## 3 Results and Discussion
### \(\beta\)-Galactosidase Recovery and Concentration Using Ultrafiltration
Moreover, the permeate flux was evaluated during the ultrafiltration process, since a low flux can lead to a lengthy and expensive process, making it one of the factors limiting deployment [12]. Figure 2A-C shows the permeate flux variation during ultrafiltration at pH 6.5, 7.0, and 7.5, respectively. In the present work, a decrease in flux during permeation was observed in all conditions, which is considered a typical behavior of concentration polarization phenomena and fouling on the membrane surface. When the solution is permeated, the protein concentration at the membrane surface increases, thereby elevating the polarized layer. Depending on the situation, a gel layer may be formed, which in turn leads to a further decrease in the permeate flux [15]. At pH 7.5, low variation in the initial permeate flux as a function of the molar mass cut-off was observed, with the values ranging from 16.0 to 13.1 L/m\({}^{2}\)-h, representing a  
Figure 2: Permeate flux during ultrafiltration at pH 6.5 (**A**), 7.0 (**B**), and 7.5 (**C**). decrease of 18.0%. Throughout the process, the highest variation observed was from 16.7 to 12.1 L/m\({}^{2}\).h, representing a reduction of 27.5%, with a maximum operation time of 100 min. The lowest initial permeate flux, except for the 100 kDa membrane, occurred at pH 6.5 (range of 12.2 to 11.1 L/m\({}^{2}\).h). The largest decrease in permeate flux was observed in the 60 kDa membrane (11.0 to 5.0 L/m\({}^{2}\).h), representing a decrease of 54.5% over the process and a maximum operating time of 130 min. The low permeate flux at this pH may have been due to protein agglomeration and the production of a deposit on the membrane surface, thereby reducing the membrane permeability. Furthermore, the protein adsorption on the membrane surface may result in a second membrane that alters the function of the original membrane [46; 47; 48]. Although the 60 kDa membrane presented similar results to the other membranes regarding the purification factor, this membrane should be analyzed and used with caution due to the process presenting a longer operating time and a lower final permeate flux when compared to the other membranes, affecting the yield and viability of the process. This reduction in the yield of the process can lead to significant increases in the concentration and purification costs of this enzyme and can even make it unfeasible at the industrial scale. This effect may have occurred due to greater fouling of the membrane, as a larger pore diameter favors the permeation of compounds similar in size to the membrane pores, leading to a greater occurrence of blockage of the pores [12]. In addition, the differences in membrane material can also affect the separation performance during ultrafiltration, since the chemical composition can affect the functionality, charge, and interactions with the material, among other factors [49]. At pH 7.0, the average flux values ranged from 21.2 to 12.0 L/m\({}^{2}\).h, with a reduction of 43.4% at a maximum operating time of 80 min. Although the application of this pH led to the highest initial flow, a high flux reduction rate was observed during the ultrafiltration process. The permeate flux variation is a phenomenon inherent in the process and is observed in several processes using ultrafiltration. [PERSON], et al. [50] studied three ultrafiltration membranes used for recovering soy protein isolates. These authors reported reductions in the permeate flux by 30%, 69%, and 30% for the 5, 20, and 50 kDa membranes, respectively. Similarly, [PERSON] and [PERSON] [51] reported fluxes of 10 and 125 L/m\({}^{2}\).h for the 5 and 10 kDa membranes, respectively, using a pressure of 3.0 kgf/cm\({}^{2}\) in the ultrafiltration of proteins and lactose from dairy effluents. These authors observed a decrease in the permeate flux, indicating that the protein increased fouling on the membrane and thereby affected the permeate flux.