Biomod/2014/UANL/DiffusionModel

 <meta http-equiv="Content-Type" content="text/html;charset=utf-8">
 <title>Fixed Top Navigation Toolbar</title>
 <meta name="author" content="Jake Rocheleau">
 <link rel="shortcut icon" href="http://designshack.net/favicon.ico">
 <link rel="icon" href="http://designshack.net/favicon.ico">
 <link rel="stylesheet" type="text/css" media="all" href="styles.css">
 <link rel="stylesheet" type="text/css" media="all" href="http://fonts.googleapis.com/css?family=Capriola">
 <script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js"></script>

 margin: 0;
 padding: 0;
 border: 0;
 font-size: 100%;
 font: inherit;
 vertical-align: baseline;
 outline: none;
 -webkit-text-size-adjust: 100%;
 -webkit-box-sizing: border-box;
 -moz-box-sizing: border-box;
 box-sizing: border-box;

} html { height: 101%; } body { font-family: Tahoma, Verdana, Arial, sans-serif; font-size: 62.5%; line-height: 1; padding-bottom: 65px; background: #444 url('images/bg.png'); }

article, aside, details, figcaption, figure, footer, header, hgroup, menu, nav, section { display: block; } ol, ul { list-style: none; }

blockquote, q { quotes: none; } blockquote:before, blockquote:after, q:before, q:after { content: ''; content: none; } strong { font-weight: bold; }

table { border-collapse: collapse; border-spacing: 0; } img { border: 0; max-width: 100%; }

h1 {

 font-family: 'Capriola', Tahoma, Arial, sans-serif;
 font-weight: normal;
 font-size: 2.95em;
 line-height: 1.2em;
 letter-spacing: -.0.03em;
 color: #383838;
 margin-bottom: 16px;

}

p { font-size: 1.2em; line-height: 1.45em; margin-bottom: 15px; color: #434343; text-align: justify; }

a { color: #5b77a4; text-decoration: underline; } a:hover { color: #7d94bb; }

w {

 display: block;
 width: 710px;
 padding: 14px 15px;
 margin: 0 auto;
 margin-top: 45px;

}

content {

 display: block;
 background: #fff;
 padding: 80px 50px;

}

logo { display: block; border: 1px solid #232323; border-bottom-width: 0; }
logobg {

 display: block;
 width: 100%;
 height: 130px;
 background: url('images/logo.png') top left no-repeat;
 text-indent: 100%;
 white-space: nowrap;
 overflow: hidden;

}

/* top navigation */

navigation {

 display: block;
 height: 35px;
 background-color: #131313;
 background-image: -webkit-gradient(linear, left top, left bottom, from(#202020), to(#131313));
 background-image: -webkit-linear-gradient(top, #202020, #131313);
 background-image: -moz-linear-gradient(top, #202020, #131313);
 background-image: -ms-linear-gradient(top, #202020, #131313);
 background-image: -o-linear-gradient(top, #202020, #131313);
 background-image: linear-gradient(top, #202020, #131313);

}

navigation ul { list-style: none; padding: 0px 7px; }

navigation ul li { display: inline; float: left; }
navigation ul li a {

 display: block; 
 padding: 0 8px; 
 color: #fff;
 font-size: 1.1em;
 text-decoration: none;
 line-height: 35px; 
 font-weight: bold; 
 margin-right: 6px;
 text-shadow: 1px 1px 1px #000;
 -webkit-transition: all 0.2s linear;
 -moz-transition: all 0.2s linear;
 transition: all 0.2s linear;

}

navigation ul li a:hover { color: #a8d6e7; }

/* hidden fixed navigation */

fixedbar {

 display: none;
 position: fixed;
 top: 0;
 width: 100%;
 height: 80px;
 background: rgba(0,0,0,0.75);

}

fixednav {

 display: block;
 width: 710px;
 margin: 0 auto;
 padding: 0px 25px;

}

fixednav li { }

fixednav li a {

 display: block;
 float: left;
 font-size: 1.75em;
 font-weight: bold;
 color: #96aed8;
 line-height: 80px;
 text-decoration: none;
 padding: 0px 8px;
 margin-right: 6px; 
 -webkit-transition: all 0.2s linear;
 -moz-transition: all 0.2s linear;
 transition: all 0.2s linear;

}

fixednav li a:hover {

 color: #fff;
 background: rgba(0,0,0,0.3);

