<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0035-001X</journal-id>
<journal-title><![CDATA[Revista mexicana de física]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. fis.]]></abbrev-journal-title>
<issn>0035-001X</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Física]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0035-001X2020000600761</article-id>
<article-id pub-id-type="doi">10.31349/revmexfis.66.761</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Analysis of an electroosmotic flow in wavy wall microchannels using the lubrication approximation]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Arcos]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Bautista]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Méndez]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Peralta]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Instituto Politécnico Nacional Escuela Superior de Ingeniería Mecánica y Eléctrica Azcapotzalco ]]></institution>
<addr-line><![CDATA[CDMX ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Nacional Autónoma de México Facultad de Ingeniería ]]></institution>
<addr-line><![CDATA[CDMX ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Tecnológico de Estudios Superiores de Huixquilucan  ]]></institution>
<addr-line><![CDATA[Huixquilucan Estado de México]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2020</year>
</pub-date>
<volume>66</volume>
<numero>6</numero>
<fpage>761</fpage>
<lpage>770</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2020000600761&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2020000600761&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2020000600761&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract We present the analysis of an electroosmotic flow (EOF) of a Newtonian fluid in a wavy-wall microchannel. To describe the flow and electrical fields, the lubrication and Debye-Hückel approximations are used. The simplified governing equations of continuity, momentum, and Poisson-Boltzmann, together with the boundary conditions, are presented in dimensionless form. For solving the mathematical problem, numerical and asymptotic techniques were applied. The asymptotic solution is obtained in the limit of very thin electric double layers (EDLs). We show that the lubrication theory is a powerful technique for solving the hydrodynamic field in electroosmotic flows in microchannels where the amplitude of the waviness changes on the order of the mean semi-channel height. Approximate analytical expressions for the velocity components and pressure distribution are derived, and a closed formula for the volumetric flow rate is obtained. The results show that the principal parameters that govern this EOF are the geometrical parameter, &#949;, which characterizes the waviness of the microchannel, and the ratio of the mean semi-channel height to the thickness of the EDL,    &#954; ¯.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Wavy wall microchannel]]></kwd>
<kwd lng="en"><![CDATA[electroosmotic flow]]></kwd>
<kwd lng="en"><![CDATA[lubrication theory]]></kwd>
<kwd lng="en"><![CDATA[domain perturbation method]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<label>1</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Karniadakis]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Beskok]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Aluru]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
</person-group>
<source><![CDATA[Microflows and Nanoflows: fundamentals and simulation]]></source>
<year>2005</year>
<publisher-loc><![CDATA[USA ]]></publisher-loc>
<publisher-name><![CDATA[Springer Science &amp; Business Media]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<label>2</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Stone]]></surname>
<given-names><![CDATA[H.A.]]></given-names>
</name>
<name>
<surname><![CDATA[Stroock]]></surname>
<given-names><![CDATA[A.D.]]></given-names>
</name>
<name>
<surname><![CDATA[Ajdari]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Ann. Rev. Fluid Mech]]></source>
<year>2004</year>
<volume>36</volume>
<page-range>381</page-range></nlm-citation>
</ref>
<ref id="B3">
<label>3</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bruus]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<source><![CDATA[Theoretical Microfluidics]]></source>
<year>2008</year>
<publisher-loc><![CDATA[Oxford ]]></publisher-loc>
<publisher-name><![CDATA[Oxford University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<label>4</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Xuan]]></surname>
<given-names><![CDATA[X.]]></given-names>
</name>
<name>
<surname><![CDATA[Xu]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Li]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<source><![CDATA[Anal. Chem. 2]]></source>
<year>2005</year>
<volume>77</volume>
<page-range>4323</page-range></nlm-citation>
</ref>
<ref id="B5">
<label>5</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Chen]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Conlisk]]></surname>
<given-names><![CDATA[A. T.]]></given-names>
</name>
</person-group>
<source><![CDATA[Biomed. Microdevices]]></source>
<year>2008</year>
<volume>10</volume>
<page-range>289</page-range></nlm-citation>
</ref>
<ref id="B6">
<label>6</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ghosal]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<source><![CDATA[Phys. Rev. E]]></source>
<year>2006</year>
<volume>74</volume>
<page-range>041901</page-range></nlm-citation>
</ref>
<ref id="B7">
<label>7</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Adjari]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Phys. Rev. Lett.]]></source>
<year>1995</year>
<volume>4</volume>
<page-range>755</page-range></nlm-citation>
</ref>
<ref id="B8">
<label>8</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Adjari]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<source><![CDATA[Phys. Rev. E]]></source>
