A diagrammatic approach to response problems in composite systems

The bulk macroscopic response of a system of particles or inclusions with field-induced forces is studied. The susceptibilities and transport coefficients in such a system are expressed as averages of a multiple scattering expansion. A special diagrammatic method is developed to analyze the structure of the expansion. The concept of irreducibility is discussed in detail and shown to be crucial in obtaining macroscopic equations characterizing the system response with coefficients depending solely on local properties of the medium. Due to the representation of particles by lines in diagrams, irreducibility is given a particularly simple topological interpretation in the diagrammatic language. The method is illustrated by a discussion of response problems in colloidal suspensions in presence of hydrodynamic interactions.

[1]  B. U. Felderhof.  Many-body hydrodynamic interactions in suspensions , 1988 .

[2]  Dick Bedeaux,et al.  On the critical behaviour of the dielectric constant for a nonpolar fluid , 1973 .

[3]  B. U. Felderhof,et al.  Linear response theory of sedimentation and diffusion in a suspension of spherical particles , 1983 .

[4]  Russel E. Caflisch,et al.  Variance in the sedimentation speed of a suspension , 1985 .

[5]  Geoffrey F. Hewitt,et al.  Multiphase Science And Technology , 1999 .

[6]  J. C. Garland,et al.  Electrical transport and optical properties of inhomogeneous media , 1978 .

[7]  P. Szymczak,et al.  Memory effects in collective dynamics of Brownian suspensions. , 2004, The Journal of chemical physics.

[8]  P. Nozières.  A local coupling between sedimentation and convection: Application to the Beenakker-Mazur effect , 1987 .

[9]  S. Torquato,et al.  Random Heterogeneous Materials: Microstructure and Macroscopic Properties , 2005 .

[10]  G. Batchelor,et al.  Sedimentation in a dilute polydisperse system of interacting spheres. Part 1. General theory , 1982, Journal of Fluid Mechanics.

[11]  S. Torquato.  Random Heterogeneous Materials , 2002 .

[12]  B. U. Felderhof,et al.  Friction matrix for two spherical particles with hydrodynamic interaction , 1982 .

[13]  C. Beenakker.  The effective viscosity of a concentrated suspension of spheres (and its relation to diffusion) , 1984 .

[14]  Paul M. Chaikin,et al.  Long-range correlations in sedimentation , 1997 .

[15]  B. U. Felderhof,et al.  Cluster expansion for the dielectric constant of a polarizable suspension , 1982 .

[16]  M. Michels.  The convergence of integral expressions for the effective properties of heterogeneous media , 1989 .

[17]  B. U. Felderhof.  Brownian motion and creeping flow on the Smoluchowski time scale , 1987 .

[18]  B. U. Felderhof,et al.  The effective viscosity of suspensions and emulsions of spherical particles , 1989 .

[19]  I. R. Mcdonald,et al.  Theory of simple liquids , 1998 .

[20]  E. J. Hinch,et al.  Particle velocity fluctuations and hydrodynamic self-diffusion of sedimenting non-Brownian spheres , 1995 .

[21]  J. D. Ramshaw.  Existence of the dielectric constant in nonpolar fluids , 1972 .

[22]  P. Mazur,et al.  A generalization of faxén's theorem to nonsteady motion of a sphere through a compressible fluid in arbitrary flow , 1974 .

[23]  G. Batchelor,et al.  Sedimentation in a dilute polydisperse system of interacting spheres. Part 2. Numerical results , 1982, Journal of Fluid Mechanics.

[24]  Anda,et al.  Diagrammatic approach to the effective dielectric response of composites. , 1989, Physical Review B (Condensed Matter).

[25]  G. W. Ford,et al.  THE THEORY OF LINEAR GRAPHS WITH APPLICATIONS TO THE THEORY OF THE VIRIAL DEVELOPMENT OF THE PROPERTIES OF GASES , 1964 .

[26]  Elisabeth Guazzelli,et al.  EFFECT OF THE VESSEL SIZE ON THE HYDRODYNAMIC DIFFUSION OF SEDIMENTING SPHERES , 1995 .

[27]  B. Cichocki,et al.  Stokesian Dynamics—The BBGKY Hierarchy for Correlation Functions , 2008 .

[28]  B. U. Felderhof,et al.  Renormalized cluster expansion for multiple scattering in disordered systems , 1988 .

[29]  R. Balescu.  Equilibrium and Nonequilibrium Statistical Mechanics , 1991 .

[30]  P. Szymczak,et al.  Memory function for collective diffusion of interacting Brownian particles , 2002 .

[31]  Rolf Landauer,et al.  Electrical conductivity in inhomogeneous media , 2008 .

[32]  J. Kirkwood.  On the Theory of Dielectric Polarization , 1936 .

[33]  SOME THEORETICAL RESULTS FOR THE MOTION OF SOLID SPHERICAL PARTICLES IN A VISCOUS FLUID , 1989 .

[34]  E. Anda,et al.  A new diagrammatic summation for the effective dielectric response of composites , 1992 .