ISOTHERMAL DISSOLUTION OF A SPHERICAL PARTICLE WITH A MOVING BOUNDARY IN A FLOW FIELD

  • E. Vázquez-Nava Centro de Investigaciones en Ciencia y Tecnología de los Alimentos, Instituto de Ciencias Agropecuarias, Universidad Autónoma del Estado de Hidalgo
  • C. J. Lawrence Department of Chemical Engineering and Chemical Technology, Imperial College London
Keywords: dissolution, moving boundary, spherical particle, Stokes flow, shear flow

Abstract

Numerical solution for isothermal dissolution process of a spherical particle with a moving boundary and the presence of hydrodynamics effects of two different flow fields in a binary solution is described in this paper. The flow fields considered are slow viscous flow or Stokes flow and straining motion or shear flow around the particle. The parabolic differential equations were discretised with finite difference method in space, and the resulting set of ordinary differential equations on time was solved by the method of lines. The analysis includes the radial convective term generated due to the density differences between the solid and liquid phases. The effect due to the natural convection caused by density differences between both phases are evaluated and compared with the effect due to the low Reynolds convective flow field. The numerical solution for the isothermal dissolution of a spherical particle in a binary melt is not only compared with integral method for small times of the process but also the results are verified with mass balance integration. The integral method solutions are found to agree with the numerical results for small time of dissolution.

References

Beerkens, R.G.C., Muijsenberg, H.P.H.,Van der Heijden, T. (1994). Modelling of sand grain dissolution in industrial glass melting tanks. Glasstech. Ber. Glass Science Technology 67 (7), 179-188.

Bird, R.B., Stewart, W.E., Lighfoot, E. (1960). Transport Phenomena. John Wiley & Sons, Inc., New York.

Bodalbhai, L., Hrma, P. (1986). The dissolution of silica grains in isothermally heated batches of sodium carbonate and silica sand. Glass Technology 27 (2), 72-78.

Caldwell, J., Chiu, C.K. (2000). Numerical solution of one-phase Stefan problems by the heat balance integral method, Part I – Cylindrical and spherical geometries. Communications in Numerical Methods in Engineering 16, 569-583.

Cable, M., Frade, J.R. (1987a). The diffusioncontrolled dissolution of spheres. Journal of Material Science 22, 1894-1900.

Cable, M., Frade, J.R. (1987b). Diffusion-controlled mass transfer to or from spheres with concentration-dependent diffusivity. Chemical Engineering Science 42(11), 2525-2530.

Cable, M., Frade, J.R. (1994). Diffusion-controlled growth or dissolution of spheres with variable temperature. Journal of the American Ceramic Society 77 (4), 999-1004.

Gelder, D., Guy, A.G. (1975). Current problems in the glass industry. In Ockendon and Hodgkins (1975), pp 71-90.

Hrma, P. (1980) A kinetic equation for interaction between grain material and liquid with application to glass melting. Silikaty 24, 7-16.

Hrma, P. (1982) Thermodynamics of batch melting. Glasstech. Ber. Glass Science Technology 55, (7), 138-150.

Mei, R., Lawrence, C.J. (1996). The flow fiel due to a body in impulsive motion. Journal of Fluid Mechanics 325, 79-111.

Nemec, L. (1995a). Energy consumption in the glass melting process. Part 1: Theoretical relations. Glasstech. Ber. Glass Science Technology 68(1), 1-10.

Nemec, L. (1995b). Energy consumption in the glass melting process. Part 2: Results of calculations. Glassteck.Ber. Glass Science Technology 68, (2), 39-49.

Nemec, L. (1995c). Some critical points of the glassmelting process: Part 1: Dissolution phenomena. Ceramics-Silikaty 39 (3), 81-86.

Ockendon, J.T., Hodkins, W.R. (1975) Moving boundary problems in heat flow and diffusion. Clarendon Press, Oxford.

Readey, D.W., Cooper, Jr. A.R. (1966). Molecular diffusion with a moving boundary and spherical symmetry. Chemical Engineering Science 21, 917-922

Ruckenstein, E., Davis, E.J. (1970). Diffusioncontrolled growth or collapse of moving and stationary fluid spheres. Journal of Colloid and Interface Science 34 (1), 142-158.

Shastri, S.S., Allen, R.M. (1998). Method of lines and enthalpy method for solving moving boundary problems. International Communications of Heat and Mass Transfer 25(4), 531-540.

Vázquez-Nava, E. (2005). Thermal and Isothermal Dissolution of a Spherical Particle. PhD Thesis. Imperial College London.
Published
2020-07-13
How to Cite
Vázquez-Nava, E., & Lawrence, C. J. (2020). ISOTHERMAL DISSOLUTION OF A SPHERICAL PARTICLE WITH A MOVING BOUNDARY IN A FLOW FIELD. Revista Mexicana De Ingeniería Química, 6(2), 157-168. Retrieved from http://www.rmiq.org/ojs311/index.php/rmiq/article/view/1891
Section
Transport phenomena