Taylor dispersion in finite-length capillaries

Abstract

The solute transport in a core-annular geometry is studied. A Newtonian or non-Newtonian (i.e., power-law) liquid flows through the core, while the solute can exchange between the liquid and the surrounding tissue. The permeability of the phase interface depends on the nature of the solute, i.e., relatively low for lipids and macromolecules but high for ions and gases. We analyse the moment’s equations of the residence time distribution (RTD). The solution of the equation for the second moment provides the exact formula for the Taylor dispersion coefficient. Unlike previous studies using a perturbation procedure where coefficient of axial dispersion cannot be defined at low permeability, the current study gives Taylor coefficient of dispersion for any value of the permeability. It is found that the coefficient in shear-thinning fluid is lower than in the Newtonian one, although the relative importance of non-Newtonian effects decreases when other factors, e.g. inter-phase transport and solubility, become dominant. The equations for the higher moments are analysed and the general structure of the solution is obtained in the form of integrals, which can be easily evaluated numerically. When the analysis is applied to solute transport between capillaries and surrounding tissues, it is shown that the classic Taylor expression does not describe dispersion of solute, e.g. glucose and albumin, in the capillary, except in situations where the Péclet number is very low. For the range of parameters typical for microvascular circulation in tissues, the higher moments play an important role and need to be considered.