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Exact solution of the diffusion‐convection equation in cylindrical geometry
Author(s) -
Ivanchenko Oleksandr,
Sindhwani Nikhil,
Linninger Andreas A.
Publication year - 2012
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.12663
Subject(s) - library science , dept , engineering , engineering physics , mathematics , chemistry , computer science , stereochemistry
Solution of this equation is invaluable for validating the accuracy of numerical techniques as well, especially in complex biological systems. Several analytical techniques such as the method of characteristics or the Laplace transformation can be applied to find an analytical solution. In a one-dimensional (1-D) linear medium with continuous infusion at one boundary, i.e., constant convection velocity, the exact solution is simple. We are interested in obtaining analytical solutions in cylindrical and spherical domains, where the convection velocity varies radially. Such solutions are very useful in studying drug distribution during convection enhanced drug delivery in human brain. A cylindrical or spherical infusion source occurs due to the choice of the infusion catheter, which may be single port or a porous membrane catheter. Unfortunately, analytical solutions of only certain particular problems in which the diffusivity can be expressed as a power function of the Peclet numbers have been presented. We present an analytical solution for the convection diffusion problem in a cylindrical domain. Assuming symmetry with central source a desired concentration field CS (r,t), would be a function of one spatial coordinate r, and time t. For convenience, we use normalized species concentration C(r,t) 1⁄4 CS/C0, ranging from zero to unity, where C0 is the inlet concentration at the source.