A Mathematical and Numerical Model for Finite Elastoplastic Deformations in Fluid Saturated Porous Media

PurposeThe objective of this paper is to develop a semi-analytical finite element method for solving chemical dissolution-front instability problems in fluid-saturated porous media.Design/methodology/approachThe porosity, horizontal and vertical components of the pore-fluid velocity and solute concentration are selected as four fundamental unknown variables for describing chemical dissolution-front instability problems in fluid-saturated porous media. To avoid the use of numerical integration, analytical solutions for the property matrices of a rectangular element are precisely derived in a purely mathematical manner. This means that the proposed finite element method is a kind of semi-analytical method. The column pivot element solver is used to solve the resulting finite element equations of the chemical dissolution-front instability problem.FindingsThe direct use of horizontal and vertical components of the pore-fluid velocity as fundamental unknown variables can improve the accuracy of the related numerical solution. The column pivot element solver is useful for solving the finite element equations of a chemical dissolution-front instability problem. The proposed semi-analytical finite element method can produce highly accurate numerical solutions for simulating chemical dissolution-front instability problems in fluid-saturated porous media.Originality/valueAnalytical solutions for the property matrices of a rectangular element are precisely derived for solving chemical dissolution-front instability problems in fluid-saturated porous media. The proposed semi-analytical finite element method provides a useful way for understanding the underlying dynamic mechanisms of the washing land method involved in the contaminated land remediation.

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Numerical Simulation of Insulin Depot Formation and Absorption in Subcutaneous Tissue Modeled as a Homogeneous Anisotropic Porous Media

Journal of Biomechanical Engineering ◽

10.1115/1.4049811 ◽

2021 ◽

Author(s):

Michael Zedelmair ◽

Abhijit Mukherjee

Keyword(s):

Porous Media ◽

Numerical Model ◽

Insulin Pump ◽

Subcutaneous Tissue ◽

Saturated Porous Media ◽

Anisotropic Porous Media ◽

Effective Option ◽

Computational Fluid Dynamics Cfd ◽

Experimental Findings ◽

Subcutaneous Adipose

Abstract In this study, a numerical model of the insulin depot formation and absorption in the subcutaneous adipose tissue is developed using the commercial Computational Fluid Dynamics (CFD) software. A better understanding of these mechanisms can be helpful in the development of new devices and cannula geometries as well as predicting the concentration of insulin in the blood. The injection method considered in this simulation is by the use of an insulin pump using a rapid acting U100 insulin analogue. The depot formation is analyzed running Bolus injections ranging from 5-15 units of insulin corresponding to 50-150µl. The insulin is injected into the subcutaneous tissue in the abdominal region. The tissue is modeled as a fluid saturated porous media. An anisotropic approach to define the tissue permeability is studied by varying the value of the porosity in parallel and perpendicular direction having an impact on the viscous resistance to the flow. Following recent experimental findings this configuration results in a disk shaped insulin depot. To be able to run the simulation over longer timeframes the depot formation model has been extended implementing the process of absorption of insulin from the depot. The developed model is then used to analyze the formation of the insulin depot in the tissue when using different flow rates and cannula geometries. The numerical model is an effective option to evaluate new cannula designs prior to the manufacturing and testing of prototypes, which are rather time consuming and expensive.

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