<year>1996</year>
<volume>53</volume>
<page-range>4996</page-range></nlm-citation>
</ref>
<ref id="B9">
<label>9</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Malevich]]></surname>
<given-names><![CDATA[A. E.]]></given-names>
</name>
<name>
<surname><![CDATA[Mityushev]]></surname>
<given-names><![CDATA[V. V.]]></given-names>
</name>
<name>
<surname><![CDATA[Adler]]></surname>
<given-names><![CDATA[P. M.]]></given-names>
</name>
</person-group>
<source><![CDATA[J. Colloid Interface Sci.]]></source>
<year>2010</year>
<volume>345</volume>
<page-range>72</page-range></nlm-citation>
</ref>
<ref id="B10">
<label>10</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Xia]]></surname>
<given-names><![CDATA[Z.]]></given-names>
</name>
<name>
<surname><![CDATA[Mei]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Sheplak]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Fan]]></surname>
<given-names><![CDATA[Z. H.]]></given-names>
</name>
</person-group>
<source><![CDATA[Microfluid. Nanofluid.]]></source>
<year>2009</year>
<volume>6</volume>
<page-range>37</page-range></nlm-citation>
</ref>
<ref id="B11">
<label>11</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Martínez]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Bautista]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
<name>
<surname><![CDATA[Escandón]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Méndez]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<source><![CDATA[Colloids Surf. A Physicochem. Eng. Asp]]></source>
<year>2016</year>
<volume>498</volume>
<page-range>7</page-range></nlm-citation>
</ref>
<ref id="B12">
<label>12</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Chen]]></surname>
<given-names><![CDATA[C.-K.]]></given-names>
</name>
<name>
<surname><![CDATA[Cho]]></surname>
<given-names><![CDATA[C.-C.]]></given-names>
</name>
</person-group>
<source><![CDATA[J. Colloid Interface Sci]]></source>
<year>2007</year>
<volume>312</volume>
<page-range>470</page-range></nlm-citation>
</ref>
<ref id="B13">
<label>13</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cho]]></surname>
<given-names><![CDATA[Ching-Chang]]></given-names>
</name>
<name>
<surname><![CDATA[Chen]]></surname>
<given-names><![CDATA[Chieh-Li]]></given-names>
</name>
<name>
<surname><![CDATA[Chen]]></surname>
<given-names><![CDATA[Cha&#8217;o-Kuang]]></given-names>
</name>
</person-group>
<source><![CDATA[J. Non-Newton. Fluid Mech]]></source>
<year>2012</year>
<volume>173</volume>
<page-range>13</page-range></nlm-citation>
</ref>
<ref id="B14">
<label>14</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Yang]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Liu]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
</person-group>
<source><![CDATA[Colloids Surf. A-Physicochem. Eng. Asp]]></source>
<year>2008</year>
<volume>328</volume>
<page-range>28</page-range></nlm-citation>
</ref>
<ref id="B15">
<label>15</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ghosal]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<source><![CDATA[J. Fluid Mech]]></source>
<year>2002</year>
<volume>459</volume>
<page-range>103</page-range></nlm-citation>
</ref>
<ref id="B16">
<label>16</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ghosal]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<source><![CDATA[Electrophoresis]]></source>
<year>2004</year>
<volume>25</volume>
<page-range>214</page-range></nlm-citation>
</ref>
<ref id="B17">
<label>17</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bautista]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
<name>
<surname><![CDATA[Sánchez]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Arcos]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Méndez]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<source><![CDATA[J. Fluid Mech.]]></source>
<year>2013</year>
<volume>722</volume>
<page-range>496</page-range></nlm-citation>
</ref>
<ref id="B18">
<label>18</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Masliyah]]></surname>
<given-names><![CDATA[J. H.]]></given-names>
</name>
<name>
<surname><![CDATA[Bhattacharjee]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<source><![CDATA[Electrokinetic and Colloid Transport Phenomena]]></source>
<year>2006</year>
<publisher-loc><![CDATA[USA ]]></publisher-loc>
<publisher-name><![CDATA[Wiley-Interscience]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B19">
<label>19</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Probstein]]></surname>
<given-names><![CDATA[R. F.]]></given-names>
</name>
</person-group>
<source><![CDATA[Physicochemical hydrodynamics]]></source>
<year>1994</year>
<publisher-loc><![CDATA[USA ]]></publisher-loc>
<publisher-name><![CDATA[John Wiley and Sons]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B20">
<label>20</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Conlisk]]></surname>
<given-names><![CDATA[A. T]]></given-names>
</name>
</person-group>
<source><![CDATA[Electrophoresis]]></source>
<year>2005</year>
<volume>26</volume>
<page-range>1896</page-range></nlm-citation>
</ref>
<ref id="B21">
<label>21</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hoffman]]></surname>
<given-names><![CDATA[J. D.]]></given-names>
</name>
</person-group>
<source><![CDATA[Numerical Methods for Engineers and Scientists]]></source>
<year>2001</year>
<publisher-loc><![CDATA[USA ]]></publisher-loc>
<publisher-name><![CDATA[CRC Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B22">
<label>22</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Leal]]></surname>
<given-names><![CDATA[L. G.]]></given-names>
</name>
</person-group>
<source><![CDATA[Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes]]></source>
<year>2007</year>
<publisher-loc><![CDATA[Cambridge ]]></publisher-loc>
<publisher-name><![CDATA[Cambridge University Press]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
