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 <front>
  <journal-meta>
   <journal-id journal-id-type="publisher-id">Foods and Raw Materials</journal-id>
   <journal-title-group>
    <journal-title xml:lang="en">Foods and Raw Materials</journal-title>
    <trans-title-group xml:lang="ru">
     <trans-title>Foods and Raw Materials</trans-title>
    </trans-title-group>
   </journal-title-group>
   <issn publication-format="print">2308-4057</issn>
   <issn publication-format="online">2310-9599</issn>
  </journal-meta>
  <article-meta>
   <article-id pub-id-type="publisher-id">103916</article-id>
   <article-id pub-id-type="doi">10.21603/2308-4057-2026-2-675</article-id>
   <article-id pub-id-type="edn">GSYOUN</article-id>
   <article-categories>
    <subj-group subj-group-type="toc-heading" xml:lang="ru">
     <subject>Research Article</subject>
    </subj-group>
    <subj-group subj-group-type="toc-heading" xml:lang="en">
     <subject>Research Article</subject>
    </subj-group>
    <subj-group>
     <subject>Research Article</subject>
    </subj-group>
   </article-categories>
   <title-group>
    <article-title xml:lang="en">Empirical predicting permeate flux in skim milk microfiltration</article-title>
    <trans-title-group xml:lang="ru">
     <trans-title>Empirical predicting permeate flux in skim milk microfiltration</trans-title>
    </trans-title-group>
   </title-group>
   <contrib-group content-type="authors">
    <contrib contrib-type="author">
     <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-6221-8230</contrib-id>
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Mamay</surname>
       <given-names>Dmitriy S.</given-names>
      </name>
      <name xml:lang="en">
       <surname>Mamay</surname>
       <given-names>Dmitriy S.</given-names>
      </name>
     </name-alternatives>
     <email>dima-mamaj@yandex.ru</email>
     <xref ref-type="aff" rid="aff-1"/>
    </contrib>
    <contrib contrib-type="author">
     <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-1784-0837</contrib-id>
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Babenyshev</surname>
       <given-names>Sergey P.</given-names>
      </name>
      <name xml:lang="en">
       <surname>Babenyshev</surname>
       <given-names>Sergey P.</given-names>
      </name>
     </name-alternatives>
     <xref ref-type="aff" rid="aff-2"/>
    </contrib>
    <contrib contrib-type="author">
     <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-5396-1548</contrib-id>
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Evdokimov</surname>
       <given-names>Ivan A.</given-names>
      </name>
      <name xml:lang="en">
       <surname>Evdokimov</surname>
       <given-names>Ivan A.</given-names>
      </name>
     </name-alternatives>
     <xref ref-type="aff" rid="aff-3"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Mamay</surname>
       <given-names>Angelina V.</given-names>
      </name>
      <name xml:lang="en">
       <surname>Mamay</surname>
       <given-names>Angelina V.</given-names>
      </name>
     </name-alternatives>
     <xref ref-type="aff" rid="aff-4"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Lisitsyn</surname>
       <given-names>Vyacheslav A.</given-names>
      </name>
      <name xml:lang="en">
       <surname>Lisitsyn</surname>
       <given-names>Vyacheslav A.</given-names>
      </name>
     </name-alternatives>
     <xref ref-type="aff" rid="aff-5"/>
    </contrib>
   </contrib-group>
   <aff-alternatives id="aff-1">
    <aff>
     <institution xml:lang="ru">North-Caucasus Federal University</institution>
     <city>Stavropol</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">North-Caucasus Federal University</institution>
     <city>Stavropol</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-2">
    <aff>
     <institution xml:lang="ru">North-Caucasus Federal University</institution>
     <city>Stavropol</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">North-Caucasus Federal University</institution>
     <city>Stavropol</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-3">
    <aff>
     <institution xml:lang="ru">North-Caucasus Federal University</institution>
     <city>Stavropol</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">North-Caucasus Federal University</institution>
     <city>Stavropol</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-4">
    <aff>
     <institution xml:lang="ru">North-Caucasus Federal University</institution>
     <city>Stavropol</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">North-Caucasus Federal University</institution>
     <city>Stavropol</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-5">
    <aff>
     <institution xml:lang="ru">North-Caucasus Federal University</institution>
