arXiv subjects

Binan Gu

Publications and source records attributed to Binan Gu.

5 recordsLinked to original sources

arXiv2026

Source-Induced Reflection in Balanced Shallow-Water Networks

Width-balance conditions at a junction are often associated with reflectionless transmission, or transparency, in some one-dimensional wave models on networks. We show that, on cyclic networks, this identification is incomplete: local balance is a vertex-level condition, while transparency also requires synchronization of the path travel times. To make this precise, we consider a shallow-water wave model and derive the channel-width-weighted scattering law for a vertex of arbitrary degree and introduce a source-relative definition of balance, reflecting the fact that the same junction may be reflective or reflectionless depending on which edges carry incoming waves. Under this definition, a balanced vertex is transparent only to the synchronized incoming-amplitude direction. For an $N$-path island, the resulting first-generation upstream reflection is governed in frequency space by the width-weighted distribution of path delays. Exact broadband cancellation requires all path travel times to agree; when they do not, commensurability of the path-length differences produces a periodic comb of frequency-selective zeros, independent of channel widths. At $N\ge 4$ we further exhibit a hybrid regime in which the reflection factor vanishes without commensurability among the path lengths.

nlin.PS↗

arXiv2025

Stochastic Modeling of Filtration with Sieving in Graded Pore Networks

We model filtration of a feed solution, containing both small and large foulant particles, by a membrane filter. The membrane interior is modeled as a network of pores, allowing for the simultaneous adsorption of small particles and sieving of large particles, two fouling mechanisms typically observed during the early stages of commercial filtration applications. In our model, first-principles continuum partial differential equations model transport of the small particles and adsorptive fouling in each pore, while sieving particles are assumed to follow a discrete Poisson arrival process with a biased random walk through the pore network. Our goals are to understand the relative influences of each fouling mode and highlight the effect of their coupling on the performance of filters with a pore-size gradient (specifically, we consider a banded filter with different pore sizes in each band). Our results suggest that, due to the discrete nature of pore blockage, sieving alters qualitatively the rate of the flux decline. Moreover, the difference between sieving particle sizes and the initial pore size (radius) in each band plays a crucial role in indicating the onset and disappearance of sieving-adsorption competition. Lastly, we demonstrate a phase transition in the filter lifetime as the arrival frequency of sieving particles increases.

physics.flu-dyn↗

arXiv2022

Flow through Pore-Size Graded Membrane Pore Networks

Pore-size gradients are often used in the design of membrane filters to increase filter lifetime and ensure fuller use of the initial membrane pore volume. In this work, we impose pore-size gradients in the setting of a membrane filter with an internal network of interconnected tube-like pores. We model the flow and foulant transport through the filter using the Hagen-Poiseuille framework coupled with advection equations via conservation of fluid and particle flux, with adsorption as the sole fouling mechanism. We study the influence of pore-size gradient on performance measures such as total filtrate throughput and accumulated contaminant concentration at the membrane downstream pore outlets. Within the limitations of our modeling assumptions we find that there is an optimal pore-radius gradient that maximizes filter efficiency independent of maximum pore length (an input parameter that influences the structure of the pore network), and that filters with longer characteristic pore length perform better.

physics.flu-dyn↗

arXiv2021

Network-based membrane filters: Influence of network and pore size variability on filtration performance

We model porous membrane filters as networks of connected cylindrical pores via a random network generation protocol, and their initial pore radii via a uniform distribution of widths that vary about some mean value. We investigate the influence of network and pore size (radius) variations on the performance of membrane filters that undergo adsorptive fouling. We find that membrane porosity variations, independently of whether induced by variations of the pore radii or of the random pore network, are an important factor determining membrane filter performance. Network and pore size variations still play a role, in particular if pore radii variations are significant. To quantify the influence of these variations, we compare the performance metrics of networks built from pores of variable radii to their (equal porosity) counterparts built from pores of uniform radius. We show that the effect of pore radii variations is to increase throughput, but also to reduce foulant control.

cond-mat.soft↗

arXiv2021

A Graphical Representation of Membrane Filtration

We analyze the performance of membrane filters represented by pore networks using two criteria: 1) total volumetric throughput of filtrate over the filter lifetime and 2) accumulated foulant concentration in the filtrate. We first formulate the governing equations of fluid flow on a general network, and we model transport and adsorption of particles (foulants) within the network by imposing an advection equation with a sink term on each pore (edge) as well as conservation of fluid and foulant volumetric flow rates at each pore junction (network vertex). Such a setup yields a system of partial differential equations on the network. We study the influence of three geometric network parameters on filter performance: 1) average number of neighbors of each vertex; 2) initial total void volume of the pore network; and 3) tortuosity of the network. We find that total volumetric throughput depends more strongly on the initial void volume than on average number of neighbors. Tortuosity, however, turns out to be a universal parameter, leading to almost perfect collapse of all results for a variety of different network architectures. In particular, the accumulated foulant concentration in the filtrate shows an exponential decay as tortuosity increases.

physics.flu-dyn↗