Apparent diffusivity and Taylor dispersion of water and solutes in capillary beds

Taylor dispersion analysis in fused silica capillaries: a tutorial review

Biological and pharmaceutical analytes like liposomes, therapeutic proteins, nanoparticles, and drug-delivery systems are utilized in applications, such as pharmaceutical formulations or biomimetic models, in which controlling their size is often critical. Many of the common techniques for sizing these analytes require method development, significant sample preparation, large sample quantities, and lengthy analysis times. In other cases, such as DLS, sizing can be biased towards the largest constituents in a mixture. Therefore, there is a need for more rapid, sensitive, accurate, and straightforward analytical methods for sizing macromolecules, especially those of biological origin which may be sample-limited. Taylor dispersion analysis (TDA) is a sizing technique that requires no calibration and consumes only nL to pL sample volumes. In TDA, average diffusion coefficients are determined via the Taylor-Aris equation by characterizing band broadening of an analyte plug under well-controlled laminar flow conditions. Diffusion coefficient can then be interpreted as hydrodynamic radius (R_H) via the Stokes-Einstein equation. Here, we offer a tutorial review of TDA, intended to make the method better understood and more widely accessible to a community of analytical chemists and separations scientists who may benefit from the unique advantages of this versatile sizing method. We first provide a tutorial on the fundamental principles that allow TDA to achieve calibration-free sizing of analytes across a wide range of R_H, with an emphasis on the reduced sample consumption and analysis times that result from utilizing fused silica capillaries. We continue by highlighting relationships between operating parameters and critically important flow conditions. Our discussion continues by looking at methods for applying TDA to sample mixtures via algorithmic approaches and integration of capillary electrophoresis and TDA. Finally, we present a selection of reports that demonstrate TDA applied to complex challenges in bioanalysis and materials science.

Shear dispersion in a capillary tube with a porous wall

An analytical expression is presented for the shear dispersion during solute transport in a coupled system comprised of a capillary tube and a porous medium. The dispersion coefficient is derived in a capillary tube with a porous wall by considering an accurate boundary condition, which is the continuity of concentration and mass flux, at the interface between the capillary tube and porous medium. A comparison of the obtained results with that in a non-coupled system identifies three regimes including: diffusion-dominated, transition, and advection-dominated. The results reveal that it is essential to include the exchange of solute between the capillary tube and porous medium in development of the shear dispersion coefficient for the last two regimes. The resulting equivalent transport equation revealed that due to mass transfer between the capillary tube and the porous medium, the dispersion coefficient is decreased while the effective velocity in the capillary tube increases. However, a larger effective advection term leads to faster breakthrough of a solute and enhances mass delivery to the porous medium as compared with the classical double-porosity model with a non-coupled dispersion coefficient. The obtained results also indicate that the finite porous medium gives faster breakthrough of a solute as compared with the infinite one. These results find applications in solute transport in porous capillaries and membranes.