Biomixing by chemotaxis and efficiency of biological reactions: The critical reaction case

Published

Journal Article

Many phenomena in biology involve both reactions and chemotaxis. These processes can clearly influence each other, and chemotaxis can play an important role in sustaining and speeding up the reaction. In continuation of our work [A. Kiselev and L. Ryzhik, "Biomixing by chemotaxis and enhancement of biological reactions," Comm. Partial Differential Equations37, 298-318 (2012)]10.1080/03605302.2011.589879, we consider a model with a single density function involving diffusion, advection, chemotaxis, and absorbing reaction. The model is motivated, in particular, by the studies of coral broadcast spawning, where experimental observations of the efficiency of fertilization rates significantly exceed the data obtained from numerical models that do not take chemotaxis (attraction of sperm gametes by a chemical secreted by egg gametes) into account. We consider the case of the weakly coupled quadratic reaction term, which is the most natural from the biological point of view and was left open in Kiselev and Ryzhik ["Biomixing by chemotaxis and enhancement of biological reactions," Comm. Partial Differential Equations37, 298-318 (2012)]10.1080/03605302.2011.589879. The result is that similarly to Kiselev and Ryzhik ["Biomixing by chemotaxis and enhancement of biological reactions," Comm. Partial Differential Equations37, 298-318 (2012)]10.1080/03605302.2011.589879, the chemotaxis plays a crucial role in ensuring efficiency of reaction. However, mathematically, the picture is quite different in the quadratic reaction case and is more subtle. The reaction is now complete even in the absence of chemotaxis, but the timescales are very different. Without chemotaxis, the reaction is very slow, especially for the weak reaction coupling. With chemotaxis, the timescale and efficiency of reaction are independent of the coupling parameter. © 2012 American Institute of Physics.

Full Text

Duke Authors

Cited Authors

  • Kiselev, A; Ryzhik, L

Published Date

  • November 27, 2012

Published In

Volume / Issue

  • 53 / 11

International Standard Serial Number (ISSN)

  • 0022-2488

Digital Object Identifier (DOI)

  • 10.1063/1.4742858

Citation Source

  • Scopus