**3. Physicochemical properties of lactose**

Lactose is a reducing disaccharide of galactose and glucose discovered in milk in the 17th century. Both the galactose and the glucose can form a hemiacetal link and create a ring structure. A β-glycosidic link connects the two pyranose structures deriving in a 4-O-β-D-galactopyranosyl-D-glucopyranose molecule. This disaccharide has a chiral center that exists as two isomers: α-lactose and β-lactose. The α-isomer rotates the plane of polarized light +92.6° and the β-isomer +34° at 20°C. When lactose is in an aqueous milieu, its ring structure opens and closes interchanging between the α- and β-isoforms (mutarotation). At some point, these isoforms acquire an equilibrium (mutarotation equilibrium). Lactose mutarotation is a slow process that is very temperature-dependent. For instance, at 18.8°C the mutarotation equilibrium is achieved in 6.5 hours with a proportion of 40% of α-lactose and 60% of β-lactose; but at 0°C, the stability can take up to 72 hours. Overall, the proportion of β-lactose is always higher than the α-lactose at mutarotation equilibrium, because the β-isoform is more soluble than the α-isoform. For example, at 35°C the solubility of α-lactose is 7 g per 100 g of water, in contrast, the solubility of β-lactose is 50 g per 100 g of water [2, 5–7]. Certainly, the solubility of both isoforms will decrease if the temperature drops. Like other sugars, lactose molecules nucleate and crystallize when the concentration of this sugar overcomes its maximum solubility at a specific temperature. The dairy industry applies this principle to crystallize lactose from whey, a by-product of cheesemaking [8].

This by-product of cheesemaking contains 0.8 – 1% protein, 0.06% fat, 4.5 – 6% lactose, and 90 – 92% of water. To crystallize lactose from the cheese whey, it needs to be first, defatted, deproteinated and evaporated to concentrate lactose between 39 and 56%. At this concentration, lactose will crystallize when the evaporated whey is cooled enough (i.e., 20-25°C). During the cooling step, lactose moves through and beyond the metastable zone (MZ), a region between the solubility and supersolubility of lactose. The spontaneous nucleation of lactose occurs when the supersolubility is exceeded, outside the MZ. Therefore, the width of the MZ determines the temperature drop necessary to induce lactose nucleation. After nucleation, crystals' growth depends on the degree of lactose saturation and the temperature, since the last one affects lactose solubility [7, 9–13]. The overall process of lactose crystallization is slow. In consequence, mutarotation can occur during the nucleation or the growth of crystals. However, if the mutarotation rate is lower than the crystallization rate, the kinetics of mutarotation will dominate over the nucleation and crystal growth. The industrial process of lactose crystallization from cheese whey is slow (up to 48 h) and requires an elevated lactose concentration to induce nucleation (high evaporation cost). Different approaches have been studied to overcome the drawbacks of lactose crystallization. Among these are the seeding of lactose nuclei, anti-solvents (i.e., ethanol and acetone), and the appliance of high-power ultrasound. Alternatively, methods other than crystallization have been investigated to recover lactose from the cheese whey, like the use of membranes [9, 11, 14–17].
