## 1 Introduction  
Fractionation of proteins by ultrafiltration (UF) is efficient when proteins differ in molecular mass by at least a factor of 10. To this aim, various membrane processes were investigated focusing on (i) tuning pH and ionic strength to maximize differences in the hydrodynamic size of particles in solution, (ii) using electrical charged membranes to retain charged proteins [1; 2; 3; 4], (iii) diafiltration process [5], and (iv) selective aggregation of proteins using thermal process [6]. The careful control of pH and ionic strength of bulk proteins' solutions might result in an improved performance of protein fractionation by ultrafiltration. Different protein mixtures were fractionated by charged UF process [7; 8; 9; 10; 11; 12; 13; 14; 15] by using both organic and inorganic membranes, achieving maximum transmission of the protein being at its isoelectric point (pI) and high retention of the one that had the same electrical charge as the membrane. The overall observation was that large increase in protein transmission through membranes can be reached using charged membranes, but the protein at its isoelectric point can create membrane fouling [16; 17; 18; 19; 20; 21; 22; 23]. Membrane fouling, in the mentioned conditions,increases when the protein is at the isoelectric point, since protein aggregation easily occurs [24; 25; 26]. A good compromise between high selectivity and low fouling must be found. Strategies to overcome the permeability-selectivity trade-off were published by [PERSON] et al. [4], in which a 300 kDa regenerated cellulose membrane positively charged was used for the fractionation of \(\alpha\)-lactalbumin (ALA) from a binary protein mixture. Using a two-stage process, 87% of pure ALA was obtained in the permeate with a flux of 170 L h-1-m-2 [4]. The same work was carried out [27] using milk serum permeate (MSP) as feed solution, obtaining 87% of ALA purity with a three-stage system. Another research group [15] achieved the complete separation of bovine serum albumin (BSA, 66.5 kDa) in one step, starting from a binary protein mixture with lactoferrin (LF, 78 kDa) by using diafiltration process and charged membranes. Despite the research efforts and knowledge promoted on the separation of proteins with similar size by charged UF membrane processes, some aspects (such as preventing irreversible fouling) need further insights and improvements. The novelty of this work, with respect to the current literature, is to promote proteins separation with similar molecular weight, but in conditions in which irreversible fouling can be prevented or limited. Besides, a deep study of protein aggregation state and charge density, when both proteins bore same charge of the membrane, was carried out for the first time, in order to have high purity of the separated protein in a single stage, currently carried out by multistage processes [4; 27]. In order to identify operating conditions that might prevent irreversible fouling, as well as guarantee high purification efficiency, we speculated that using binary protein mixture in bulk conditions far from their isoelectric points and having both proteins with the same electrical charge as the membrane would promote the target improvements, since electrical repulsion and then low adsorption between proteins and membrane is promoted. We also aimed at achieving purification in a single step. To easily compare results with literature data, the well-studied \(\beta\)-lactoglobulin and \(\alpha\)-lactalbumin binary mixture was used as a model system. Charged regenerated cellulose ultrafiltration membrane was applied. The work started with a systematic characterization of single protein solutions to determine parameters which could affect their separation (zeta potential, protein size, and tendency to aggregate).