# Calculating linear flow rate for CIM® monoliths

Linear flow rate calculations are commonly used with traditional chromatography resins to calculate the residence times of analytes prior to scaling up. Monolithic columns are not affected by diffusion limitations, hence residence time calculations become redundant when scaling up.

That said, linear flow rates are still interesting in CIM® preparative monoliths (CIMmultus™ and CIM® Tube), and lower than you might think because the short bed length (cylinder wall thickness) corresponds to a very high surface area on the external cylinder wall (Image 1). In a packed particle column, that would correspond to a very large diameter, which would of course have the effect of causing even high volumetric flow rates to correspond to low linear flow rates.

#### Preparative columns: CIMmultus™ and CIM® Tube

The linear flow rate can be calculated with the following equation and supporting data, which is available on the Product Sheet, or in the table below.

Where F is the flow rate in mL/min, L is the bed height, Do and Di are the outer and inner diameter of the column (tabulated below).

This relative complexity can be explained. Because of the difference in the surface areas of the external and internal cylinder walls, linear flow rate at the outer (inlet) surface of the (thick-wall-cylindrical) monolith is slower than the linear flow rate at the inner (outlet) surface. In other words, linear flow rate accelerates between the inlet and outlet surfaces. This does not have any negative consequences because mass transport is convective, and that permits us to express flow rate simply in CV/min or CV/h. Linear flow rate differences that would have massive effects on porous particle columns have negligible effect on capacity and separation performance of monoliths.

#### Other columns: CIMac™, CIMmic™, CIM® Disk

These columns use an axial flow profile, and the calculation of linear flow rate only depends on the bed height, or length of the monolith layer.

Where F is the flow rate in mL/min, L is the bed height and V is the nominal volume of the column (data tabulated below).