The goat milk whey was provided by Association of Small Ranchers of the Angicos wilderness (Associação dos Pequenos Agropecuaristas do Sertão de Angicos-APASA). The polymers utilized were PEG of molecular weight 1500 Daltons (Impex-Lot 35263-D), 4000 (Synth-Lot 152264), 8000 (Sigma-Lot 120M0004V). The salt utilized was potassium phosphate (KPi), monobasic (Vetec-Lot 1200572, Purity 99%) and dibasic (Isofar-Lot 111027, Purity 98%). In all systems, deionized water was used. The samples were filtered, filtered through cellulose acetate membrane with a porosity of 0.45 µm using acetonitrile (Sigma, Lot SHBD1824V, Purity 99.9%) and trifluoroacetic acid (Sigma-Lot BCBM0756V, Purity 99%).

The aqueous biphasic systems were formed according to the methodology described by Coimbra et al. [11] and Alves [14] . Three molecular weight of PEG (1500, 4000, and 8000) were tested. The binodal curve was determined by the cloud point method using titration procedure. The tie-lines were determined using the methodology described by Jorge [15] . Both analyzes were performed in an equilibrium cell connected to a thermostatic bath at 298 K. Calibration curves were constructed considering the mass fraction of each component versus density in order to quantify the compositions of equilibrium phases. The curves were compiled with the points of the binodal curve, where the density of the mixture was measured at the cloud point, and the liquid-liquid equilibrium data of the ternary system were plotted using the Oringin 7.0.

The quantification of α-La and β-Lg protein was performed by high performance liquid chromatography (Shimadzu, Prominence, Kyoto, Japan series) containing a ternary pumping system (LC-20AT), autosampler (SIL-20AHT), column oven (CTO-20A), detector per diode array (SPD-M20A) and interface (CBM-20A). LC solution data were evaluated using an acquisition software, version 1.25 and Rigaku data treatment. The chromatographic separation occurred in reversed phase, the column and parameters utilized were the same as presented in Buffoni [16] , a Jupiter C4 column (2504.6 mm, 300 Å pore size, 5 µm particle size, Phenomenex) was used, the oven temperature was 30˚C, mobile phase flow equal to 1 mL/min, injection volume equal to 20 µL, the eluent was monitored using a detector per diode array at 205 nm. The eluents solutions and elution gradient utilized were the same described by Enne [17] , where the mobile phase (A) was composed of water of HPLC grade containing 0.1% of trifluoroacetic acid, and mobile phase (B) was composed of Acetonitrile containing 0.1% of trifluoroacetic acid. The elution gradient was 35% B from 0 to 1 min, 35% - 38% B from 1 to 8 min, 38% - 42% B from 8 to 16 min, 42% - 46% B from 16 to 22 min, 46% - 90% B from 22 to 24 minutes, 90% B from 24 to 25 min, 90% - 35% B from 25 to 30 min, 35% from 30 to 35 min.

The separation process was evaluated in terms of partition coefficient, selectivity, yield and purity, which were determined through as described below.

a) Partition Coefficient (K): it was determined considering the ratio between the protein concentration in the upper phase and the concentration of the same protein in the lower phase:

where K is the partition coefficient, C_UP and C_LP are the protein concentrations in the upper and lower phase, respectively.

b) Selectivity: it is defined by the ratio between the partition coefficients of α-La and β-Lg in the two balance phases:

where S represents selectivity of α-La compared to β-Lg, K_αLa and K_βLg are the partition coefficients of α-La and β-Lg, respectively.

c) Yield and Purity: These two values were calculated according to equations defined by Chen [18] . For the α-La and β-Lg proteins yield:

where Y_αLa,UP and K_βLg,LP correspond to α-La yield in the upper phase and β-Lg yield in the lower phase, respectively; K_αLa and K_βLg are the partition coefficients of α-La and β-Lg, respectively; V_r correspond to the volume ratio between the phases.

And for the α-La and β-Lg proteins purity:

where P_αLa,UP and P_βLg,LP correspond to the purity percentage of α-La proteins in the upper phase and β-Lg in the lower phase, respectively.

