By contrast, the super-atom regime is dominated by boundary reflection. Our results challenge standard entropic transport theory and provide design rules for passive, geometry-driven density gradients - no pump, no drive.

Figures (5)

• Figure 1: System Geometry and Mechanism. (a) Top-down view of the 3D simulation unit cell ($W{\times}H{=}4{\times}4$, $h{=}2.2$). Particles flow between wide ($w_{\mathrm{L}}{=}4$) and narrow ($w_{\mathrm{R}}{=}1$) openings. (b) Schematic comparison: Classical geometric diode theory predicts accumulation in the wide chamber ($N_0 > N_1$) due to funnel reflection. Our argon simulations reveal the opposite: massive accumulation in the narrow chamber ($N_1 > N_0$), driven by regime-dependent funnel rectification.
• Figure 2: Cascaded amplification (seed 185). Initial uniform vs steady-state. Boundary reflection drives end accumulation; gradient sharpens with chain length. Funnel asymmetry adds rectification on top.
• Figure 3: Isolating the driver of accumulation. (a) Asymmetric funnels drive a massive ramp: $N_9 \gg N_0$ ($N_9/N_0 \approx 4.0$). (b) Symmetric funnels show a uniform profile ($N_1/N_0 \approx 1.18$), proving that funnel rectification, not boundary reflection, drives the gradient in the argon regime.
• Figure 4: Mechanism Confirmation. (a) In the 2-chamber setup (argon parameters, 16 seeds), particles strongly accumulate in the narrow side ($N_1 \approx 79{,}700$ vs $N_0 \approx 14{,}800$, $p < 0.0001$). (b) Sweeping particle radius $r$ confirms that this rectification is specific to the ballistic/Knudsen regime ($r \lesssim 0.005$) and vanishes for larger collisional particles.
• Figure 5: Chain-length sweep.$N_0/N_{\mathrm{mid}}$ vs $L$ for $L \in \{5, 10, 15, 20, 25, 30\}$ chambers (5 seeds each, 120k steps). Funnel-aspect sweep in Supplementary Information.