scholarly journals Imbibition of Newtonian Fluids in Paper-like Materials with the Infinitesimal Control Volume Method

Micromachines ◽  
2021 ◽  
Vol 12 (11) ◽  
pp. 1391
Author(s):  
Kui Song ◽  
Ruijie Huang ◽  
Xiaoling Hu
Keyword(s):  
Control Volume ◽  
Point Of Care ◽  
Pure Water ◽  
Microfluidic Devices ◽  
Newtonian Fluids ◽  
Cellulose Ester ◽  
Control Volume Method ◽  
Regular Triangle ◽  
Volume Method ◽  
Circular Paper

Paper-based microfluidic devices are widely used in point-of-care testing applications. Imbibition study of paper porous media is important for fluid controlling, and then significant to the applications of paper-based microfluidic devices. Here we propose an analytical approach based on the infinitesimal control volume method to study the imbibition of Newtonian fluids in commonly used paper-like materials. Three common paper shapes (rectangular paper strips, fan-shaped and circular paper sheets) are investigated with three modeling methods (corresponding to equivalent tiny pores with circle, square and regular triangle cross section respectively). A model is derived for liquid imbibition in rectangular paper strips, and the control equations for liquid imbibition in fan-shaped and circular paper sheets are also derived. The model is verified by imbibition experiments done using the mixed cellulose ester filter paper and pure water. The relation of imbibition distance and time is similar to that of the Lucas−Washburn (L−W) model. In addition, a new porosity measurement method based on the imbibition in circular paper sheets is proposed and verified. Finally, the flow rates are investigated. This study can provide guidance for the design of different shapes of paper, and for better applications of paper-based microfluidic devices.

scholarly journals A New Formulation of Maxwell’s Equations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 868
Author(s):  
Simona Fialová ◽  
František Pochylý
Keyword(s):  
Numerical Methods ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Control Volume ◽  
Control Volume Method ◽  
Integral Forms ◽  
New Formulation ◽  
Electrical Induction ◽  
Volume Method ◽  
Integral Identities

In this paper, new forms of Maxwell’s equations in vector and scalar variants are presented. The new forms are based on the use of Gauss’s theorem for magnetic induction and electrical induction. The equations are formulated in both differential and integral forms. In particular, the new forms of the equations relate to the non-stationary expressions and their integral identities. The indicated methodology enables a thorough analysis of non-stationary boundary conditions on the behavior of electromagnetic fields in multiple continuous regions. It can be used both for qualitative analysis and in numerical methods (control volume method) and optimization. The last Section introduces an application to equations of magnetic fluid in both differential and integral forms.

scholarly journals A Framework and Numerical Solution of the Drying Process in Porous Media by Using a Continuous Model

2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Hong Thai Vu ◽  
Evangelos Tsotsas
Keyword(s):  
Porous Media ◽  
Control Volume ◽  
Continuous Model ◽  
Control Volume Method ◽  
Drying Process ◽  
Transport Parameters ◽  
Governing Equations ◽  
Numerical Tools ◽  
Volume Method ◽  
The Continuum

The modelling and numerical simulation of the drying process in porous media are discussed in this work with the objective of presenting the drying problem as the system of governing equations, which is ready to be solved by many of the now widely available control-volume-based numerical tools. By reviewing the connection between the transport equations at the pore level and their up-scaled ones at the continuum level and then by transforming these equations into a format that can be solved by the control volume method, we would like to present an easy-to-use framework for studying the drying process in porous media. In order to take into account the microstructure of porous media in the format of pore-size distribution, the concept of bundle of capillaries is used to derive the needed transport parameters. Some numerical examples are presented to demonstrate the use of the presented formulas.

Basic Boundary Conditions for Incompressible and Compressible Flows Using Unstructured Meshes

2003 ◽  
Author(s):  
Branislav Basara
Keyword(s):  
Convergence Rate ◽  
Boundary Conditions ◽  
Compressible Flows ◽  
Unstructured Grids ◽  
Control Volume ◽  
Unstructured Meshes ◽  
Control Volume Method ◽  
Polyhedral Cells ◽  
Volume Method ◽  
Basic Boundary

The paper compiles the basic and frequently used boundary conditions in CFD calculations. Regardless of the type of boundary conditions, Dirichlet or Neumman, there are very important differences in the implementation procedure depending on the solved equations as well as on variables which are updated on the boundaries. Boundary conditions in the frame of the control volume method presented here, are adopted for the unstructured grids consisting of arbitrary polyhedral cells. There are no limitations on the employment of boundary conditions regarding mesh type. Some special treatments to improve results and the convergence rate are proposed. The emphasis is on the wall and the pressure boundaries.

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