Diffusion with Chemical Reaction in Biological Systems

  • Pieter Stroeve
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 191)


The interplay between diffusion and chemical transformation takes place in practically an infinite number of systems, either in nature or in the chemical industry. A variety of academic disciplines have actively studied the phenomena of diffusion with chemical reaction in order to understand the basic laws and to utilize them in predicting the behavior of systems or to design chemical processes which produce desirable species. Obviously, the study of mass transport and chemical transformation in biological systems is of great importance in the biological sciences. Likewise, the chemical reactions of molecules in industrial systems often involve significant diffusion effects and the interplay of the two effects needs to be understood to design efficient chemical systems. The laws that describe diffusion with chemical reaction are very general and apply to very disparate systems. As was pointed out by Weisz (1973) in an informative review article, discoveries made in various disciplines often were made independently of each other. The emergence of the interdisciplinary field of bioengineering has helped in bringing together knowledge developed in engineering, the pure and the biological sciences.


Mass Transfer Coefficient Oxygen Transport Mass Transfer Rate Reaction Front Damkohler Number 
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  1. Aris, R., 1957, On shape factors for irregular particles — I. the steady state problem. Diffusion and reaction, Chem. Eng. Sci., 6, 262–268.CrossRefGoogle Scholar
  2. Aris, R., 1975, The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts, Vol. 1. Clarendon Press, Oxford, England.Google Scholar
  3. Astarita, G., 1967, Mass Transfer with Chemical Reaction, Elsevier, Amsterdam, The Netherlands.Google Scholar
  4. Astarita, G., Savage, D.W., and Bisio, A., 1983, Gas Treating with Chemical Solvents. Wiley-Interscience, New York, U.S.A.Google Scholar
  5. Bailey, J.E., and Ollis, D.F., 1977, Biochemical Engineering Fundamentals, McGraw-Hill, New York, U.S.A.,Google Scholar
  6. Bauer, C., Gros, H., and Bartels, H., eds., 1980, Biophysics and Physiology of Carbon Dioxide, Springer, Berlin, West Germany.Google Scholar
  7. Bird, R.B., Stewart, W.E., and Lightfoot, E.N., 1960, Transport Phenomena. Wiley, New York, U.S.A.Google Scholar
  8. Bouwer, S., Hoofd, L., and Kreuzer, F., 1984, Private communications, University of Nijmegen, The Netherlands.Google Scholar
  9. Damköhler, G., 1937, Einfluss von Diffusion, Strömung und Warmte-transport auf die Ausbeute bei chemisch-technischen Reaktionen, in: Der Chemieingenieur., A. Eucken, M. Jacob, eds. Bd. 3, Teil, p. 359., Leipzig, Germany.Google Scholar
  10. Danckwerts, P.V., 1970, Gas-Liquid Reactions. McGraw-Hill, New York, U.S.A.CrossRefGoogle Scholar
  11. De Koning, J., Hoofd, L.J.C., and Kreuzer, F., 1981, Oxygen Transport and the function of myoglobin. Theoretical model and experiments in chicken gizzard smooth muscle. Pflügers Arch., 389, 211–217.PubMedCrossRefGoogle Scholar
  12. Dorson, W.J., and Voorhees, M.E., 1976, Analysis of oxygen and carbon dioxide transfer in membrane lungs, in: Artificial Lungs for Acute Respiratory Failure. Theory and Practice. W.M. Zapol and J. Qvist, eds., p. 43, Academic Press, New York, U.S.A.Google Scholar
  13. Friedlander, S.K., and Keller, K.H., 1965, Mass transfer in reacting systems near equilibrium, Use of the affinity function. Chenu Eng. Sci., 20, 121–129.CrossRefGoogle Scholar
  14. Gallagher, P.M., Athayde, A.L., and Ivory, C.F., 1984, The facilitated transport of carbon dioxide through aqueous bicarbonate membranes. I. Formulation and solution. Unpublished manuscript, Notre Dame University, U.S.A..Google Scholar
  15. Goddard, J.D., 1977, Further applications of carrier-mediated transport theory, A survey. Chem. Eng. Sci., 32, 795–809.CrossRefGoogle Scholar
