August 12th, 2020, 10-11am
Speaker: Daniel Chin, Michael Yue Li (NYU)
Title: Moving Droplets on a Wall
Abstract: In this work, we use the penalty Immersed Boundary Method (pIBM) to simulate the movement of liquid droplets hanging on a vertical wall. We propose a 2D numerical method based on pIBM to tackle the moving contact line problem. Note that the vertical wall is hydrophilic and does not allow slip in most cases, however, in reality we do observe droplets advance on hydrophilic surfaces. We use Lagrangian markers to represent the droplet interface and compute surface tension. The forcing scheme is designed to unify both the surface tension and the unbalanced Young's forces at the contact point into one general equation. We also employ a dynamic re-sampling technique to ensure the uniform distribution of Lagrangian markers.
August 5th, 2020, 10-11am
Speaker: Dr. Eduardo Corona (NYIT)
Title: A Crash Course on Boundary Integral Equation methods, with applications to complex fluid suspensions simulation
Abstract: When one first learns to solve boundary value problems for PDEs, we are told to "discretize" the derivative operators within, for example, using finite difference or finite element methods. For an increasingly large class of PDE problems, re-formulating them as Boundary Integral Equations (BIE) has emerged as an alternative approach with lots of advantages, leading to highly competitive fast simulation frameworks. In this talk, I will use problems from my research on many rigid body suspension flows to explain, step by step, how to solve elliptic PDE problems using this Boundary Integral formulation.
July 29th, 2020, 10-11am
Speaker: Dr. Joel Newbolt (Harvard SEAS)
Title: Flow-mediated collective dynamics of flapping swimmers
Abstract: Fish and birds moving in groups are thought to benefit from hydro- or aero-dynamic interactions between individuals. Yet disagreement between theoretical predictions and biological observations has led some to reject the fluid-dynamical picture of schools of fish and flocks of birds. To study these flow interactions in a controlled way, we built a robotic "school" of flapping hydrofoil swimmers that have prescribed flapping kinematics while their forward-swimming motions and formations result from flow interactions. Surprisingly, we find that the flows naturally generated during swimming can also prevent collisions and separations. Stable formations extend in a region around a solitary swimmer, and the stable positions can be controlled by changes in flapping kinematics and phase. These behaviors are reflected in 2-dimensional models using point-vortex or free-shear-layer methods, but can also be recovered from a reduced-order model which produces remarkable agreement with the experimentally observed modes by relating the follower's thrust to its flapping speed relative to the wake flow.
July 22th, 2020, 10-11am
Speaker: Hamad El Kahza, Tanvi Patel (NYIT)
Title: On Mathematical modeling of erosion and sedimentation
Abstract: Erosion and sedimentation, in the environmental context, is represented as the evolution of solid bodies due to the forces exerted by the fluid or air on the contact surface, which both often lead to reconfiguration and change of the topology and structure of the geological structures. These processes are notably very complicated and challenging to study in reality. In this work, we formulate novel and idealized mathematical models to examine the internal evolution of flow-networks in the setting of cylindrical channels, undergoing a unidirectional flow, by using asymptotic and numerical techniques. Starting from the Stokes equations combined with an advection-diffusion solid transport, we propose a model to construct a complete analysis of both the erosion and sedimentation in geological structures and porous media. The considered approach is of the form of threshold laws: the fluid-solid interface erosion and sedimentation occur, when the total shear stress is respectively, greater and lower than some specific critical values, depending on the solid material. As a consequence of the erosion and sedimentation, the structure channels' radii expand and shrink respectively.
July 15th, 2020, 10-11am
Speaker: Yixuan Sun (NJIT)
Title: Modeling and design optimization for pleated membrane filter
Abstract: Pleated membrane filters, which offer larger surface area to volume ratios than unpleated membrane filters, are used in a wide variety of applications. However, the performance of the pleated filter, as characterized by a flux-throughput plot, indicates that the equivalent unpleated filter provides better performance under the same pressure drop. Earlier work (Sanaei & Cummings 2016) used a highly-simplified membrane model to investigate how the pleating effect and membrane geometry affect this performance differential. In this work, we extend this line of investigation and use asymptotic methods to couple an outer problem for the flow within the pleated structure to an inner problem that accounts for the pore structure within the membrane. We use our new model to formulate and address questions of optimal membrane design for a given filtration application.
July 8th, 2020, 10-10:30am
Speaker: Dave Persaud
Title: Flow and fouling in a pleated membrane filter
Abstract: Pleated membrane filters are widely used in many applications, and offer significantly better surface area to volume ratios than equal-area unpleated membrane filters. However, their filtration characteristics are markedly inferior to those of equivalent unpleated membrane filters in dead-end filtration. While several hypotheses have been advanced for this, one possibility is that the flow field induced by the pleating leads to spatially non-uniform fouling of the filter, which in turn degrades performance. In this paper we investigate this hypothesis by developing a simplified model for the flow and fouling within a pleated membrane filter. Our model accounts for the pleated membrane geometry (which affects the flow), for porous support layers surrounding the membrane, and for two membrane fouling mechanisms: (i) adsorption of very small particles within membrane pores; and (ii) blocking of entire pores by large particles. We use asymptotic techniques based on the small pleat aspect ratio to solve the model, and we compare solutions to those for the closest-equivalent unpleated filter.
