Block freeze concentration by centrifugation and vacuum increases the content of lactose-free milk macronutrients

For Peer Review Block freeze concentration by centrifugation and vacuum increases the content of lactose-free milk macronutrients Journal: Journal of Food Science Manuscript ID JFDS-2022-0729.R1 Wiley - Manuscript type: Original Article (Direct Via EEO) Date Submitted by the Author: 10-Sep-2022 Complete List of Authors: DANTAS, ADRIANA Orellana-Palma, Patricio Kumar, Dinesh Hernandez, Eduard; Agri-Food Engineering and Biotechnology Prudencio, Elane Keywords: milk products, milk proteins, nutrients, engineering, milk components Free-text Keywords: Centrifugation, Vacuum Topic: Food Engineering, Materials Science, and Nanotechnology ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review JFDS-2022-0729 Title: Block freeze concentration by centrifugation and vacuum increases the content of lactose-free milk macronutrients Associate Editor: Mauer, Lisa Dear Editor Firstly, we would like to thank you for the opportunity to reconsider our manuscript for publication in Journal of Food Science. We also would like to point out that all the comments made by Reviewers have been taken into account. We believed that all corrections were essential for the improvement of our manuscript. As suggested by Reviewers, changes were made in the manuscript, and the comments have been discussed and incorporated in this enhanced version, which is highlighted in red. Reviewers' comments: Reviewer #1: 1. Lump citations such as (Canella et al., 2019a; D. Arend et al., 2022; Demoliner 116 et al., 2020; Sequera et al., 2019) is not recommended. Please specify each liquid food application for each citation/reference. Author’s comments: We agree with the Reviewer. Therefore, we have rewritten these sentences (See Page 7, Lines 166–170). 2. Please state a good reason for the combination of PFC and BFC. State any past research on PFC and BFC and their results, then find the research gap/limitation that leads to the PFC and BFC combination. Author’s comments: Thank you for the observations. Although PFC is not the object of study of this work, we have rewritten the Introduction addressing your comment. Therefore, we have added information related to a good reason for the combination of PFC and BFC, studies on PFC and BFC combination, and gaps related to PFC and BFC combination. To see this information, and also to have a better understanding of our purpose, please read page 7 line 166 until page 9, line 212. Page 1 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 3. Please proofread the paper as there are some words that I think are not suitable to be used. Example: Protein analysis was "realized" according to the Kjeldahl method (line 159). The word "realized" can be replaced with another word. Author’s comments: We have agreed with the reviewer and replaced the word "realized" (See Page 10, Line 231). Thank you for your constructive comment. 4. Define lactose-free milk. Authors’ comments: We agree with the Reviewer and this comment was addressed in the Introduction section (See Page 4, Lines 93–125). We have discussed some details involved in the production and definition of lactose-free milk. 5. Concentrate yield for the effect of centrifugal time is not even higher than 50%. Please add any past researches that did the same method and their results. Please also add a statement on either centrifugal time is an important parameter or not for this study. Authors’ comments: Thank you for the recommendation. We did a broad study on the topic and improved the discussion (See Page 16, Lines 361–399). 6. How this method is applicable to milk manufacturing? Please mention it in the conclusion. Author’s comments: We appreciate your comment. Reviewer 2 also asked us to make changes to the Conclusion section. So we have rewritten it. 7. What is the difference amount of concentrate 1 and 2, in mass? Authors’ comments: continuation below 1st cycle Initial sample mass (milk) ~734g Concentrate mass ~33g Page 2 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 2nd cycle Initial sample mass (ice) ~692g Concentrate mass ~137g 8. Please mention the analytical equipment used to analyze the products as the authors claim this method can maintain the sensorial characteristic of the milk. Author’s comments: Descriptive analysis presents great applicability for the monitoring and adjustment of sensory characteristics of milk products. This method does not require training, has a low financial impact, and optimizes time and resources in dairy industries. In addition, it gives information highly correlated with traditional methods, providing a total assessment of products and taking all sensory traits into account. Therefore, for a better understanding, the following comment was removed from the manuscript: “Then, it is expected that lactose-free milk submitted to these FC processes may have distinct sensorial characteristics.” 9. Do the results from this study compared with the current method used in the industry? Please mention it. Author’s comments: We agree with the Reviewer and this comment was addressed. Therefore, the following information was added in the final version of the manuscript: “According to Beldie and Moraru (2021), the concentration of milk in the dairy industry is typically achieved by thermal evaporation or membrane technology such as reverse osmosis. The efficiency of these processes is very similar to those obtained by the freeze concentration process used in the present study. In thermal evaporation, the maximum concentration level achievable is 55% for skim milk and 50% for whole milk, while for the membrane process, the maximum concentration varies between 25% and 30% solids. Thermal evaporation is also known to reduce the quality of the final concentrated product due to prolonged exposure to heat, which negatively affects the color, taste, and nutritional value of milk. Furthermore, evaporators are prone to biofilm formation by spore-forming mesophilic or thermophilic bacteria. A major drawback of membrane separation is that the process is significantly affected by membrane fouling, Page 3 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review which leads to flux decline and limits the final achievable concentration of the product (Beldie & Moraru, 2021). Given the above, we can verify that block freeze concentration by centrifugation and vacuum can be used by the industry aiming for the macronutrient concentration of lactose-free milk.” (See Page 21, Lines 484–498) Reviewer #2: This research article presents an interesting evaluation of block freeze concentration by centrifugation and vacuum to increase the content of lactose-free milk macronutrients. However, some