By G.K. Suraishkumar
This publication addresses the research, within the continuum regime, of organic structures at a number of scales, from the mobile point to the economic one. It offers either primary conservation ideas (mass, cost, momentum and effort) and proper fluxes caused by applicable riding forces, that are vital for the research, layout and operation of organic platforms. It comprises the idea that of cost conservation, a massive precept for organic platforms that isn't explicitly lined in the other publication of this sort. The booklet is geared up in 5 components: mass conservation; cost conservation; momentum conservation; strength conservation and a number of conservations at the same time utilized. All mathematical features are offered step-by-step, permitting any reader with a uncomplicated mathematical historical past (calculus, differential equations, linear algebra, etc.) to stick with the textual content conveniently. The e-book promotes an intuitive knowing of all of the suitable ideas and in so doing enables their program to useful matters with regards to layout and operation of organic structures. meant as a self-contained textbook for college kids in biotechnology and in business, chemical and biomedical engineering, this publication also will symbolize an invaluable reference advisor for pros operating within the above-mentioned fields.
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Extra resources for Continuum Analysis of Biological Systems: Conserved Quantities, Fluxes and Forces
1-1. Diffusion through Pores in a Membrane Let us consider a membrane made up of pores in an impermeant matrix – a matrix through which solutes cannot dissolve and diffuse. The pores, however, are filled with a solvent through which the solute diffuses. 4 Steady State Diffusion 41 Fig. 1-2 Different tortuosities that are possible in membranes =1 >1 solute in the solvent are the same and hence K = 1 is a good approximation, d is membrane thickness, is tortuosity (Fig. 1-2), a measure of the mean distance travelled by the solute in relation to the thickness of the membrane and = Porosity = Volume fraction of pores in the membrane = Volume of pores Total volume of the membrane including pores When the Pores are Comparable in Size to the Solute When the pores become sufficiently small, the diffusivity in a pore is less than that in free solution.
For example, when concentrations are uniform over a surface, the curvature is not significant, and the thickness is very less compared to the length or breadth, the above approximation holds; using this approximation, the diffusion across the surfaces of tissues or large organs such as the skin or the kidney can be considered as a steady state diffusion. 1 Steady State Diffusion Across Membranes There are two broad ways in which diffusion across a membrane can be viewed (i) Dissolve-diffuse mechanism: The solute first dissolves in the membrane and then diffuses through it.
Similarly, the mass flux can be written from Eq. 1-1, as ji = ρi vi − ρi n n ∑ j =1 ρ j ∑ j =1 ρ j v j From Eq. 2-10) Some useful relationships between the above velocities, fluxes, and mass (or mole) fractions, are covered in the exercises at the end of this chapter. 2 A Constitutive Equation In the previous chapter, we discussed the representation of a general conservation principle, namely the mass conservation principle. The equation that represents such a principle is called the ‘conservation equation’ or the ‘equation of change’ which describes the system.