July 8th, 2020, 10:30-11am
Speaker: Mikhail Smirnov
Title: Characterizing the effects of pleat packing density in pleated membrane filters performance
Abstract: Pleated filter cartridges are widely used to remove undesired impurities from a fluid. A filter membrane is sandwiched between porous support layers, then pleated and packed into an annular cylindrical cartridge with a central hollow duct for outflow. Although this arrangement offers a high ratio of surface filtration area to volume, the filter performance is not as efficient as a flat filter. This stems from several possible hypotheses including the additional resistance due to the packing density of the pleats, the complex flow dynamics within the pleated membrane and possible damage of membrane filter during the pleating process. In this work, we present an extension to the purely 2D model presented in the work by Sanaei et al. (JFM 2016) to investigate the effects of variations along the axis of the filter cartridge in 3D. We also introduce a more sophisticated description of the cartridge geometry that accounts for the cylinder's curvature. Using asymptotic methods to simplify the flow throughout the cartridge, makes this possible to investigate systematically how the number of pleats or pleat packing density affects the performance of the pleated membrane filters, where the ultimate goal of this study will be to find an optimal number of pleats to achieve a particular optimum filtration performance.
July 1st, 2020, 10-11am
Speaker: Binan Gu
Title: Graphical Representation of Membrane Filters
Abstract: We formulate the filtering problem in a random network where vertices and edges of the underlying graph represent pore junctions and throats. We study the adsorptive and sieving fouling mechanisms simultaneously and define each mode more carefully. The main goal is to relate membrane filter properties reflected in spectral graph theory to the performance of the filter. We also provide a formula for network tortuosity in terms of the transition matrix of a sieving particle which we assume to perform a weighted random walk on the network.
June 24th, 2020, 10-11am
Speaker: Zeshun Zong (NYU, UCLA)
Title: On cell proliferation in a tissue engineering scaffold pore, effects of nutrient concentration and scaffold internal geometry
Abstract:
Cell proliferation within a porous tissue engineering scaffold perfused with nutrient solution depends sensitively on the choice of pore geometry, flow rates, and nutrient concentration. Regions of high pore curvature encourage cell proliferation, while a critical flow rate is required to promote growth. Moreover, the dynamics of the nutrient culture medium consumption influence the cell growth. In experiments, such factors should be chosen meticulously to match the characteristics of the underlying cells and the particular goal of incubation. However, determining these factors poses a significant challenge that cannot be addressed by experimentation alone. In this talk, we present a first-principle mathematical theory for the nutrient concentration coupled to the growth of cells seeded on the pore walls, which is driven by the fluid flow within a tissue engineering scaffold pore. In addition, using asymptotic analysis based on the pore small aspect ratio, we derive a reduced model that enables a comprehensive analysis of the system to be performed. This approach reduces the numerical burdens, captures the experimental observations and suggests improvements to the design of a tissue engineering scaffold and the appropriate operating regime.
June 17th, 2020, 10-11am
Speaker: Zhengi (Skye) Chen (NYU, University of Columbia)
Title: Diffusion effects on filtration process
Abstract:
Membrane science is an area of study, which motivates the development and improvement of filtration technology in various industries. Membrane filters structures are equipped with specific properties, such as pore size and void fraction, which both vary depending on different applications. The requirement of filtration is to achieve the separation of particles and fluid, while minimizing the energy consumption at the same time. However, membrane fouling is inevitable during the filtration process and affects membrane functionality in any filtration stage. Membrane fouling is a very complex process and is determined by many properties such as the membrane internal morphology, internal membrane pore structure, flow rate and contaminant properties. In a very slow filtration process or during the late stage of filtration, when the flow rate is naturally low and P\'eclet number is small, particle diffusion is essential and can not be neglected, while in typical filtration models, especially in moderate and fast filtration process, it is completely ignored. The objective of this study is to investigate how the filtration process changes under possible effects brought by particle diffusion. We discuss how membrane morphology evolves and investigate the filtration performance during the filtration process. We also compare the results with the situation where diffusion is less important (in a fast filtration process) and make a prediction about what kind of membrane filter should be employed to achieve a particular optimum filtration performance in a slow process.
June 10th, 2020, 10-11am
Speaker: She Yue (Connie) Liu
Title: Flow and fouling in elastic membrane filters with complex pore morphology
Abstract: Filtration technology has been increasingly used for industrial purposes and the study of membrane science is beneficial for filtration efficacy prediction and performance analysis. Real membranes have complex geometry, with pores inside the membrane branch and interconnected with each other. Membrane fouling, as an indispensable consequence for removing particles, occurs in the course of the filtration process and deteriorates the membrane permeability. Note that, in this work, we only consider standard blocking as a fouling mechanism, which decreases membrane porosity. However, for membranes with elastic materials, the pressure within the membrane results in membrane pore radius expansion and further influences the filtration performance. In this work, we present a mathematical model with multi-layer bifurcating interior morphology. Two pervasive filtration forcing mechanisms are considered for modeling: (i) constant pressure drop; and (2) constant flux through the membrane. We investigate how filtration behaves under two different forcing mechanisms and describe the morphology change due to fouling and elasticity. Simulations are made when first considering a constant flux scenario and switch to a constant pressure situation after pressure reaches a certain threshold. We also compare the results with membranes with no elasticity and analyze the filtration efficiency under different membrane materials.