aspects must be considered in order to improve the manuscript. Author’s comments: We understand the Reviewer’s point of view and highlight the relevance of the comments. Line 27: It is alright to use pronouns, but try to limit their usage Author’s comments: We agree with the Reviewer and this comment was addressed. (See Page 2, Line 36). Line 28: Don’t have to mention the experimental design in the abstract; it’s alright to give a 2-3 brief intro and the relevance of the current research Author’s comments: We agree with the reviewer regarding the brief presentation in the Abstract, and therefore, we have made changes in this section (See Page 2, Lines 30–36). Concerning the mention of the experimental design, our research group doesn't see problems in this sense, since the same approach was used in the abstract of Santana et al. (2020), who performed assays of blueberry juice freeze concentration. Even so, we have suppressed the specific design (23) (see page 2, lines 36 and 37). We didn't remove more information than this one because the sentences that follow each other would be meaningless or confused. Reference: Santana, T., Moreno, J., Petzold, G., Santana, R., & Sáez-Trautmann, G. (2020). Evaluation of the temperature and time in centrifugation-assisted freeze concentration. Applied Sciences, 10, Article 9130. https://doi.org/10.3390/app10249130 Page 4 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review Line 30: “were” analyzed Author’s comments: We agree with the reviewer, and therefore, we have rewritten the Abstract section (See Page 2, Lines 35–39). Line 31: Too exaggerated: do not use “greater effect”. What does a greater effect translate to? Author’s comments: We agree with the reviewer, and therefore, we have rewritten the Abstract section (See Page 2, Lines 39 and 40). The phrase “The centrifugation temperature had a greater effect on the concentrate yield and concentration index” was replaced by “Concentrate yield and concentration index were mainly affected by the centrifugation temperature”. Line 32: It seems that there is an article usage problem here. Line 32: The noun phrase significant effect seems to be missing a determiner before it. Consider adding an article. Author’s comments: We agree with the reviewer, and therefore, we have rewritten the Abstract section (See Page 2, Lines 40–42). The phrase “Regarding the efficiency, individual factors did not have significant effect on the response, but their interactions did.” was replaced by “On the other hand, individual factors did not have a significant effect on the efficiency, only their interactions.” Line 49: you can also include the sustainability aspect of it. Author’s comments: We agree with the reviewer and this comment was addressed. (See Page 3, Lines 58–65) Line 51: The singular verb is does not appear to agree with the plural subject contents. Consider changing the verb form for subject-verb agreement. Author’s comments: We agree with the reviewer, and therefore, we have rewritten this sentence (See Page 3, Lines 58–60). The phrase “In turn, milk with higher solids contents is gaining in popularity in much research of dairy products” was replaced by “In turn, dairy products that provide a high amount of solids (especially protein) are gaining in popularity among consumers, with consequent interest from researchers”. Page 5 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review Line 54-55: Rewrite Author’s comments: We appreciate your valuable comment and have chosen to remove this sentence, not least because there is a word limit established by the journal for this section. Line 78: It may be unclear who or what “This” refers to. Consider rewriting the sentence to remove the unclear reference. Author’s comments: We agree with the reviewer, and therefore, we have rewritten the Introduction section (See Page 4, Lines 77–84). Line 74-97: These two paragraphs can be combined into one rather than being vague in certain lines Author’s comments: Based on your comment, as well as the suggestions of reviewer 1, we have made changes in the Introduction section. As per your suggestion, all content of milk and intolerance was kept in one paragraph. As recommended by reviewer 1, more information about lactose-free milk was added. (See Page 4, Lines 77–125). Line 87-90: This appears to be a sentence fragment. Consider rewriting it as a complete sentence. Author’s comments: We agree with the reviewer, and therefore, we have rewritten all these sentences (See Page 4, Lines 81–93). Line 94-97: Not clear what’s precisely being conveyed here Author’s comments: We understand the reviewer's point of view, but we need to emphasize that after all the context presented, the sentence itself is clear and understandable. In the previous sentences, it was discussed what lactose malabsorption is, and all the negative consequences that this situation can lead to human health. In lines 97–105, we reported that despite all these problems, lactose malabsorbers don’t need to restrict milk or dairy from their diet, thanks to existing technologies for the production of lactosefree milk and dairy products. Still, our society is constantly changing in terms of the way we feed and nourish ourselves, and as a consequence, the industry tries to keep up with Page 6 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review this movement. The production of concentrated lactose-free milk could support both the industry and consumers. That's because, the consumer can do direct use of this product, depending on its nutritional requirements (related to sports practices, lifestyle, and age), socio-cultural factors, and intrinsic product characteristics. Likewise, from concentrated milk, the industry can innovate in obtaining lactose-free derivatives, as we know that concentration is often the first step in their manufacture. Among the many products that utilize milk or milk components, we can mention supplements for athletes, infant formulas, supplements for the elderly, as well as more common products such as cheeses, concentrated yogurts, ice cream, and dairy beverages. Line 111: Please elaborate on the previous studies on milk/whey and establish Author’s comments: We agree with the reviewer. The following sentences were added: “More specifically, Camelo-Silva et al. (2022) freeze concentrated milk until the third stage and used the sample from the first stage for ice cream production (Ice cream 1). This ice cream was contrasted to the ice cream from regular milk (Ice cream 2), and the authors concluded that Ice cream 1 presented good chemical, physical, rheological, and microstructural properties. Likewise, in the approach of Barros et al. (2022), FC was employed as an indirect technology for ice cream