Effective transport properties of disordered, multi-phase composites: Application of real-space renormalization group theory

Shah, N.; Ottino, Julio M.

doi:10.1016/0009-2509(86)87009-9

Cited by 53 publications

(14 citation statements)

References 33 publications

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“…In position space renormalization group (PSRG) theory (Stinchcombe and Watson, 1976;Bernasconi, 1978;Reynolds et al, 1980;Tsallis et al, 1983;Shah and Ottino, 1986), the original network is divided into identical unit cells of linear dimension b. Figure l a shows such a unit cell with b = 2 for a simple cubic network.…”

Section: Theorymentioning

confidence: 99%

Prediction of the effective diffusivity in pore networks close to a percolation threshold

Zhang

Seaton

1992

AIChE Journal

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Section: Theorymentioning

confidence: 99%

Prediction of the effective diffusivity in pore networks close to a percolation threshold

Zhang

Seaton

1992

AIChE Journal

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“…Other applications to percolating systems include the calculation of the effective conductance of lattices (Bernasconi, 1978) and composites (Shah and Ottino, 1986), the effective permeability of rocks (King, 1989), effective dispersivities of flows (Jaekel and Vereecken, 1997), the effective hydraulic conductivity of heterogeneous media (Hristopulos and Christakos, 1999;Renard et al, 2000), and the effective elastic properties of porous media (Poutet et al, 1996).…”

Section: Renormalizationmentioning

confidence: 99%

On predicting the effective elastic properties of polymer bonded explosives using the recursive cell method

Banerjee

Adams

2004

International Journal of Solids and Structures

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“…For example, the inversion schemes put forward by Budiansky and O'Connell [ 1976]; Cruz Orive [1976] or Gokhale [1996] involve integration of elliptic integrals, the value of which are highly dependent on accurate measurements. These two simplifications make the computations much less complex [Shah and Ottino, 1986;Williams, 1992]. Last, Madden [1983] showed that a 2 x 2 x 2 network is fairly accurate, causing errors of less than 4%.…”

Section: 776mentioning

confidence: 99%

Effect of semibrittle deformation on transport properties of calcite rocks

Siddiqi¹,

Evans²,

Dresen³

et al. 1997

J. Geophys. Res.

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Abstract. We investigated the effect of mechanical deformation on transport properties by deforming synthetic calcite/quartz aggregates to strains (e) up to 5øA at confining pressures (Pc) up to 300 MPa, and at temperatures (T) from 300 K to 873 K. Subsequently, we measured permeability (k) using a wide-range permeameter at effective pressures (Pc) of 15-155 MPa and room temperature. We then measured electrical conductivity (rr) in an impedancemeasuring assembly over the same pressure range at room temperature. The values of permeability and conductivity of the undeformed material at Pe=100 MPa were 4xl 0 -28 m 2 and 0.07 S/m. Samples deformed at 673 K and P½=200 MPa, or at room temperature and P½=50-300 MPa, show small variations in permeability and conductivity: k changed only by up to a factor of 3 and c• increased by up to 10%. But, when a sample was deformed at 873 K and P½=200 MPa, electrical conductivity dropped by 1 order of magnitude and permeability dropped by 2 orders of magnitude. To assess whether changes in length scales of the pore structure owing to deformation may account for large variation in transport properties, we counted cracks and pores, measured their lengths and widths, defined a damage parameter (•), and computed effective hydraulic and electrical conductivity using renormalization group methods. The undeformed rocks and the samples deformed at low confining pressure have severe damage, appear to be close to failure, and hence have high transport coefficients. Materials deformed at high pressures and temperatures have lower flaw densities, cormectivities, and transport coefficients after deformation. We found that renormalization methods are suitable to model connectivity loss and large changes in transport properties owing to changes in flaw density and length scales. Pore connectivity and transport properties vary strongly during semibrittle deformation.

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Effective transport properties of disordered, multi-phase composites: Application of real-space renormalization group theory

Cited by 53 publications

References 33 publications

Prediction of the effective diffusivity in pore networks close to a percolation threshold

Prediction of the effective diffusivity in pore networks close to a percolation threshold

On predicting the effective elastic properties of polymer bonded explosives using the recursive cell method

Effect of semibrittle deformation on transport properties of calcite rocks

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