Two-dimensional standing gradient osmotic flow: a generalization of the “isotonic convection approximation”
A linear two-dimensional model of a flow system for solute and fluid transport in intercellular spaces has been obtained by using the so called “isotonic convection approximation”, already employed in the one-dimensional case (Segel (1970)). This is equivalent to ignoring the convective components in the relevant differential equation. The solutions found by means of the eigenfunctions of a Sturm-Liouville system have been compared with the numerical solutions of the general non-linear model, in which also the convective terms are present.The results of the linear model agree fairly well with those of the non-linear one, in the range of interest of parameters. This fact shows that the ignorance of the profile of fluid velocity does not introduce significant errors in the evaluation of solute and fluid fluxes.The differences of results between the one-dimensional and the twodimensional, the linear and non-linear models, give a way to evaluate the relative effects of the diffusive and convective terms in the differential equation and to estimate the errors introduced by the one-dimensional approximation.