Cleaning chromatography columns and hydrodynamics

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If you had to prove that your method for cleaning chromatography columns works and you had different sizes and shapes of columns, which one would you pick as a worst case to focus on? You have tall, skinny columns and short, fat columns, as well as different sizes. These are cylindrical glass columns that range from a diameter of 1.6 cm to 5 cm and a length of 10 cm to 100 cm. Assume they all contain the same chromatography media and are all rinsed with the same linear flow rate. Assume that they all have the same basic design and are composed of the same materials. These would be cleaned by running a small volume of sodium hydroxide throught the column (same percent of total column volume for each column) and then rinsed with a salt solution (buffer). Important considerations are that the sodium hydroxide contacts all portions of the media for a minimum length of time and rinsing sufficiently removes all of the sodium hydroxide. I ask because I'm not sure of what sort of fluid dynamics are going on within the column and whether column shape or size might affect how well the solutions are able to reach all areas of the column.
 

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Thank you Andy. Darcy's Law seems to explain that the total discharge (flow rate) is proportional to the permeability, cross-sectional area, viscosity and pressure drop, and inversely proportional to the length of the column, which all makes sense to me. But I guess I'm looking for some law of physics (or such) that might explain why fluid traveling through a long, narrow column might behave differently than fluid through a short, wide column, for example. If one particular set of dimensions would be more likely to result in regions of the media being exposed to lower flow rates than other regions (maybe at the edges where the top and bottom caps contact the sides), then that would be the set of dimensions I would prove my cleaning process against since it would be the worst case.
 
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Hmmm. I think the fluid would flow faster down the middle of the column due to the resistance at the sides. (Duh!) And therefore, wouldn't a short fat column be more likely to allow accumulation of contaminants at the top and bottom edges where the caps contact the cylinder - since the flow would be quite low here. On a longer, narrower column, wouldn't the increase in pressure due to the length cause more fluid to flow into this area?
 
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Andy Resnick
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Thank you Andy. Darcy's Law seems to explain that the total discharge (flow rate) is proportional to the permeability, cross-sectional area, viscosity and pressure drop, and inversely proportional to the length of the column, which all makes sense to me. But I guess I'm looking for some law of physics (or such) that might explain why fluid traveling through a long, narrow column might behave differently than fluid through a short, wide column, for example. If one particular set of dimensions would be more likely to result in regions of the media being exposed to lower flow rates than other regions (maybe at the edges where the top and bottom caps contact the sides), then that would be the set of dimensions I would prove my cleaning process against since it would be the worst case.
My understanding is that the columns are tightly packed with beads (or something like that); Darcy's law can be viewed as Poiseuille flow when friction effects dominate- somthing like air resistance. It's similar to Brinkman's equation: the NS equation with a friction term added. The fluid flow is nearly uniform everywhere for this situation.

If you are more concerned with the specifics at the top and bottom corners, then you need to be a lot more careful.

There's online packed column calculators that you may find useful:

http://www.chemsof.com/column/column.htm
http://www.katmarsoftware.com/pcol.htm
 
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