Determination of concentration-dependent transport coefficients in nanofiltration: Defining an optimal set of coefficients

Phenomenological analysis of transport of mono- and divalent ions in nanofiltration

“…(1) was small, of the order 10 3 s/m. As a result, the Peclét number AJ V and the parameter Aω s were both much smaller than 1 in all experiments [33,34,36]. This should similarly apply to the divalent salts in this work, since the sizes of divalent ions used here hence their frictions and, ultimately, the values of A (cf.…”

“…By generalizing arguments for monovalent salts presented earlier [33,34,36] it may be shown that for a single n 1 :n 2 salt (the subscripts "1" and "2" denote the counter-and co-ions, respectively) the coefficients A and ω s may be related to frictional, thermodynamic and membrane structure characteristics as follows:…”

“…However, in Eqs. (2) and (3) it is lumped into frictions factors formally defined using superficial velocities and gradients normal to the membrane surface [33].…”

“…Recently, we proposed a phenomenological approach that directly yields the values of coefficients and their variation with concentration and avoids the difficulty of using a specific physical models for calculating the coefficient [33,34]. A similar but slightly simpler approach was proposed by Yaroshchuk a few years earlier [35].…”

Ion transport in the polyamide layer of RO membranes: Composite membranes and free-standing films

“…Filtration data are then analyzed using phenomenological relations such as the Spiegler-Kedem (SK) equation [23], which may include the case of variable coefficients as well [24,25]. Recently, this approach was successfully implemented to analyze variation of salt permeability with concentration in NF and RO [3,[24][25][26][27]] and a few important results could be derived. Perhaps most important conclusion drawn from this analysis was that convection contributes very little to salt transport in thin-film composite NF and RO membranes.…”