Figure 1 presents the phase diagram for the system polyethylene glycol, potassium phosphate and water considering different molecular mass of PEG. The deviation in the experimental data of the bimodal curves was 4.01%.

According to Figure 1, it’s possible to observe that the molecular mass of the polymer affects the equilibrium. The system formed by PEG 8000 presents higher biphasic region, decreasing the region when PEG 4000 is used and even more when PEG 1500 is applied. This result is coherent with literature [19] [20] .

To determine tie-line, different methodologies can be used. Chumpitaz [21] also evaluated the system consisted by PEG 1500 + KPi + water in several conditions. Figure 2 presents the lie-lines determined by Chimpitaz [21] and in this work using the methodology described by Jorge [15] , both in the same conditions of temperature, pressure, pH, and global composition of ATS.

Good adjust of the tie-line can be observed for the tie-line obtained in this work (s.d = 0.01). However, the tie-line obtained by Cumpitaz [21] presented a higher deviation mainly in the lower phase. To determine tie-lines, the author defined previously the global composition, and the composition of the phases was obtained by the quantification of the compounds by mass difference. Due to the better adjust of the methodology of Jorge [15] , this methodology was kept for the other systems in this study. Figure 3 presents the binodal curves and tie-lines obtained for the system PEG (1500, 4000, 8000) + KPi + water.

From Figure 3, it’s possible to observe the good adjust of all tie-lines. In all systems, the polymer was concentrated in the upper phase, and KPi in the lower phase.

Table 1 shows the partition coefficient, selectivity and process yield and purity of α-La and β-Lg proteins, when different amount of goat milk whey was employed. For this experiment, the aqueous two-phase systems were formed by 14% of PEG 1500, 18% of KPi and 68% of water.

According to Table 1, the experiment using 1 mL of goat milk whey in-nature presented better partition coefficient (K_α-La = 5.78; K_β-Lg = 0.09), selectivity (63.71), yield (α-La_F.up = 78.61; β-Lg_F.lp = 94.54) and high purity (α-La_F.up = 77.08; β-Lg_F.lp = 94.99). This occurred due to it low amount of water. The increase of goat milk whey quantity in the aqueous two-phase systems promoted the increased of water in the global system, changing the equilibrium. This occurrence prevented the separation of proteins in the systems using higher amount of goat milk whey.

The results also demonstrated the efficiency of aqueous two-phase systems in the separation of these proteins, since 85% of β-Lg was recovery in the lower phase, and 92% of α-La in the upper phase.

It is important to emphasize that the partition coefficient of these proteins were coherent with studies of literature that also applied polyethylene glycol, potassium phosphate and water at the same operational conditions, however using pure α-La e β-Lg proteins [22] [23] . This indicates the success of application of the aqueous two-phase in the real systems.

After the determination of the best amount of goat milk whey to be used, it was evaluated the partition of the proteins in the ATSs formed by PEG (150, 4000, 8000) + KPi + water. Table 2 presents the partition coefficient, selectivity and process yield and purity of α-La and β-Lg proteins.

According to Table 2, the system formed by PEG 1500 presented higher partition coefficient for α-La (K_α-La = 5.78), and lower partition coefficient for β-Lg. This system also presented a result of selectivity considered satisfactory, since the sample is a real sample, i.e., goat milk whey in nature with other compounds presents. The system containing PEG 8000 did not partitioned the proteins. Table 2 also shows that the results were coherent with literature, in which, increasing of molecular mass of poly-

*up = upper phase, lp = lower phase.

*up = upper phase, lp = lower phase.

mer promotes decreasing of the partition coefficient [9] [23] . This behavior is attributed to the increased of proportions of hydrophilic terminations groups in the polymer molecules with a lower molecular weight (or shorter chain length), this fact reduces the overall hydrophobicity of the polymer rich phase [9] . Besides, due to the lower viscosities, the polymers with lower molecular mass promoted fast time to get the equilibrium.

The results demonstrated good efficiency in the separation of proteins for the system consisted by PEG 1500 + KPi + water, where: 78.61% of α-La was concentrated in the upper phase, and 95% of β-Lg was concentrated in the lower phase.