When pumping mobile phase through a particular bed, a certain pressure drop δP over the column will result. The relationship between particle diameter dp and the flow velocity u is given by the Darcy´s law for non-compressible solvents:
Accordingly, δP is proportional to the linear velocity u, the column lengths L and the viscosity of the mobile phase η, and inversely proportional to the constant k0 and the square of the particle diameter dp. The constant k0 is a function of the interstitial porosity εi according to the Karman-Cozeny equation:
The equation above shows that the interstitial porosity εi has a tremendous influence on the permeability of the bed and therewith also on the pressure drop. For a well packed reversed phase be the interstitial porosity can be assumed to be 0.33 which leads to k0 = 4.45.10-4. The column permeability (dp2·k0) does in practice depend entirely upon the particle diameter and the particle size distribution. The latter is a very important parameter, since the particles of an HPLC packing material are never mono-disperse.
Broad distribution has two negative effects:
Hence, broad particle size distribution should be avoided.
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