manufacture. However, instead of milk, cheese whey was used as a raw material for the FC process, and the concentrate from the second stage was evaluated as a milk substitute in ice cream. After testing 4 replacement levels, the authors concluded that the incorporation of concentrated whey at a 50% substitution level was better in terms of color, flavor, and texture attributes. In addition to the structural characteristics of the final product, the other advantage of this study was the added value to the whey, which is often seen only as a by-product of the cheese industry. De Liz et al. (2020) also utilized freeze concentrated whey in their experiments, but with another proposal: goat’s whey freeze concentrate was used as an encapsulant agent for probiotic encapsulation (Bifidobacterium animalis ssp. lactis BB-12) by spray drying. The powdered probiotic samples from the encapsulation process presented good stability after storage at 4 °C and 25 °C for 40 days (> 7 log CFU g−1), showing that goat whey concentrates had an excellent behavior as a cell protective material. Also, it was noted that, as a wall material, goat whey concentrate exhibited favorable thermal properties before and after encapsulation. Equally, Machado Canella et al. (2020), worked Page 7 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review with a based-goat raw material. However, their sample did not consist of goat whey, but semi-skimmed goat milk. After optimization of the FC process, it was obtained a concentrate yield of 77.97%. Moreover, the content of total solids changed from 9.94 to 32.87 (g 100 g−1), with an emphasis on protein (from 3.53 to 9.43 g 100 g−1).” To understand the full context, please read page 6, lines 126–165. Line 126-132: It’s not evidently established what differentiates your research from that of Dantas et al. (2021); rewrite and introduce your hypothesis here more effectively Author’s comments: We agree with Reviewer 2 and this comment was addressed. Note that the work realized by Dantas et al. (2021) used a different technique of freeze concentration. This work (Dantas et al., 2021) evaluated the behavior of lactose-free milk when submitted to the Progressive freeze concentration. Given the considerable amount of total solids retained in the solid fraction (ice), this ice was thawed, frozen again, and subjected to the vacuum-assisted BFC. In the present study, it was explored a different technique, i. e., the lactose-free milk was submitted to the centrifugation-assisted block freeze concentration process. In the sequence, as performed by Dantas et al. (2021), the ice fraction was subjected to the vacuum-assisted BFC aiming for the better utilization of the nutrients that were retained there. Finally, as recommended by Reviewer 2 and attending to other suggestions from Reviewer 1, this part was rewritten. (See Page 7, Lines 166–212). Line 136: Please clearly present the hypothesis and contribution of your study in the Introduction section. Author’s comments: We agree with the reviewer. Therefore, we have rewritten the Introduction as discussed in the previous comment. Line 128-131: Rewrite Author’s comments: We agree with the reviewer. So, the phrases “Recent work (Dantas et al., 2021) suggests the combination of progressive FC and BFC supported by vacuum, as a strategy for concentration of lactose-free milk. However, given the interesting results obtained by other authors, when who worked with Page 8 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 2 28 Abstract 29 30 Lactose-free milk is rising in popularity among consumers due to its claim to be a better 31 digestible product compared to regular fluid milk. For that reason, concentrating this 32 food is a good alternative for increasing its versatility and usability in different dairy 33 industry segments. Block freeze concentration (BFC) is a simple technology used to 34 concentrate liquid foods through ice crystal formation and subsequent removal of 35 water. Thus, this work aimed to test two variants of the BFC technique on lactose-free 36 milk concentration. In the first approach, it was investigated the centrifugation-assisted 37 BFC of skim lactose-free milk by applying a factorial experimental design. Temperature, 38 time, and rotation speed were the factors; and the response variables included the 39 concentrate yield, concentration index, and efficiency of the process. Concentrate yield 40 and concentration index were mainly affected by the centrifugation temperature. On 41 the other hand, individual factors did not have a significant effect on the efficiency, only 42 their interactions. In the case of centrifugation-assisted BFC in a single step, the 43 condition at 40 °C, 70 min, and 4500 rpm was considered the best, given the highest 44 values of efficiency and concentrate yield (80.87 and 67.02, respectively), and still an 45 excellent value for concentration index (2.05). Conversely, the condition at 30 °C, 45 46 min, and 3500 rpm was chosen to integrate a freeze concentration process in two-stage. 47 Then, the ice obtained from the first cycle was subjected to the vacuum-assisted BFC, 48 which consisted in the second cycle. The concentrate obtained from the vacuum49 assisted BFC presented contents of total solids, carbohydrates, and protein 2.95, 3.00, 50 and 2.91 times more than the initial lactose-free milk, respectively. Therefore, we Page 15 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 3 51 believe that the concentrates obtained can be used for the development of innovative 52 lactose-free dairy products. 53 54 Practical Application 55 56 Using concentration processes in the dairy industry can significantly contribute to 57 enhancing the overall efficiency of milk processing since huge quantities of water from 58 milk can be reduced, increasing the total solids content. In turn, dairy products that 59 provide a high amount of solids (especially protein) are gaining in popularity among 60 consumers, with consequent interest from researchers. In addition, milk concentration 61 shows advantages in terms of processing, packaging, transportation, and handling. Since 62 most changes occur in an aqueous environment, the removal of some part of water 63 results in the preservation of milk. It is noteworthy that dairy industries are concerned 64 principally with food preservation, green technologies, and the production of high65 quality products. Thus, concentration processes could favor the development of milk 66 products rich in proteins to meet certain demands on functional and nutritional 67 properties, for example in beverages and formulated food. 68 69 70 71 72 73 74 Page 16 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 4 75 1. Introduction 76 77 Dairy is an