  16. Goddard, J.D., 1981a, Electric field effects in carrier-mediated ion transport, AIChE Symp. Ser., 77(202), 114–122.Google Scholar
  17. Goddard, J.D., 1981b, A model of facilitated transport in concentrated two-phase dispersions, Chem. Engr. Commun., 9, 345–361.CrossRefGoogle Scholar
  18. Goddard, J.D., Schultz, J.S., and Suchdeo, S.R., 1974, Facilitated transport via carrier-mediated diffusion in membranes: Part II. Mathematical aspects and analysis, AIChE Journ., 20, 625–645.CrossRefGoogle Scholar
  19. Gros, G., and Moll, W., 1974, Facilitated diffusion of CO2 across albumin solutions, J. Gen. Physio1., 64, 356–371.CrossRefGoogle Scholar
  20. Hatta, S., 1928, On the absorption velocity of gases by liquids. I. Absorption of carbon dioxide by potassium hydroxide solution, Techno1. Report Tohoku Imperial University (Japan), 8, 1–25.Google Scholar
  21. Hill, A.V., 1928, The diffusion of oxygen and lactic acid through tissues, Proc. Roy. Soc, B104, 39–96.Google Scholar
  22. Hoofd, L., and Kreuzer, F., 1981, The mathematical treatment of steady state diffusion of reacting species, AIChE Symp. Ser., 77(202), 123–129.Google Scholar
  23. Ivory, C.F., 1982, Forced facilitation in carrier-mediated transport. Paper 51f. AIChE Meeting, November 14–19, Los Angeles, California, U.S.A..Google Scholar
  24. Kawashiro, T., and Scheid, P., 1976, Measurement of Krogh’s diffusion constant of CO2 in respiring muscle at various CO2 levels: Evidence for facilitated diffusion, Pflügers Arch. 362, 127–133.PubMedCrossRefGoogle Scholar
  25. Klug, A., Kreuzer, F., and Roughton, F.J.W., 1956a, Simultaneous diffusion and chemical reaction in thin layers of haemoglobin solution. Proc. Roy. Soc. B., 145, 452–472.CrossRefGoogle Scholar
  26. Klug, A., Kreuzer, F., and Roughton, F.J.W., 1956b, The diffusion of oxygen in concentrated haemoglobin solutions, Helv. Physiol. Pharm. Acta., 14, 121–128.Google Scholar
  27. Kreuzer, F., 1970, Facilitated diffusion of oxygen and its possible significance: a review, Respir. Physiol., 9, 1–30.PubMedCrossRefGoogle Scholar
  28. Kreuzer, F., and Hoofd, L., 1984, Facilitated diffusion of O2 and CO2, in: Handbook of Physiology, Am. Physiol. Soc. Washington, D.C., U.S.A., in press.Google Scholar
  29. Kutchai, H., Jacquez, J.A., and Mather, F.J., 1970, Nonequilibrium facilitated oxygen transport in hemoglobin solution, Biophys J., 10, 38–54.PubMedCrossRefGoogle Scholar
  30. Kutchai, H., and Staub, N.C., 1969, Steady-state, hemoglobin-facilitated O2 transport in human erythrocytes, J. Gen. Physio1., 53, 576–589.CrossRefGoogle Scholar
  31. Lightfoot, E.N., 1968, Low-order approximations for membrane blood oxygenators, AIChE J., 14, 669–670.CrossRefGoogle Scholar
  32. Longmuir, I.S., Forster, R.E., and Woo, C.-Y., 1966, Diffusion of carbon dioxide through thin layers of solution, Nature, 209, 393–394.CrossRefGoogle Scholar
  33. Meldon, J.H., De Koning, J., and Stroeve, P., 1978, Electrical potentials induced by CO2 gradients in protein solutions and their role in CO2 transport, Bioelectrochem. Bioenerg., 5, 77–87.CrossRefGoogle Scholar
  34. Meldon, J.H., and Kang, Y.-S., 1983, The transport of carbon dioxide in purified protein solutions, AIChE Symp. Ser., 79 (227), 36–42.Google Scholar
  35. Meldon, J.H., Stroeve, P., and Gregoire, C.E., 1982, Facilitated transport of carbon dioxide: A review, Chem. Eng. Commun., 16, 263–300.CrossRefGoogle Scholar
  36. Nernst, W., 1904, Theorie der Reaktionsgeschwindigkeit in heterogenen Systemen, Z. Phys. Chem., 47, 52–79.Google Scholar
  37. Oomens, J.M.M., De Koning, J., and Stroeve, P., 1977, A comparison of oxygen transfer into hemoglobin solutions and whole blood flowing in rectangular channels, AIChE J., 23, 390–393.CrossRefGoogle Scholar
  38. Roughton, F.J.W., 1952, Diffusion and chemical reaction velocity in cylindrical and spherical systems of physiological interest, Proc. Roy. Soc. London B, 140, 203–229.CrossRefGoogle Scholar
