Graph membrane transport model

The network thermodynamics model has been applied to understand the effects of diffusion coupling in the membrane transport of binary flows. In the formalism of network thermodynamics, a membrane is treated as a sequence of discrete elements called lumps, where both dissipation and storage of energy may occur. These lumps are joined in the bond graphs, and have a resistance R, and capacitance (volume) C, which are defined by... 

The bond graph method of network thermodynamics is widely used in studying homogeneous and heterogeneous membrane transport. Electroosmosis and volume changes within the compartments are the critical properties in the mechanism of cell membrane transport, and these properties can be predicted by the bond graph method of network thermodynamics. In another study, a network thermodynamics model was developed to describe the role of epithelial ion transport. The model has four membranes with series and parallel pathways and three transported ions, and simulates the system at both steady-state and transient transepithelial electrical measurements. 

The bond-graph network of liquid membrane process can be successfully exploited for modeling the separation and transport ability of complex reaction-diffusion phenomena. However, such models involving appropriate mathematical formulations are especially useful in predicting the system s response to the changes in operating conditions and specific characteristics of the liquid membrane components. In general, such models are not... 

With this convention, we should now be ready to construct the bond-graph network of the black-box model for transport across membranes in Section 2.3. Since we have formulated this model and its representative linear network in Fig. 2 in terms of chemical potentials, we rewrite (4.41) in terms of the corresponding potentials y, y quite similarly as (4.23)... 

In combination with the conventions from Section 4.2 concerning the bond-graph representation of material capacitances, we can now translate the black-box model Fig. 3 in Section 2.3 for transport across membranes including relaxation processes into the bond-graph language as... 

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