important source of essential nutrients including high-quality 78 proteins, calcium, vitamins (vitamins B12, vitamin A, riboflavin, thiamin), and 79 micronutrients (Mg and K), in many populations. However, milk consumption has 80 reduced over the last few decades, notedly in developed countries, where unfavorable 81 gastrointestinal symptoms are a frequent cause for avoidance. In turn, full dairy 82 avoidance from the diet may enhance the risk of nutrient insufficiency and thus 83 contribute to metabolic bone disease, low bone mineral density, or metabolic 84 syndromes (Appleby et al., 2007; Pearlman & Akpotaire, 2019). The presence of the 85 disaccharide lactose in milk is commonly assigned to these dairy restrictions due to a 86 health status known as lactose malabsorption (Shrestha et al., 2021). There are some 87 reasons for the manifestation of lactose malabsorption (such as celiac disease, microbial 88 infections, or malnutrition that damages the intestinal villi), but the main one is the 89 lactase non-persistence (LNP) (OMIM#223100), a phenotypic enzyme deficiency that 90 affects different cultures (EFSA, 2010). The enzyme in question is lactase-phlorizin 91 hydrolase, simply called lactase, which is responsible for hydrolyzing lactose to galactose 92 and glucose, thus facilitating its digestion. In LNP clinical cases, there is a decrease in the 93 lactase activity in the intestinal lumen after weaning (Kuchay, 2020). As a consequence, 94 LNP individuals may experience distinct kinds of systemic and intestinal symptoms: 95 vomiting, nausea, headache, abdominal pain, flatulence, gut distension, constipation, 96 diarrhea, muscle pain, loss of concentration, allergies, mouth ulcers, heart arrhythmia, 97 and increased micturition (Qibtia et al., 2021). Taking into account this entire scenario, 98 it is required to produce innovative and alternative technologies to serve lactose Page 17 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 5 99 malabsorbers who do not wish to limit dairy products from their diet, given the 100 significance of specific nutrients contained in milk. In this context, fluid lactose-free milk 101 is already a well-established way to help this population, as well as those who are 102 tolerant but also want to avoid lactose for any other reasons (as discussed in the work 103 by Castellini and Graffigna [2022]). Only in the United States, this kind of milk had 201 104 million gallons sold in 2020, experiencing 19% growth on both a dollar and volume basis 105 compared to the previous year (Dairy Foods, 2021). There are two most common forms 106 of industrial production of lactose-free or lactose-reduced milk. The first is lactose 107 enzymatic hydrolysis, via using of β-galactosidase from Kluyveromyces lactis, 108 Kluyveromyces faragilis, or Aspergillus oryzae, releasing galactose and glucose into milk 109 as a result of the reaction (De Oliveira Neves & de Oliveira, 2021; Inanan, 2022). The 110 other technology frequently approached are ultrafiltration and nanofiltration 111 membranes, which mechanically separate out the lactose molecules (Winkless, 2021). 112 Nevertheless, researchers are constantly searching for better filtration performance and 113 separation capacity, for example, the work by Morelos-Gomez et al. (2021), who 114 developed graphene oxide membranes for lactose separation. In any of the procedures, 115 the final product must present a lactose concentration in accordance with the guidelines 116 of the country or region. For instance, according to the European Food Safety Agency 117 (EFSA), final products labeled as “lactose-free” must have a lactose concentration lower 118 than 0.1 g 100 mL−1 (EFSA, 2010). This same limit is established by the Brazilian 119 guidelines published by the Health Surveillance Agency (ANVISA) (BRASIL, 2017). In the 120 same way, ANVISA establishes that dairy products classified as “lactose-reduced” or 121 “low-lactose” are those that contain lactose in a range of 0.1–1.0 g 100 mL−1. On the 122 other hand, the Food and Drug Administration (FDA) does not define the terms “lactosePage 18 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 6 123 free” or “lactose-reduced”, but suggests that these claims should be truthful and not 124 misleading. These products or those with similar claims are expected to be free of milk 125 allergen, or in this case, free of lactose (FDA, 2022). 126 Freeze concentration (FC) is an environmentally friendly and emerging 127 technology employed to concentrate food solutions with heat-sensitive constituents 128 such as coffee, milk, and fruit juices. Regarding the milk, thermal treatment in a 129 temperature variation from 70 to 100°C may denature the whey protein (e.g., β130 lactoglobulin and α-lactalbumin) and provoke the formation of aggregates (Qian et al., 131 2017). Thus, FC has been revealed to be very efficient in the maintenance of bioactive 132 compounds, volatile compounds, and biological activity (cytotoxic activity and 133 antioxidant) due to the low temperature (below 0 °C) used in the process (Gunathilake, 134 2020). Thereby, the beneficial effects of FC have been newly reported in blueberry juice 135 (Casas-Forero et al., 2020a, b; Casas-Forero et al., 2021a), strawberry juice (Adorno et 136 al., 2017), orange juice (Haas et al., 2022), pineapple juice (Orellana-Palma et al., 2020a), 137 waste potato juice (Kowalczewski et al., 2019), apple juice (Ding et al., 2019; Qin et al., 138 2019), broccoli extract (Azhar et al., 2020), green tea (Meneses et al., 2021), milk 139 (Camelo-Silva et al., 2022; Machado Canella et al., 2020), and whey (Barros et al., 2022; 140 De Liz et al., 2020). More specifically, Camelo-Silva et al. (2022) freeze concentrated milk 141 until the third stage and used the sample from the first stage for ice cream production 142 (Ice cream 1). This ice cream was contrasted to the ice cream from regular milk (Ice 143 cream 2), and the authors concluded that Ice cream 1 presented good chemical, 144 physical, rheological, and microstructural properties. Likewise, in the approach of Barros 145 et al. (2022), FC was employed as an indirect technology for ice cream manufacture. 