Modelling and Simulation of a Packed Bed of Pulp Fibers Using Mixed Collocation Method

Ganaie, Ishfaq Ahmad; Arora, Shelly; Kukreja, V. K.

doi:10.1155/2013/875298

Cited by 4 publications

(1 citation statement)

References 34 publications

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“…Peirce [142] proposed the cubic Hermite collocation method for solving the coupled integral-partial differential problems directing the propagation of a hydraulic fracture in a condition of planar strain. Ganaie et al [143][144][145][146] applied the collocation method with a cubic Hermite for solving the following PDEs:…”

Section: Application Of Hermite As a Basis Functionmentioning

confidence: 99%

Survey of Hermite Interpolating Polynomials for the Solution of Differential Equations

Kumari

Kukreja

2023

Mathematics

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With progress on both the theoretical and the computational fronts, the use of Hermite interpolation for mathematical modeling has become an established tool in applied science. This article aims to provide an overview of the most widely used Hermite interpolating polynomials and their implementation in various algorithms to solve different types of differential equations, which have important applications in different areas of science and engineering. The Hermite interpolating polynomials, their generalization, properties, and applications are provided in this article.

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Section: Application Of Hermite As a Basis Functionmentioning

confidence: 99%

Survey of Hermite Interpolating Polynomials for the Solution of Differential Equations

Kumari

Kukreja

2023

Mathematics

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Numerical solution of heat conduction problems using orthogonal collocation on finite elements

Arora

Kaur

2015

Journal of the Nigerian Mathematical Society

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An accessible platform to quantify oxygen diffusion in cell-laden hydrogels and its application to alginate-immobilized pancreatic beta cells

Champion,

Ebrahimi Orimi,

Gauvin

et al. 2024

Preprint

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Hydrogels are commonly used to immobilize mammalian cells, serving various purposes such as providing mechanical cues in three-dimensional cultures and acting as barriers for immunoprotection in transplantation. For instance, islet encapsulation holds promise in delivering insulin-producing cells for diabetes cellular therapy. Cell immobilization, by creating a barrier to bulk fluid motion, leads to diffusion limited molecular transport and concentration gradients of nutrients such as oxygen being consumed by the immobilized cells. Oxygen mass transport models aid in designing immobilization strategies but rely on input parameters like oxygen diffusivity, often assumed rather than experimentally measured due to limited resources or expertise. We propose an accessible, cost-effective, and easy to operate system to experimentally determine the diffusion coefficient of cell-laden hydrogels, with application tested to alginate-immobilized pancreatic beta cell (MIN6). As compared to water, the oxygen diffusion coefficient was significantly reduced in alginate gels. The oxygen diffusion coefficient was inversely correlated with the dynamic loss modulus for gels with similar chemical composition, and significantly reduced when the alginate concentration was increased from 2% to 5%. The viability of immobilized MIN6 cells was highly dependent both on gel concentration and cell density, as predicted by Thiele modulus and effectiveness factor values calculated from measured oxygen diffusion coefficients. The proposed platform, combining a simple experimental setup and the use of dimensionless numbers, offers a straightforward means to predict maximal diffusion distances in cell immobilization strategies. This platform can be implemented in the rational design of cell encapsulation, immobilized cell culture, and tissue engineering strategies.

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Modelling and Simulation of a Packed Bed of Pulp Fibers Using Mixed Collocation Method

Cited by 4 publications

References 34 publications

Survey of Hermite Interpolating Polynomials for the Solution of Differential Equations

Survey of Hermite Interpolating Polynomials for the Solution of Differential Equations

Numerical solution of heat conduction problems using orthogonal collocation on finite elements

An accessible platform to quantify oxygen diffusion in cell-laden hydrogels and its application to alginate-immobilized pancreatic beta cells

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