  39. Ryan, D., Carbonell, R.G., and Whitaker, S., 1981, A theory of diffusion and reaction in porous media, AIChE Symp. Ser., 77 (202), 46–62.Google Scholar
  40. Sasidhar, V., Ruckenstein, E., 1983, Relaxation method for facilitated transport, J. Membr. Sci., 13, 67–84.CrossRefGoogle Scholar
  41. Scholander, P.F., 1960, Oxygen transport through hemoglobin solutions, Science, 131, 85–90.CrossRefGoogle Scholar
  42. Schultz, J.S., Goddard, J.D., Suchdeo, S.R., 1974, Facilitated transport via carrier-mediated diffusion in membranes. Part I. Mechanistic aspects, experimental systems and characteristic regimes, AIChE J., 20, 417–445.CrossRefGoogle Scholar
  43. Slattery, J.C., 1981, Momentum, Energy and Mass Transfer in Continua, Krieger, Huntington, N.Y., U.S.A..Google Scholar
  44. Smith, K.A., Meldon, J.H. and Colton, C.K., 1973, An analysis of carrier-facilitated transport, AIChE J., 19, 102–111.CrossRefGoogle Scholar
  45. Spaan, J.A.E., 1973, Transfer of oxygen into haemoglobin solution, Pflügers Arch. ges. Physiol., 342, 289–306.CrossRefGoogle Scholar
  46. Stroeve, P., 1984, Diffusion with Chemical Reaction in Two-Phase Heterogeneous Media, in: Advances in Transport Processes, Vol. Ill, p. 361–386, A.S. Mujumdar, R.A. Mashelkar, eds., Wiley Eastern, New Delhi, India.Google Scholar
  47. Stroeve, P., Smith, K.A., and Colton, C.K., 1976a, Facilitated diffusion of oxygen in red blood cell suspensions, Adv. Exptl. Med. and Biol., 75, 191–198.Google Scholar
  48. Stroeve, P., Smith, K.A., and Colton, C.K., 1976b, An analysis of carrier facilitated transport in heterogeneous media, AIChE J., 22, 1125–1132.CrossRefGoogle Scholar
  49. Stroeve, P., Colton, C.K., and Smith, K.A., 1976c, Steady state diffusion of oxygen in red blood cell and model suspensions, AIChE J., 22, 1133–1142.CrossRefGoogle Scholar
  50. Stroeve, P., and Ziegler, E.M., 1980, The transport of carbon dioxide in high molecular weight buffer solutions, Chem. Eng. Commun., 6, 81–103.CrossRefGoogle Scholar
  51. Stroeve, P., Ward, W.J., 1981, Transport with chemical reactions, AIChE Symp. Ser., 202, Vol. 77.CrossRefGoogle Scholar
  52. Thiele, E.W., 1939, Relation between catalytic activity and size of particle. Industrial Engr. Chem., 31, 916–920.CrossRefGoogle Scholar
  53. Weisz, P.B., 1973, Diffusion and chemical transformation. An interdisciplinary excursion, Science, 179, 433–440.PubMedCrossRefGoogle Scholar
  54. Weisz, P.B., and Prater, C.D., 1954, Interpretation of measurements in experimental catalysis. Adv. Cata1ysis, 6, 143–207.CrossRefGoogle Scholar
  55. Whitaker, S., 1973, The transport equations for multi-phase systems, Chem. Engr. Sci., 28, 139–147.CrossRefGoogle Scholar
  56. Whitaker, S., 1983, Transport processes with heterogeneous reaction, 25th Conicet Anniversary Reactor Design Conference, Santa Fe, Argentina, August.Google Scholar
  57. Whitman, W.G., 1923, The two-film theory of absorption, Chem. And Met. Engr. 29, 147–153.Google Scholar
  58. Wittenberg, J.B., 1959, Oxygen transport — a new function proposed for myoglobin, Biol. Bull., 117, 402–403.Google Scholar
  59. Wittenberg, J.B., 1970, Myoglobin in oxygen entry into muscle, Physiol. Rev., 50, 559–636.PubMedGoogle Scholar
  60. Wittenberg, B.A., Wittenberg, J.B., and Caldwell, P.R.B., 1975, Role of myoglobin in the oxygen supply to red skeletal muscle, J. Biol. Chem., 250, 9038–9043.PubMedGoogle Scholar
  61. Wittenberg, J.B. and Wittenberg, B.A., 1981, Facilitated oxygen diffusion by oxygen carriers, in: Oxygen and Living Processes, D.L. Gilbert, ed., Springer-Verlag, New York, U.S.A..Google Scholar
  62. Zeldovitch, J.B., 1939, On the theory of reactions on powders and porous substances, Acta Phys.-chim. URSS, 10, 583–594.Google Scholar

Copyright information

© Plenum Press, New York 1985

Authors and Affiliations

  • Pieter Stroeve
    • 1
  1. 1.Chemical Engineering DepartmentUniversity of CaliforniaDavisUSA

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