146 However, instead of milk, cheese whey was used as a raw material for the FC process, Page 19 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 7 147 and the concentrate from the second stage was evaluated as a milk substitute in ice 148 cream. After testing 4 replacement levels, the authors concluded that the incorporation 149 of concentrated whey at a 50% substitution level was better in terms of color, flavor, 150 and texture attributes. In addition to the structural characteristics of the final product, 151 the other advantage of this study was the added value to the whey, which is often seen 152 only as a by-product of the cheese industry. De Liz et al. (2020) also utilized freeze 153 concentrated whey in their experiments, but with another proposal: goat’s whey freeze 154 concentrate was used as an encapsulant agent for probiotic encapsulation 155 (Bifidobacterium animalis ssp. lactis BB-12) by spray drying. The powdered probiotic 156 samples from the encapsulation process presented good stability after storage at 4 °C 157 and 25 °C for 40 days (> 7 log CFU g−1), showing that goat whey concentrates had 158 excellent behavior as a cell protective material. Also, it was noted that, as a wall 159 material, goat whey concentrate exhibited favorable thermal properties before and 160 after encapsulation. Equally, Machado Canella et al. (2020) worked with a based-goat 161 raw material. However, their sample did not consist of goat whey, but semi-skimmed 162 goat milk. After optimization of the FC process, it was obtained a concentrate yield of 163 77.97%. Moreover, the content of total solids changed from 9.94 to 32.87 (g 100 g−1), 164 with an emphasis on protein (from 3.53 to 9.43 g 100 g−1). As well, FC has ever been 165 used to immobilize extracellular ice nucleators (Zhou et al., 2014). 166 Among FC processes, block freeze concentration (BFC) has been studied to 167 concentrate various liquid foods. For example, coffee extract in the work by Sequera et 168 al. (2019), beet (Beta vulgaris L.) by-products extract in the work by D. Arend et al. 169 (2022), goat milk by Canella et al. (2019a), sapucaia nut cake milk in the study by 170 Demoliner et al. (2020), and strawberry juice by Jaster et al. (2018). In this technique, Page 20 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 8 171 the solution to be concentrated is totally frozen, followed by partial gravitational 172 thawing. Thus, the ice block acts as a solid carcass through which the concentrated food 173 traverses (Machado Canella et al., 2018). Aiming to improve separation efficiency, the 174 BFC can be assisted by other techniques, such as ultrasound, centrifugation (Baykal & 175 Dirim, 2019), and vacuum (Orellana-Palma et al., 2017a). 176 The associated use of different concentration methods has also been described 177 in the literature; for example, progressive FC (PFC) of coconut water followed by 178 controlled thawing of ice (Jayawardena et al., 2020), and suspension FC and centrifugal 179 filtration of apple juice (Qin et al., 2021). Thereby, the combination of PFC and BFC has 180 been seen as an interesting opportunity to increase the amount of concentrate 181 extracted from the ice fraction. In addition, the process could reach a higher phase 182 separation than an isolated FC method. Studies addressed by Miyawaki and Inakuma 183 (2021) and Prestes et al. (2022) demonstrated that each method (individually) also 184 presents acceptable extraction results. However, as a complete unit, both methods are 185 enhanced, and in turn, it achieves a more effective extraction, leading to a higher quality 186 in the final concentrate, with excellent process parameters results. In this context, a 187 recent work proposed the combination of PFC and BFC supported by vacuum to 188 desalinize salt solutions (Hernández et al., 2021). These saline solutions simulated 189 seawater fluid, indicating that PFC and vacuum-assisted BFC can have practical 190 applicability. Moreover, Dantas et al. (2021) suggested the combination of PFC and 191 vacuum-assisted BFC as a strategy for the concentration of lactose-free milk, with a 192 significant increase of total solids (from 8.8 to 18.5 g 100 g –1). Firstly, the authors 193 evaluated the behavior of the sample when submitted to the PFC. Then, given the 194 considerable amount of total solids retained in the ice, this fraction was subjected to the Page 21 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 9 195 vacuum-assisted BFC. In conclusion, despite the potential of PFC and BFC combination, 196 there are still gaps in this separation method, since there are no studies on other liquid 197 foods such as juices or extracts. Also, there is no investigation of effects on the final 198 amount, physicochemical parameters, bioactive components, and antioxidant capacity. 199 And finally, there is no consideration of the initial parameters of the sample (density, 200 viscosity, solutes, among others), or even, the option to use BFC and later PFC. 201 From previous studies on centrifugation-assisted BFC (Casas-Forero et al., 2021b; 202 Guerra-Valle et al., 2022; Orellana-Palma et al., 2021), the present work considers the 203 application of this technology at a first moment. Subsequently, as performed by Dantas 204 et al. (2021), an ice fraction was subjected to the vacuum-assisted BFC aiming for better 205 utilization of the nutrients retained in this portion. Therefore, the approach of this 206 research provides data on the use of BFC processes (both centrifugation-assisted BFC 207 and vacuum-assisted BFC) to concentrate carbohydrates and protein from lactose-free 208 milk. Our general objective is to evaluate the viability of these processes as non-thermal 209 technologies to enhance the content of important nutrients in lactose-free milk. The 210 development of concentrated liquid milk, and its transference to the food industry, is 211 expected to increase the sustainability of the food system (processing), the health of 212 consumer diet, and the food industry competitiveness. 213 214 2. Material and methods 215 216 2.1 Material 217 Page 22 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 10 218 UHT lactose-free skim milk (CARREFOUR®, Madrid, Spain) from a local supermarket 219 in Barcelona (Spain) was used in the freezing concentration experiments. It contained 220 8.80 g 100 g−1 of total solids, 3.2 g 100 g−1 of proteins, 4.8 g 100 g−1 of carbohydrates 221 (lactose <0.01%), and lipid <0.5 g 100 g−1. 222 223 2.2 Physicochemical analysis 224 225 The total solids content of initial lactose-free milk, concentrated milk fractions, 226 and ice fractions was determined exactly as the protocol described by Dantas et al. 227 (2021). Therefore, a standard curve of total solids content against °Brix readings was 228 plotted employing different concentrations of lactose-free skim milk. Thus, at the end 229 of each freeze concentration test, the °Brix result was converted and expressed as total 230 solids content (g 100 g−1) through a linear regression (y = 0.8715x – 0.3553, R2 = 0.999). 231 Protein analysis was performed according to the Kjeldahl method (AOAC, 2005). 