Longitudinal Diffusion Term (B/u):

The second term within the equation arises since of longitudinal diffusion of the solute in the gas phase. A few of the solute molecules tend to diffuse along concentration gradients. Thus, a solute band will broaden as the molecules spread into regions of lower concentration ahead of the band and behind it. Actually, the solute molecules spend part of their time in the gas phase and part in the liquid phase. This type of diffusion is much faster in the gas phase than in liquids. Typically, the diffusion coefficient in the gas phase is about a million times more than in the liquids.

Generally, in GLC, the diffusion in liquids is neglected. The diffusion takes time and will increase with time required to elute the band from the column. Therefore, in the equation, the contribution due to longitudinal diffusion decreases as the velocity of the carrier gas increases. Instead, the inverse relationship between the longitudinal diffusion and the carrier gas velocity is not surprising because the solute spends lesser time in the column when the carrier velocity is high. The diffusion from the centre of the band to two edges has lesser time to occur. It may be important to point out here that in liquid chromatography, an effect of longitudinal diffusion is negligible because diffusion coefficients in liquids are several orders of magnitude lower than in gases. Here B will depend on diffusion coefficient of the solute in the mobile phase (D_M) and another factor (γ) accounting for the irregularity of diffusion pathways through the packing material.

B = 2_γD_M

B/u = 2_γD_M/µ

where, γ = is the correction  factor accounting  for irregularity  of diffusion pathways through the packing material, and

D_M = is the diffusion coefficient of solute in the gas phase.