arXiv subjects

Debanik Bhattacharjee

Publications and source records attributed to Debanik Bhattacharjee.

4 recordsLinked to original sources

arXiv2026

Hindered transport of spherical particles in cylindrical pores: The role of structural heterogeneity in rejection-permeability trade-offs

Membrane separations rely on balancing rejection and permeability. Extensive work has clarified how pore structure and operating conditions control each quantity in idealized or weakly heterogeneous systems. However, it remains unclear how this trade-off emerges in strongly heterogeneous media, where coupled distributions of pore and particle sizes shape the local balance between advection and diffusion and generate substantial variability in performance among distribution realizations. Here we present a steric hindered-transport framework for spherical particles in cylindrical pores that explicitly resolves both single and coupled dual heterogeneity in size distributions. We show that the ensemble-averaged rejection increases with the particle-pore aspect ratio $\lambda$ and with the P\'eclet number $Pe$, while advection enhances steric exclusion by up to $\sim$20\% at intermediate $\lambda$. Dual heterogeneity broadens the distribution of effective $Pe$, increases the variability and incidence of anomalous rejection trends, while systematically shifting the rejection-permeability trade-off toward higher permeability at fixed rejection. These results suggest that controlled heterogeneity can serve as a design lever to expand the attainable operating space for simultaneous high selectivity and high throughput.

cond-mat.soft↗

arXiv2025

Spatio-temporal dynamics of surfactant driven secondary invasion in Gaussian pore networks

Capillarity-dominated two-phase displacement in porous media often continues beyond the initial invasion-percolation (IP) breakthrough, as surfactants alter interfacial properties and reopen pathways once sealed by capillary forces. This study examines such secondary invasion, where adsorption-driven reductions in interfacial tension and contact-angle shifts lower entry thresholds in yet uninvaded throats, enabling further displacement at a fixed inlet pressure. To capture this process, we employ a time-dependent pore-network framework that couples IP with a reduced-order transport-adsorption module. Local fluxes are governed by Poiseuille flow, interfacial adsorption follows a Langmuir isotherm, and wettability evolution is modeled through a calibrated phenomenological relation. Heterogeneity is prescribed by Gaussian throat-size distributions whose variance controls structural disorder. The resulting invasion trajectories are sigmoidal, consistent with Gaussian cumulative statistics, indicating that surfactant mass-transfer kinetics and network variance primarily rescale invasion timescales while preserving the overall functional form. The framework thus connects interfacial conditioning to time-varying capillary thresholds and reveals how surfactant-mediated processes govern post-breakthrough dynamics in heterogeneous porous systems.

cond-mat.soft↗

arXiv2025

The evolution of invasion patterns due to surfactant adsorption in anomalous pore distribution: Role of Mass Transfer and Laplace Pressure

Here, we develop a time-dependent pore network model (PNM) to simulate the effects of surfactant-induced IFT reduction on immiscible displacement driven by constant inlet pressure, with pressure drops across the network calculated using a random resistor network and mass conservation equations. Node-specific flux and velocity are derived using the Hagen-Poiseuille equation, and surfactant adsorption is modeled using the Langmuir isotherm, capturing its impact on fluid-fluid and solid-fluid interfaces within the invaded path. Since the evolution of the invasion pattern comprises the cooperative mechanisms of surfactant mass transfer to the interfaces and the resulting changes in capillary and Laplace pressures, we employ two strategies to quantify this complex feedback behavior: mass transfer-based, introducing a mass transfer timescale, and Laplace pressure-based, scaling with the inlet pressure. Results reveal that an anomalous or heavy-tailed pore throat distribution accelerates the onset of secondary invasions, which enhances the dominance of Laplace pressure. As the distribution becomes less anomalous or more symmetric, mass transfer becomes the dominant mechanism. This interplay highlights the intricate balance between mass transfer and capillary effects in governing the spatio-temporal evolution of immiscible fluid invasion.

cond-mat.soft↗

arXiv2017

Droplet spreading: Role of characteristic length scales and modified disjoining pressure

The numerical prediction of droplet base radius and contact angle depends on the choice of characteristic radius and height of droplet. In this study, a developed model on the basis of lubrication approximation is used to investigate the effect of characteristic parameters on the spreading of droplets over substrates. Based on two main stages of spreading (initial and equilibrium), characteristic radius and height were first evaluated. The model predictions were then compared with experimental results in literature for both impermeable and permeable substrates. The study provides evidence that the choice of characteristic length scales based on either stage enables accurate prediction of the droplet base radius and contact angle. In addition, a new scaling relation for the predictions of the numerical disjoining pressure, with an error of $\pm$5\%, is proposed.

physics.flu-dyn↗