232 In turn, galactose, glucose, and lactose were determined following Schuster-Wolff233 Bühring et al. (2011), with some modifications. Therefore, the sample (1 mL) was initially 234 diluted in distilled water (8 mL) and mixed. In this solution were added 0.5 mL of Carrez 235 Reagent 1 and 2, which was vortexed for 1 min. Then, after 15 min of rest, a nylon 236 syringe filter (0.45 μm of diameter pore) (Agilent, Santa Clara, California, United States) 237 was used to filter the mixture. Each sample was injected in triplicate onto a carbohydrate 238 column (ION 300) (Interaction Chromatography, San Jose, CA, USA) of an HPLC system 239 (Hewlett Packard Series 1100, Agilent Technologies, Waldbronn, Germany). A refraction 240 index (Detector Beckman 156, San Ramon, California, United States) was employed as Page 23 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 11 241 detector. The column temperature was maintained at 28 °C, and the mobile phase used 242 was a sulfuric acid solution (0.013 M), with a flow rate of 0.4 mL min−1. 243 244 2.3 Freeze concentration systems of lactose-free skim milk 245 246 Two freeze concentration protocols (centrifugation-assisted BFC and vacuum247 assisted BFC) were used for the lactose-free milk concentration. 248 249 2.3.1 Centrifugation-assisted BFC 250 251 The centrifugation-assisted BFC process was performed in accordance with the 252 methodology proposed by Orellana-Palma et al. (2017b), but with some modifications. 253 Lactose-free milk (45 mL) was placed in centrifugal plastic tubes (internal diameter equal 254 to 27 mm) and frozen in a static freezer (12 h, − 20 °C), since according to Samsuri et al. 255 (2015), this time helps in the formation of large ice crystals, contributing positively to 256 the concentration process during the phases separation. The tubes were previously 257 enveloped with polystyrene foam. After the freezing, the frozen samples were rapidly 258 transferred to a centrifuge (Hettich model Rontanta 460R, Tuttlingen, Germany) with 259 temperature control. The data from four tubes were considered as a single batch, that 260 is, 4 tubes were put in the centrifuge and their data were collected together. This 261 procedure was replicated three times for each predetermined condition. Since the 262 samples were centrifuged, the ice fraction was separated from the concentrate fraction 263 using a filter. Page 24 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 18 403 of them, had a significant negative effect on the CI. This is in accordance with what was 404 discussed above regarding the time. From Figure 2a and Table 2, it can be seen that the 405 centrifugation rotation speed also negatively affected the CI, since the highest values 406 were found at the lowest rotation speed (3500 rpm). In opposition, interactions 407 between two factors were non-significant and had a positive effect on the response. 408 Concerning the Efficiency (Figure 2b), the individual factors had no significant effect, 409 only two interactions (time:temperature:rotation speed and time:rotation speed). 410 Santana et al. (2020) also calculated the concentration efficiency for blueberry juice 411 when subjected to the centrifugation-assisted freeze concentration, and likewise, 412 individual factors did not affect this response. A different result was noted for Y (Figure 413 2c), where it was observed that all individual factors and two interactions had a 414 significant effect on the response. 415 In view of all the above, the experimental condition at 40 ºC, 70 min, and 4500 416 rpm (Treatment 8) was considered ideal for the freeze concentration in a single step, 417 given the highest values of efficiency and concentrate yield (80.87% and 67.02%, 418 respectively), and still an excellent value for concentration index (2.05). Dantas et al. 419 (2021), who used progressive FC combined with vacuum-assisted BFC to concentrate 420 lactose-free milk, found an estimated CI value of 1.42. On the other hand, this present 421 work proposes a one-step approach, with a highest value of CI. Therefore, these findings 422 contribute to its industrial application and process agility. The variations in process 423 parameter terms and in final solute concentration can be explicated by the ice front 424 expanse for each FC technology. Centrifugation-assisted BFC exhibited lower solute 425 retention and better final concentration in Ci than progressive FC due to a phenomenon 426 denominated constitutional supercooling, i.e., the ice growth rate is determined by the Page 31 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 19 427 heat transfer area and the cooling temperature, which is a relevant factor in the design 428 of FC apparatus (Orellana-Palma et al., 2020a). The concentrated lactose-free milk from 429 Treatment 8 presented the following values (g 100 g−1) for protein, lactose, glucose, and 430 galactose, respectively: 6.50 ± 0.26, 0.27 ± 0.01, 5.53 ± 0.07, and 5.27 ± 0.06. The initial 431 values for each of these components are shown in Table 3. Thus, it is clear that the 432 obtained amounts were at least 2-fold higher when compared to the initial milk sample. 433 Nevertheless, we also investigated the FC in two steps in order to further 434 improve the results and decrease the total solids in the frozen matrix, since it was noted 435 that Treatment 1 had the highest content of retained solids in the ice (7.28 g 100 g−1). 436 Thus, we are interested in the recovery of these solids. As already mentioned, the 437 second cycle was performed using another methodology (vacuum-assisted BFC). In this 438 case, the vacuum was applied to the ice immediately after the centrifugation step. The 439 integrity of the ice in the condition at 30 °C, 45 min, and 3500 rpm was also decisive in 440 the choice of this treatment for the application of vacuum. 441 442 3.2 Vacuum-assisted BFC 443 444 As enlightened by the maker, the lactose-free skim milk employed in this work 445 was lactose-free due to prior enzymatic hydrolysis with β-galactosidase. Thus, the 446 resulting milk presented large quantities of the monosaccharides galactose and glucose 447 (about 2.4 g 100 g−1 of each). Therefore, the contents of glucose, galactose, lactose, and 448 protein of two cycles were measured and are shown in Table 3. A high separation of 449 solids content (CI = 3.57 for the concentrate) was obtained using vacuum-assisted BFC. 450 Carbohydrates and protein contents were also maximized using a second cycle. In Page 32 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 20 451 addition, the solids content verified in Ice 2 was reduced considerably. Machado Canella 452 et al. (2020) stated that this behavior is expected because the natural division of 453 gravitational thawing is improved due to external driving force (vacuum). Equally, η(%) 454 and Y(%) values were improved when vacuum-assisted BFC was performed (91.20 ± 0.91 455 and 71.50 ± 1.31, respectively). 