## 2 Materials and Methods  
### Materials  
The experimental material comprising high-protein milk powders was produced experimentally on a pilot scale with the use of membrane techniques and the following: micellar casein concentrate (MCC) and serum protein concentrate (SPC), and commercial products--whey protein concentrate (WPC), casein hydrolysate (CH), whey protein hydrolysate (WPH), and whey protein isolate (WPI) (Superior Sp. z o.o., Olsztyn, Poland). Production of Micellar Casein Concentrate and Serum Protein Concentrate  
Raw whole milk originated from a dairy farm administered by the University of Warmia and Mazury in Olsztyn. Cream and skim milk were separated by centrifugation at the University's dairy plant. Raw skim milk was pasteurized with the use of a plate heat exchanger at 72 \({}^{\circ}\)C; the holding time was 16 s. The milk was then cooled to 4 \({}^{\circ}\)C, and refrigerated overnight (\(\leq\)4 \({}^{\circ}\)C) until processing [16]. After pasteurization, skim milk was microfiltered three times (three-stage process, 50 \({}^{\circ}\)C) in a pilot-scale ceramic microfiltration system (described below) in continuous feed-and-bleed mode with a 3\(\times\) concentration factor (CF) to produce MF retentate and MF permeate. A two-stage diafiltration (DF) process was carried out on the same day, to complete the three-stage microfiltration process [16]. Skim milk was microfiltered in a pilot-scale microfiltration system (Figure 1) equipped with graded permeability (GP) 0.1-\(\upmu\)m ceramic Membralox membranes (model EP1940 GL0.1\(\upmu\)AGP1020, alumina, Pall Corp., East Hills, NY, USA). The membranes had a pore diameter of 0.1 \(\upmu\)m, and a surface area of 0.72 m\({}^{2}\) (three membrane elements with an area of 0.24 m\({}^{2}\) each). They consisted of 19 channels (4 mm in diameter, 1.02 m in length) in each of the tubular stainless-steel modules. The channels were installed vertically in the system; the permeate and retentate streams passed from the bottom to the top of the module. The GP MF unit featured a feed pump (LKH-10-155-FSS-DIN 3.0 kW) and a retentate recirculation pump (LKH-10-155-FSS-DIN 4.0 kW), which were supplied by Alfa Laval (Kansas City, MO, USA). Slim milk was poured into the system's feed tank; only the retentate valve was opened, and all other valves were closed. Feed and retentate recirculation pumps were activated, and their working capacities were set at 40% and 30%, respectively. After five-minute recirculation, the permeate valve was gradually opened to achieve the fully open position. Subsequently, the setting of the retentate outlet valve was slowly adjusted to stabilize the flow of the retentate and permeate streams and achieve 3\(\times\) CF. The actual CF was calculated based on the volume of the retentate and the permeate collected in 30 s. When the removal rates of the retentate and the permeate were below 3\(\times\) CF (i.e., 2 kg of the permeate was removed per kg of the retentate), the retentate outlet valve/recirculation diaphragm valve was adjusted to achieve and maintain 3\(\times\) CF. The removal rates of the retentate and the permeate were monitored and adjusted at 30 min intervals to maintain 3\(\times\) CF. Figure 1: Simplified diagram of the MF system used in the study: M—manometer, V\({}_{\rm R}\)—retentate outlet valve, V\({}_{\rm P}\)—permeate outlet valve. Throughout microfiltration, the retenate and the permeate were continuously discharged into separate stainless-steel tanks, where they were immediately cooled down to 4 \({}^{\circ}\)C. The retenate stream was then returned to the feed vat to increase permeate yields and obtain a final CF of 3\(\times\). Typical inlet pressure was 2.5 bar, and retenate outlet pressure was 1.4 bar with the permeate valve fully open to maintain atmospheric pressure on its side. The flux (kg/m\({}^{2}\) per hour) was measured at 30 min intervals, and the permeate and the retenate were sampled for analysis.