Effective properties of suspensions/emulsions, porous and composite materials V.M. Starov ⁎ , V.G. Zhdanov Department of Chemical Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK Available online 16 January 2007 Abstract A new method (a version of a mean field method) is suggested to calculate effective properties of suspensions/emulsions, porous and dispersed materials. The aim is to demonstrate a wide range of applicability of the new method. To show the idea of the new method the dependence of the effective diffusion coefficient in the porous medium on the porosity is deduced. Based on the same method the following dependences are deduced: the effective viscosity of suspensions and emulsions as functions of volume fraction of suspended particles or droplets, elastic modules of rubber/polymer sheets with cracks and elastic modules of composite materials on the volume fraction of inclusions in the case of an arbitrary number of different types of inclusions. In all cases the calculated dependences are compared with available experimental data and published theoretical models. © 2006 Elsevier B.V. All rights reserved. Contents 1. Introduction ............................................................... 2 2. Effective diffusion in porous media ................................................... 3 3. Viscosity of concentrated suspensions: Influence cluster formation ................................... 4 3.1. Comparison with experimental data ............................................... 6 4. Viscosity of concentrated emulsions ................................................... 8 4.1. Developed flocculation ...................................................... 9 4.2. Low flocculated emulsions: transition to developed flocculation................................ 10 5. Effective viscosity and permeability of porous media ......................................... 12 6. Elastic properties of rubber/polymer sheets with cracks ........................................ 13 7. Elastic properties of composite materials with different types of inclusions.............................. 14 7.1. Calculation of the effective elastic modules in the case of only one type of inclusions .................... 15 Acknowledgement ............................................................. 16 Appendix A1. Calculation of the effective diffusion coefficient using the cell method........................... 16 Appendix A2. Calculation of the diffusion coefficient using the suggested new method .......................... 17 References ................................................................. 16 1. Introduction The differential method, which is a version of a mean field method, has been originally developed for the calculation of the effective dielectric constant of suspensions and emulsions [1]. The further theoretical approximations for calculations of the effective dielectric constant of emulsions are presented in [2]. The comparison of the different theoretical methods with experimental data is given in Fig. 1 [6]. The curve 3 is drawn according to the deduced equation [1] shows the best agreement with the available experimental data. Unfortunately, neither in the original paper [1] nor in the subsequent publications (see for Advances in Colloid and Interface Science 137 (2008) 2 – 19 www.elsevier.com/locate/cis ⁎ Corresponding author. E-mail addresses: V.M.Starov@lboro.ac.uk (V.M. Starov), V.G.Zhdanov@lboro.ac.uk (V.G. Zhdanov). 18 0001-8686/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cis.2006.11.025