Abstract
Models simulating the propagation of acoustic waves in the successive stages of the gelation process are presented. The early stage of gelation has been considered with scattering theory for very low concentrations of suspensions. The system may be simulated by the line of the independent Maxwell elements. When concentration of the suspension increases, the interaction of the particles can be presented by an acoustic model, which consist of a chain of coupled Maxwell elements. After the gelation point, the system becomes rigid, and three dimensional tensoral fields distribution of stress and strain was used.References
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[2] Chemical processing of ceramics, B.J. Lee, E.J.A. Pope [Eds.], New York 1994.
[3] D. Stauffer, Gelierungstheorie — Vers¨aumte Zusammenarbeit von Physik und Chemie, Ber. Bunsenges. Phys. Chem., 102, 1672–1678 (1998).
[4] Farady Discussions-Gels, 101 (1995).
[5] J. Ranachowski and T. Łas, Non-destructive testing of some dielectric solids materials [in Polish], [in:] The Present Problems of the High Voltage Technology, PWN, Warszawa 1965, 365–397.
[6] J. Ferguson and Kembłowski, Applied rheology of fluids, MARCUS, Łódz 1995.
[7] R. De Boer and W. Ehlery, A historical review of the formulation of porous medies theories, Acta Mech., 74, 1–8 (1998).
[8] M.A. Biot, Theory of propagation of elastic waves in a fluid-saturated porous solid, J. Acoust. Soc. Am., 28, 168–191 (1956).
[9] M.A. Biot and D.G. Willis, The elastic coefficients of the theory of consolidation, J. Appl. Mech., 24, 594–601 (1957).
[10] W. Phillipoff, Relaxations in polymer solutions. Liquids and gels, Physical Acoustics, P. Mason [Ed.], New York, Vol. II, part B (1965), 1–90.
[11] R.S. Marvin and H. Oeser, Distribution of relaxation times, J. Research Nat. Bur. Standards, B66, 171–177 (1962).
[12] J. Lewandowski, Acoustic and effective material parameters of heterogeneous viscoelastic bodies, Acta Mech., 57, 143–158 (1985).
[13] J. Lewandowski, Acoustic and dynamic properties of two-phase media with non-spherical inclusions, Ultrasonics, 33, 61–68 (1995).
[14] J.J. McCoy, A theory of stress wave propagation through inhomogeneous solids, J. Appl. Mech., 44, 462–471 (1977).
[15] I. Malecki and J. Ranachowski, The acoustic cross-section method for evaluation of porous material parameters, Bull. Pol. Ac. Sci., Ser. Tech. Sci., 45, 43–56 (1997).
[16] P.R. Williams and R.L. Williams, Rheometrical aspects of the viscoelastic dispersion of shear waves in gel-like mechanical network, J. Non-Newtonian Fluid Mech., 78, 203–225 (1998).
