Optimizing Tangential Flow Exosome Capture: A Peclet Number Analysis

Hi all,

So this is slightly different from my previous post, but is perhaps much more important for the work that I am doing. This analysis is important because it allows us to determine the appropriate conditions at which to operate the system. Currently, I operate the device at a flow rate of 10 microliters/minute and with a top channel height of 100 microns. Since the device is operated in laminar flow conditions, then for particles on the top streamlines  of the flow (near the top of the channel) to interact with the membrane at the bottom of the channel, there must be some sort of active diffusion process. However, as there is also advection (convection) present in the system, the two processes must be balanced to allow for enough time for the particles to interact with the membranes. Therefore the diffusion time must be significantly lower than the residence time of the sample in the system (e.g. rate of diffusion > residence time). To determine under what conditions this is favorable, we can do a simple calculation of the Peclet number.

The Peclet number is a dimensionless number that is derived from nondimensionalizing the advection-diffusion equation and tells us the ratio of the rate of advection to the rate of diffusion, which is better shown as:

where V is the fluid velocity, H is the height of the channel, L is the length of the channel, and D is the particle diffusivity. We can estimate the diffusivity of a 50 nm exosome using the Stokes-Einstein equation, which is applicable for a solute of much larger radius than the solvent particles and is given as:

where k is the Boltzmann constant, T is the temperature in Kelvin, mu is the fluid viscosity and R is the solute (exosome) radius. Plugging the appropriate variables in to this, we get that a 50 nm exosome has a diffusivity of 8.7 x 10^-8 cm^2/s. Then, for a flow rate of 10 microliters/minute, the Peclet number for the system is Pe = 191. Ideally, for a system in which the rate of diffusion is greater than the residence time of the sample, the Peclet number will be less than 1. This means that parameters have to be adjusted to achieve this. As it is not really feasible to make a device that is very long, nor is it possible to change the diffusivity, then we have to adjust the flow rate and the height of the system. If we adjust the top channel height to 50 microns and slow the flow rate to 0.1 microliters/minute then the Peclet number reduces to Pe = 0.48. This is more of an ideal situation in terms of the driving force, though it severely affects the processing time of the samples.