Download e-book for kindle: The Physics of Fluids in Hierarchical Porous Media: by John H. Cushman

Environmental Studies

By John H. Cushman

ISBN-10: 9048149096

ISBN-13: 9789048149094

ISBN-10: 940158849X

ISBN-13: 9789401588492

Porous media are ubiquitous all through nature and in lots of smooth applied sciences. as a result of their omnipresent nature, porous media are studied to 1 measure or one other in just about all branches of technology and engineering. this article is an outgrowth of a two-semester graduate direction on multiscale porous media provided to scholars in utilized math, physics, chemistry, engineering (civil, chemical, mechanical, agricultural), and environmental and soil technological know-how. The textual content is basically in response to Dr Cushmans' teams efforts to construct a rational method of learning porous media over a hierarchy of spatial and temporal scales. No different textual content covers porous media on scales starting from angstroms to miles. Nor does the other textual content advance and use this sort of range of instruments for his or her examine. The textual content is designed to be self-contained, because it provides all appropriate mathematical and actual constructs.

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Additional resources for The Physics of Fluids in Hierarchical Porous Media: Angstroms to Miles

Example text

G. 6) where Fa is the force conjugate to Aa, and the internal energy &(t) = &(A1 (t), ... An(t), e). 8) -Fa dAa+ aede. For a quasi-static adiabatic process between neighboring states we have

500 X 0 LL... 1. of [37]. 500 •• C\J X 0 LL... 2. 00 F 2 {X), X= lkla, adapted from Figure 2 of [37]. 2. SEQUENTIAL FILTERING Let us next generalize this example a little further. At . 0~ (11113) . A, the measured value of¢ corresponds to the true value of¢. W.. A)- 1 . A. At 1. N and We call it an ideal filter because there is one range of length scales [I! , we keep usable (needed) information on¢ in perfect condition and yet totally destroy unwanted smaller-scale information. The functions I a,N+1 and I a,N are graphed in Figs.

HOMOGENEOUS ELASTIC SOLID WITH SMALL DEFORMATION (INFINITESIMAL-STRAIN, TEMPERATURE REPRESENTATION) In experiments, entropy is not a controllable parameter, but temperature often is controllable. As such, it is a more appropriate choice for an independent variable. For small deformation, the infinitesimal strain is also more appropriate as an independent variable than is the deformation gradient. To transfer to a temperature representation we replace the internal energy density, E, with its Legendre transform (Helmholz energy density) A=E-TrJ.

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The Physics of Fluids in Hierarchical Porous Media: Angstroms to Miles by John H. Cushman

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