Taylor Dispersion - Diwakaran R P

Introduction

The laminar flow regime is the most predominant one that exists within the microfluidic realm due to the channel sizes and flow rates used. One of the major reasons for this is that there is extremely low lateral mixing(convective) between different streams used which gives rise to very interesting applications like abc1. The laminar flow velocity profile is parabolic, with no-slip conditions at the boundaries of the liquid channel. abc2:insert picture for velocity profile. This parabolic velocity profile gives rise to some fascinating phenomena; if a colored liquid strip-like plug is introduced into a stream of clear liquid abc3:insert video and pumped along with it, the plug stretches itself like a bow into a thing parabolic strip matching the shape of the velocity profile. This facilitates the mixing through diffusion in the radial direction as the boundary of the solute plug increases with time due to the stretching and eventually, the diffusion causes the parabolic strip to look like a spectrum or a broad plug with different regions of dispersion. abc4: insert reference. The size of the dispersion band depends on the liquid velocity, channel dimensions, and the coefficients of diffusion of the solute and the liquid around it. This phenomenon can be used to determine the hydrodynamic radii of solutes. abc5: insert reference.

Analysis of Taylor Dispersion

To understand the Taylor Dispersion, the starting point is to understand Poiesuille flow. Consider a circular liquid channel of radius 'h' and the velocity profile of the flow driven only by a pressure difference is given by abc6: insert equation. The velocity is clearly the highest at the center and the lowest at the walls of the channel, due to the no-slip conditions. This gives rise to the parabolic profile. If a solute strip was introduced and stretched into this parabolic profile, the concentration of the solute at the apex of the parabola will be higher compared to the liquid around it, thereby causing the solute to diffuse radially towards the channel walls. And, at the base or the ends of the parabola(closer to the walls of the channel), the concentration of the solute is higher than the liquid around it making them diffuse towards the center of the channel. Thus, we have two opposing effects happening at the apex and base of the parabola causing the strip to transform into a broadened plug. There is also dispersion from the apex of the parabola in the direction of the flow as there is a concentration difference similar to that of in the radial direction. This axial dispersion when combined with multiple injections of solute strips, causes a uniform distribution of solute concentration centered around a point that moves with the mean velocity of the fluid.

References

1. Taylor Geoffrey Ingram. 1953, Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A219186–203,

2. Squires and Quake, Reviews of Modern Physics, v77(3), 2005