Advertisement

Mass Transfer

  • Günter BrennEmail author
Chapter
Part of the Mathematical Engineering book series (MATHENGIN)

Abstract

The present chapter discusses problems of mass transport which may be solved analytically. The processes may consist of mass transport by equimolar diffusion, which involves the diffusion equation as the underlying differential equation for the spatiotemporal evolution of the species concentration. As far as convective processes are concerned, the intention to have analytical descriptions clearly puts the restriction to laminar flow in simple geometries.

Keywords

Schmidt Number Sherwood Number Droplet Surface Oblate Spheroid Prolate Spheroid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Abramowitz, M., Stegun, I.A. (eds.): Handbook of Mathematical Functions, pp. 503–535. Dover, New York (1972)Google Scholar
  2. 2.
    Abramzon, B., Sirignano, W.A.: Approximate theory of a single droplet vaporization in a convective field: effects of variable properties, Stefan flow and transient liquid heating. In: Proceedings of the 2nd ASME-JSME Thermal Engineering Joint Conference, vol. 1, Honolulu (Hawaii) (1987), 11–18Google Scholar
  3. 3.
    Baehr, H.D., Stephan, K.: Wärme- und Stoffübertragung (Heat and Mass Transfer, in German), 3rd edn. Springer, Berlin, Heidelberg, New York (1998)CrossRefGoogle Scholar
  4. 4.
    Borchers, W.: University of Erlangen-Nürnberg (Germany), private communication (2002)Google Scholar
  5. 5.
    Brenn, G.: Concentration fields in evaporating droplets. Int. J. Heat Mass Transfer 48, 395–402 (2005)CrossRefzbMATHGoogle Scholar
  6. 6.
    Brenn, G., Wiedemann, T., Rensink, D., Kastner, O., Yarin, A.L.: Modeling and experimental investigation of the morphology of spray dryed particles. Chem. Eng. Technol. 24, 1113–1116 (2001)CrossRefGoogle Scholar
  7. 7.
    Brenn, G., Yarin, A.L.: Diffusive mass transfer from free and pendant drops. In: Proceedings of the 17\(^{th}\) Annual Conference Liquid Atomiz. and Spray Syst. (ILASS Europe), Zürich, 2–6 September 2001, abstract p. 56 (2001)Google Scholar
  8. 8.
    Brodkey, R.S.: The Phenomena of Fluid Motions. Addison-Wesley, Reading (MA, USA) (1967)Google Scholar
  9. 9.
    Charlesworth, D.H., Marshall, W.R.: Evaporation from drops containing dissolved solids—Parts I and II. AIChE J 6, 9–23 (1960)CrossRefGoogle Scholar
  10. 10.
    Clift, R., Grace, J.R., Weber, M.E.: Bubbles, Drops, and Particles. Academic Press, New York (1978)Google Scholar
  11. 11.
    Duffie, J.A., Marshall, W.R.: Factors influencing the properties of spray-dried materials—Part I. Chem. Eng. Prog. 49, 417–423 (1953)Google Scholar
  12. 12.
    Duffie, J.A., Marshall, W.R.: Factors influencing the properties of spray-dried materials—Part II. Chem. Eng. Prog. 49, 480–486 (1953)Google Scholar
  13. 13.
    Ford, I.J.: Models of crystallisation in evaporating droplets. Mater. Res. Soc. Symp. Proc. 398, 637–642 (1996)CrossRefGoogle Scholar
  14. 14.
    Frössling, N.: Über die Verdunstung fallender Tropfen (On the evaporation of falling drops, in German). Gerlands Beiträge zur Geophysik 52, 171–216 (1938)Google Scholar
  15. 15.
    Incropera, F.P., DeWitt, D.P., Bergman, T.L., Lavine, A.S.: Principles Heat Mass Transfer, 7th edn. Wiley, New York (2013)Google Scholar
  16. 16.
    Kamke, E.: Differentialgleichungen - Lösungsmethoden und Lösungen. Volume I. In: Gewöhnliche Differentialgleichungen (Differential Equations—Solution Methods and Solutions. vol. I, Ordinary Differential Equations, in German). B.G. Teubner, Stuttgart (Germany) (1983)Google Scholar
  17. 17.
    Makino, A., Law, C.K.: On the controlling parameter in the gasification behaviour of multicomponent droplets. Combust. Flame 73, 331–336 (1988)CrossRefGoogle Scholar
  18. 18.
    Masliyah, J.H., Epstein, N.: Numerical solution of heat and mass transfer from spheroids in steady axisymmetric flow. Proc. Int. Sympos. Two-Phase Systems (Prog. Heat Mass Transfer 6), 613–632 (1972)Google Scholar
  19. 19.
    Morse, P.M., Feshbach, H.: Methods of Theoretical Physics Part II. McGraw Hill, New York (1961)zbMATHGoogle Scholar
  20. 20.
    Ranz, W.E., Marshall, W.R.: Evaporation from drops—Part II. Chem. Eng. Progr. 48, 173–180 (1952)Google Scholar
  21. 21.
    Sano, Y., Keey, R.B.: The drying of a spherical particle containing colloidal material into a hollow sphere. Chem. Eng. Sci. 37, 881–889 (1982)CrossRefGoogle Scholar
  22. 22.
    Tonini, S., Cossali, G.E.: An exact solution of the mass transport equations for spheroidal evaporating drops. Int. J. Heat Mass Transfer 60, 236–240 (2013)CrossRefGoogle Scholar
  23. 23.
    Yarin, A.L., Brenn, G., Kastner, O., Rensink, D., Tropea, C.: Evaporation of acoustically levitated droplets. J. Fluid Mech. 399, 151–204 (1999)CrossRefzbMATHGoogle Scholar
  24. 24.
    Yarin, A.L., Brenn, G., Kastner, O., Tropea, C.: Drying of acoustically levitated droplets of liquid-solid suspensions: evaporation and crust formation. Phys. Fluids 14, 2289–2298 (2002)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Institute of Fluid Mechanics and Heat TransferGraz University of TechnologyGrazAustria

Personalised recommendations