On the relationship between the roughness length of a scalar quantity and the corresponding sublayer-Stanton number

Considering SHEPPARD'S effective diffusivity approach for the molecular-turbulent sublayer, the relationship between the roughness length of a scalar quantity, zp, and the corresponding sublayer-Stanton number, Bi, is re-formulated. This re-formulation leads to Bi(-1) = kappa(-1) ln (1 + zo/zp), where zo is the roughness length for momentum. Based on this equation, it is evident that (a) the relationship Bi(-1) = kappa(-1) ln (zo/zp) commonly used is a doubtful approximation for the interfacial sublayer, and (b) the sublayer-Stanton number is positive-definite even if zp >= zo > 0. This is in contrast to negative Bi(-1) values found in the literature. Moreover, it is shown that Bi(-1) values derived with SHEPPARD's approach are much smaller than those provided by the more adequate REICHARDT's approach.