456 While investigating the values more deeply, the results suggest that 457 centrifugation and vacuum have different effects on milk components. This is because 458 the CI of Conc 1 for protein was equal to 3.66, while the CI of Conc 2 was equal to 3.97. 459 Similar behavior occurred for carbohydrates (average of galactose and glucose values): 460 CI of Conc 1 was equal to 3.49, while the CI of Conc 2 was equal to 3.76. That is, vacuum461 assisted BFC seems to have a slightly better performance compared to centrifugation462 assisted BFC in terms of these macronutrients. However, when analyzing the total solids 463 (CI of Conc 1 = 4.06, CI of Conc 2 = 3.57), we noticed an inverse behavior, suggesting the 464 effect of centrifugation-assisted BFC on the other milk constituents (minor components) 465 outweighs the effect on the macronutrients studied. Kawasaki et al. (2006) developed a 466 work that can help to understand these results. They studied PFC of multicomponent 467 solutions, and found that the small molecular mass solutes concentrated and separated 468 more satisfactorily than the higher molecular mass solutes. This coincided well with the 469 magnitude of the diffusion coefficient of each solute. Likewise, Nakagawa et al. (2010) 470 noted that phenol (M.M = 94 g mol–1) was more concentrated in the liquid zone than 471 dye (M.M = 993 g mol–1). So, the dissimilarities found between total solid solids content 472 vs. carbohydrates and proteins could be explained due to the difference in the mobility 473 when the substances meet the freezing front. The molecular size and the concentration 474 affect the mobility of the solutes. Therefore, as a suggestion for future research on Page 33 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 21 475 lactose-free milk FC, we propose an extensive investigation of mineral and vitamin 476 contents, in addition to specific determinations of the protein fraction (for instance, αs1, 477 αs2-, β-, and κ-casein), given the increasing demand for kinds of milk that offer 478 additional advantages over common milk in terms of digestive health. In this regard, 479 Canella et al. (2019b), who freeze concentrated skim goat milk by BFC, found the content 480 of important minerals (such as magnesium and calcium) can be enhanced by the 481 increasing freeze concentration cycles. Moreover, it was discussed that a substantial 482 increase in the flavor and taste of food products can be verified when unitary operations 483 based on vacuum and low temperatures are used (Sun & Zheng, 2006). 484 According to Beldie and Moraru (2021), the concentration of milk in the dairy 485 industry is typically achieved by thermal evaporation or membrane technology such as 486 reverse osmosis. The efficiency of these processes is very similar to those obtained by 487 the freeze concentration process used in the present study. In thermal evaporation, the 488 maximum concentration level achievable is 55% for skim milk and 50% for whole milk, 489 while for the membrane process, the maximum concentration varies between 25% and 490 30% solids. Thermal evaporation is also known to reduce the quality of the final 491 concentrated product due to prolonged exposure to heat, which negatively affects the 492 color, taste, and nutritional value of milk. Furthermore, evaporators are prone to biofilm 493 formation by spore-forming mesophilic or thermophilic bacteria. A major drawback of 494 membrane separation is that the process is significantly affected by membrane fouling, 495 which leads to flux decline and limits the final achievable concentration of the product 496 (Beldie & Moraru, 2021). Given the above, we can verify that block freeze concentration 497 by centrifugation and vacuum can be used by the industry aiming for the macronutrient 498 concentration of lactose-free milk. Page 34 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 22 499 500 3.3 Validation of experimental results 501 502 Table 4 shows the values of Wexp, Wpred, and RSM. The results were similar to 503 those found by Orellana-Palma et al. (2017b) (0.6–0.9 for ice mass ration, Wexp or Wpred) 504 in the cryoconcentration of blueberry juice. They noted a decrease in values as the 505 freeze concentration cycles increased, and attributed this to the increase in the 506 percentage of concentrate over consecutive stages. Our results showed analogous 507 behavior, since, when analyzing the first and second cycle, the Wpred values were 0.95 508 and 0.79, respectively. Similarly, Orellana-Palma et al. (2017c) noticed a decrease in W 509 values as the test time increased, and this was also attributed to the increase in the 510 percentage of concentrate over time. Likewise, our results showed this trend, such as 511 Treatments 2 and 4, where conditions were kept the same except for the increase in 512 time. By comparing these treatments, we observed a significant decrease in Wexp and 513 Wpred values, as well as Treatments 5 and 7. Additionally, the RMS values fluctuated 514 between 1.0% and 3.7%, indicating an excellent fit, since a bad fit corresponds to RSM 515 values over 25% (Lewicki, 2000). Therefore, the experimental conditions used to 516 concentrate lactose-free milk macronutrients were ideal. Moreover, the RMS values 517 were lower than the values obtained by Petzold et al. (2015) and Orellana-Palma et al. 518 (2017b) (4.9%, and 8.7%, respectively). 519 520 4. Conclusions Page 35 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 23 521 The results of this study suggest that it is possible to obtain an interesting 522 concentrated sample without damaging its initial properties, obtaining a final product 523 post BFC process with a high content of macronutrients. While investigating the effect 524 of process parameters on centrifugation-assisted BFC of lactose-free milk, we observed 525 that all individual factors presented a significant effect on concentrate yield and 526 concentration index. On the other hand, the same did not occur to efficiency, where it 527 was observed that only two interactions had a significant effect on this response, which 528 in turn presented values from 78% to 81%. To obtain concomitantly the maximum 529 concentrate yield and efficiency values, the operating condition can be set at a time of 530 70 min, centrifugation temperature of 40 ºC, and rotation speed of 4500 rpm. The 531 results of this approach were promising, considering the simplicity and ease of the 532 procedure. Nonetheless, a second stage for the freeze concentration process was 533 proposed (by vacuum-assisted BFC), which also demonstrated to be an efficient method 534 to concentrate skim lactose-free milk. In this system, the protein was well concentrated 535 in the liquid phase (∼3.97-fold higher than Ice 1), as well as the carbohydrates (glucose 536 and galactose) (∼3.7-fold higher than Ice 1). These findings support the idea that the 537 concentration of lactose-free milk by centrifugation-assisted BFC jointly with an 538 additional separation by vacuum-assisted BFC could be considered an innovative 539 technology to obtain a liquid sample rich in macronutrients. Either concentrate 1 or 540 concentrate 2 could be used for the development of new lactose-free dairy products. In 541 this sense, future studies must be carried out to evaluate the feasibility of scaling the 542 BFC system from laboratory scale to pilot plant scale, aiming the production on a mass 543 scale. Thus, this technique would be an attractive alternative for dairy industries. 