     <city>Stavropol</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">North-Caucasus Federal University</institution>
     <city>Stavropol</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <pub-date publication-format="print" date-type="pub" iso-8601-date="2025-09-11T00:00:00+03:00">
    <day>11</day>
    <month>09</month>
    <year>2025</year>
   </pub-date>
   <pub-date publication-format="electronic" date-type="pub" iso-8601-date="2025-09-11T00:00:00+03:00">
    <day>11</day>
    <month>09</month>
    <year>2025</year>
   </pub-date>
   <volume>14</volume>
   <issue>2</issue>
   <fpage>331</fpage>
   <lpage>338</lpage>
   <history>
    <date date-type="received" iso-8601-date="2025-01-14T00:00:00+03:00">
     <day>14</day>
     <month>01</month>
     <year>2025</year>
    </date>
    <date date-type="accepted" iso-8601-date="2025-06-03T00:00:00+03:00">
     <day>03</day>
     <month>06</month>
     <year>2025</year>
    </date>
   </history>
   <self-uri xlink:href="https://jfrm.ru/en/issues/23601/23781/">https://jfrm.ru/en/issues/23601/23781/</self-uri>
   <abstract xml:lang="ru">
    <p>Native micellar casein and whey proteins can be obtained from skim milk by microfiltration. It is a popular method that yields high-quality dairy products. The article introduces an empirical approach to predicting the permeate flux value during microfiltration of skim milk. The research objective was to produce retentates with a target ratio of protein fractions in the true protein.&#13;
The physicochemical profile of skim milk was studied by standard methods. The experimental microfiltration involved a Spectrum Labs KrosFlo® Research II TFF System.&#13;
The research revealed the optimal operating modes of microfiltration and diafiltration for 0.1 μM membranes (Vladisart, Russia): operating pressure 0.2–2.5 bar, circulation rate 65–140 mL/min, temperature 50 ± 1°C. These modes made it possible to obtain a ratio of casein to whey proteins that exceeded 95:5. At the optimal ratios of pressure, circulation rate, and temperature, the amount of casein proteins grew from 2.2 to 4.0% in relation to whey proteins.&#13;
The grid search analysis confirmed a set of similar values of Y = f(X1, X2, X3). Microfiltration of skim milk proved effective at different combinations of pressure, circulation rate, and temperature, depending on the production technology, target products, and target ratio of mass fractions of casein and whey proteins in the true protein.</p>
   </abstract>
   <trans-abstract xml:lang="en">
    <p>Native micellar casein and whey proteins can be obtained from skim milk by microfiltration. It is a popular method that yields high-quality dairy products. The article introduces an empirical approach to predicting the permeate flux value during microfiltration of skim milk. The research objective was to produce retentates with a target ratio of protein fractions in the true protein.&#13;
The physicochemical profile of skim milk was studied by standard methods. The experimental microfiltration involved a Spectrum Labs KrosFlo® Research II TFF System.&#13;
The research revealed the optimal operating modes of microfiltration and diafiltration for 0.1 μM membranes (Vladisart, Russia): operating pressure 0.2–2.5 bar, circulation rate 65–140 mL/min, temperature 50 ± 1°C. These modes made it possible to obtain a ratio of casein to whey proteins that exceeded 95:5. At the optimal ratios of pressure, circulation rate, and temperature, the amount of casein proteins grew from 2.2 to 4.0% in relation to whey proteins.&#13;
The grid search analysis confirmed a set of similar values of Y = f(X1, X2, X3). Microfiltration of skim milk proved effective at different combinations of pressure, circulation rate, and temperature, depending on the production technology, target products, and target ratio of mass fractions of casein and whey proteins in the true protein.</p>
   </trans-abstract>
   <kwd-group xml:lang="ru">
    <kwd>Filtration</kwd>
    <kwd>separation</kwd>
    <kwd>dairy industry</kwd>
    <kwd>casein</kwd>
    <kwd>whey proteins</kwd>
    <kwd>empirical approach</kwd>
   </kwd-group>
   <kwd-group xml:lang="en">
    <kwd>Filtration</kwd>
    <kwd>separation</kwd>
    <kwd>dairy industry</kwd>
    <kwd>casein</kwd>
    <kwd>whey proteins</kwd>
    <kwd>empirical approach</kwd>
   </kwd-group>
   <funding-group>
    <funding-statement xml:lang="ru">The research was supported by the Russian Science Foundation, grant no. 24-26-20084, https://rscf.ru/en/project/ 24-26-20084/</funding-statement>
    <funding-statement xml:lang="en">The research was supported by the Russian Science Foundation, grant no. 24-26-20084, https://rscf.ru/en/project/ 24-26-20084/</funding-statement>
   </funding-group>
  </article-meta>
 </front>
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