Haldenwang Pierre, Bernales Braulio, Guichardon Pierrette, Ibaseta Nelson
Aix Marseille Univ, CNRS, Centrale Marseille, M2P2, 38 rue Joliot-Curie, 13451 Marseilles, France.
Membranes (Basel). 2019 Apr 3;9(4):48. doi: 10.3390/membranes9040048.
In cross-flow membrane filtration, fouling results from material deposit which clogs the membrane inner surface. This hinders filtration, which experiences the so-called limiting flux. Among the models proposed by the literature, we retain a simple one: a steady-state reversible fouling is modelled with the use of a single additional parameter, i.e., N d , the ratio of the critical concentration for deposition to the feed concentration at inlet. To focus on fouling, viscous pressure drop and osmotic (counter-)pressure have been chosen low. It results in a minimal model of fouling. Solved thoroughly with the numerical means appropriate to enforce the nonlinear coupling between permeation and concentration polarization, the model delivers novel information. It first shows that permeation is utterly governed by solute transfer, the relevant non-dimensional quantities being hence limited to N d and P e i n , the transverse Péclet number. Furthermore, when the role played by N d and moderate P e i n (say P e i n < 40 ) is investigated, all results can be interpreted with the use of a single non-dimensional parameter, F l , the so-called fouling number, which simply reads F l ≡ P e i n N d - 1 . Now rendered possible, the overall fit of the numerical data allows us to put forward analytical final expressions, which involve all the physical parameters and allow us to retrieve the experimental trends.
在错流膜过滤中，污垢是由堵塞膜内表面的物质沉积造成的。这阻碍了过滤过程，导致出现所谓的极限通量。在文献提出的模型中，我们采用了一个简单的模型：用一个单一的附加参数(N_d)（即沉积临界浓度与入口进料浓度之比）对稳态可逆污垢进行建模。为了专注于污垢问题，粘性压降和渗透（反）压被设定得较低。这就产生了一个最小化的污垢模型。通过适用于强化渗透与浓度极化之间非线性耦合的数值方法进行全面求解后，该模型给出了新的信息。它首先表明，渗透完全由溶质传递控制，因此相关的无量纲量仅限于(N_d)和横向佩克莱数(P_{ein})。此外，当研究(N_d)和适中的(P_{ein})（例如(P_{ein}<40)）所起的作用时，所有结果都可以用一个单一的无量纲参数——所谓的污垢数(Fl)来解释，其表达式为(Fl\equiv P_{ein}N_d - 1)。现在，数值数据的整体拟合成为可能，这使我们能够提出包含所有物理参数的解析最终表达式，并使我们能够重现实验趋势。