544 Furthermore, an interesting challenge is the application of the two stages-BFC in other Page 36 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 24 545 liquid food matrices, such as juices and/or extracts, and to study its effect on different 546 properties. For instance, some properties currently valued are the presence of bioactive 547 components and the antioxidant capacity. 548 549 Acknowledgments 550 551 The authors are grateful to the Coordination of Improvement of Higher 552 Education Personnel (CAPES, Brazil) (CAPES-PRINT, Project number 553 88887.310560/2018-00); to National Council for Scientific and Technological 554 Development (CNPq, Brazil) by the financial support (CNPq, 405965/2016-8); and to 555 Coordination of Improvement of Higher Education Personnel (CAPES, Brazil) by the 556 scholarship (001). The authors thank Mr. Diogo Pontes Costa, from the Postgraduate 557 Program in Design, Federal University of Santa Catarina, Center for Communication and 558 Expression, for the design and development of the figures in this article. The authors are 559 also grateful to the Universitat Politecnica de Catalunya (Spain) for scientific support. 560 561 Conflict of interest 562 The authors declare that they have no conflict of interest. 563 564 565 566 567 568 Page 37 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 25 569 References 570 571 AOAC, (2005). Official methods of analysis, 18th ed. Association of Official Analytical 572 Chemists, Gaithersburg, MD, USA. 573 Adorno, W. T., Rezzadori, K., Arend, G. D., Chaves, V. C., Reginatto, F. H., di Luccio, M., 574 & Petrus, J. C. (2017). 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A better route to lactose-free milk? Materials Today, 48, Page 1. 829 https://doi.org/10.1016/j.mattod.2021.07.019 830 Zhou, Z., Jin, J., Yue, T., & Lee, T. C. (2014). Optimization of covalent immobilization of 831 extracellular ice nucleators from Erwinia herbicola on magnetic Fe3O4/chitosan 832 nanoparticles for potential application in freeze concentration. Food and 833 Bioprocess Technology, 7(11), 3259–3268. https://doi.org/10.1007/s11947-014834 1318-6 Page 49 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 37 Tables Table 1 Factors values at the low (− 1) and high (+ 1) levels studied. Factors Centrifugation temperature (°C) Rotation speed (rpm) Centrifugation time (min) − 1 30 3500 45 + 1 40 4500 70 Page 50 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 38 Table 2 Results of efficiency, concentration index, and concentrate yield. Treatment Independent variables Responses Centrifugation temperature (°C) Rotation speed (rpm) Time (min) Efficiency (η) (%) Concentration index Concentrate yield (%) 1 30 3500 45 79.41 ± 0.62ab 4.06 ± 0.04a 18.09 ± 0.44e 2 30 4500 45 79.54 ± 1.30a 3.61 ± 0.29a 29.77 ± 2.87d 3 30 3500 70 78.76 ± 1.26ab 3.74 ± 0.32a 23.39 ± 2.68de 4 30 4500 70 78.51 ± 1.20ab 2.82 ± 0.01b 45.11 ± 3.62c 5 40 3500 45 79.56 ± 1.11a 3.04 ± 0.15b 45.25 ± 3.41c 6 40 4500 45 78.23 ± 0.82ab 2.36 ± 0.02c 56.42 ± 0.83b 7 40 3500 70 76.65 ± 0.08b 2.26 ± 0.04c 62.46 ± 0.25ab 8 40 4500 70 80.87 ± 0.93a 2.05 ± 0.06c 67.02 ± 2.11a a,b,c,d,eWithin a column, different superscript lowercase letters denote significant differences (P < 0.05) between the treatments. Page 51 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 39 Table 3 Carbohydrate and protein content (mean ± standard deviation) of concentrates and ice fractions from first and second freeze concentration cycles. Lactose-free milk Conc 1 Ice 1 Conc 2 Ice 2 Total solids (g 100 g−1) 8.8 35.38 ± 0.31 7.28 ± 0.18 26.02 ± 0.25 2.29 ± 0.22 Protein (g 100 g–1) 3.2 11.71 ± 0.31 2.35 ± 0.35 9.34 ± 0.09 0.83 ± 0.08 Glucose (g 100 g–1) ∼ 2.4* 8.64 ± 0.32 2.02 ± 0.02 7.62 ± 0.02 0.64 ± 0.01 Galactose (g 100 g–1) ∼ 2.4* 8.14 ± 0.29 1.91 ± 0.02 7.18 ± 0.04 0.63 ± 0.01 Lactose (g 100 g–1) < 0.01 0.523 ± 0.005 0.174 ± 0.001 0.448 ± 0.001 < 0.01 Conc 1 and Ice 1 were fractions obtained by centrifugation-assisted freeze concentration at 30 ºC, 45 min, and 3500 rpm. Conc 2 and Ice 2 are fractions obtained by vacuum-assisted block freeze concentration from Ice 1. *The manufacturer does not provide data for monosaccharides, but only for total carbohydrates (4.8 g 100 g–1). Therefore, glucose and galactose contents were expressed as approximate values, as discussed in section 3.2 Vacuum-assisted BFC of this work. Page 52 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 40 Table 4 Experimental results validation for three different factors. Treatment Centrifugation temperature (°C) Rotation speed (rpm) Time (min) Wpred Wexp RSM (%) 1 30 3500 45 0.95 ± 0.01a 0.94 ± 0.01a 1.39 2 30 4500 45 0.91 ± 0.02a 0.89 ± 0.02b 1.77 3 30 3500 70 0.93 ± 0.02a 0.92 ± 0.01ab 1.48 4 30 4500 70 0.82 ± 0.01b 0.82 ± 0.02c 1.00 5 40 3500 45 0.84 ± 0.03b 0.82 ± 0.02c 2.32 6 40 4500 45 0.736 ± 0.003c 0.743 ± 0.001d 1.02 7 40 3500 70 0.73 ± 0.01c 0.70 ± 0.01e 3.66 8 40 4500 70 0.63 ± 0.02d 0.65 ± 0.02f 2.76 a,b,c,d,eWithin a column, different superscript lowercase letters denote significant differences (P < 0.05) between the treatments. Page 53 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review 41 Figure Legends Figure 1: Freeze concentration schematic diagram of lactose-free milk in two steps. Figure 2: Effect of temperature, rotation speed, and time on the (a) Concentration Index, (b) Efficiency, and (c) Concentrate Yield. Page 54 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review Figure 1: Freeze concentration schematic diagram of lactose-free milk in two steps. 828x506mm (118 x 118 DPI) Page 55 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science For Peer Review B: Temperature A: Time C: Rotation speed ABC BC AB AC ABC AC BC C: Rotation speed A: Time AB B: Temperature B: Temperature C: Rotation speed A: Time BC ABC AB AC − + − + − + Page 56 of 56 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 Journal of Food Science