}

content{margin-left:0.7;}

.navbar{ top:0px; position:fixed; width:96.8%; z-index: 9999 !important;

background-color: #A68F6A;

left: 152px }

div img {

 position: absolute;
 top:  0px; 
 left: 0px;

}

div imglogo {

 position: absolute;
 top:  20px; 
 left: 20px;

}

footer {
           position: relative;
           /* Altura total del footer en px con valor negativo */
           margin-top: -50px;
           /* Altura del footer en px. Se han restado los 5px del margen
              superior mas los 5px del margen inferior
           */
           height: 40px; 
           padding:5px 0px;
           clear: both;
           background: #286af0;
           text-align: center;
           color: #fff;

z-index: 9999 !important;

</style> </head>

<body>

<!--Nav-->

 <div class="navbar-header">
   <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
     <span class="icon-bar"></span>
     <span class="icon-bar"></span>
     <span class="icon-bar"></span>
   </button>
   <a class="navbar-brand" href="#"></a>
 </div>
 <div class="navbar-collapse collapse navbar-responsive-collapse">
   <ul class="nav navbar-nav">

<li><a href="http://openwetware.org/wiki/Biomod/2014/UANL">Home</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2014/UANL/Background">Background</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2014/UANL/Method">Method</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2014/UANL/MedicalApplication">Medical Application</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2014/UANL/IndustrialApplication">Industrial Application</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2014/UANL/Discussion">Discussion</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2014/UANL/DiffusionModel">Diffusion Model</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2014/UANL/KineticModel">Kinetic Model</a></li> <li><a href="http://openwetware.org/wiki/Biomod/2014/UANL/Team/">Team</a></li>

   </ul>
 </div>

</div> >

   <div>
 <img src="http://openwetware.org/images/3/36/Fractals-mathematics_00306962.png" />

</div>

   <div id="content">

<h1>Diffusion Model</h1>
     <p>In order to make the reactants transport process into the liposome more efficient, it is important to develop a mathematical expression that takes into account the multiple variables that may affect the process.

Although a liposome is not a living cell, the osmotic transport through its lipidic membrane can be mathematically modeled the same way as a cell because of its resemblance to the external membrane structure. There are two transport mechanisms for molecules to enter a cell: energy-independent or energy-dependent. Energy independent mechanisms are spontaneous; in this particular case, reactants enter the liposome by concentration gradient driven molecular diffusion. The reactants diffusion into the liposome can be treated as a pseudosteady process and it can be expressed by Fick’s law of diffusion:

</p>

<IMG STYLE="position:absolute; TOP:360px; LEFT:170px;" SRC="http://openwetware.org/images/6/67/Ec1.png"> Equation 1 can be rewritten as: <IMG STYLE="position:absolute; TOP:470px; LEFT:230px;" SRC="http://openwetware.org/images/d/d7/Ec2.png"> where H represents the fraction of the diaphragm’s area that is available for diffusion. Then mass balances on both sides of the membrane can be expressed as[4]: <IMG STYLE="position:absolute; TOP:620px; LEFT:185px;" SRC="http://openwetware.org/images/1/11/Ec3.png">

where A is the membrane’s area. By dividing equations 3 and 4 in V and subtract them, the result can be combined with the flux equation to obtain:

<IMG STYLE="position:absolute; TOP:865px; LEFT:185px;" SRC="http://openwetware.org/images/b/bb/Ec4.png"> in which: <IMG STYLE="position:absolute; TOP:1000px; LEFT:185px;" SRC="http://openwetware.org/images/4/43/Ec5.png"> where β is a geometrical constant characteristic of the particular membrane. The differential equation can be solved assuming the following initial condition:

<IMG STYLE="position:absolute; TOP:1200px; LEFT:185px;" SRC="http://openwetware.org/images/f/fb/Ec6.png"> Integrating the differential equation gives the following result:

<IMG STYLE="position:absolute; TOP:1350px; LEFT:185px;" SRC="http://openwetware.org/images/3/33/Ec7.png"> Rearranging the equation:

<IMG STYLE="position:absolute; TOP:1540px; LEFT:185px;" SRC="http://openwetware.org/images/9/98/Ec8.png"> From the equation 6 and 8 it can be noticed that the diffusion coefficient (D) is inversely proportionate to the geometrical constant β, meaning that the membrane area (A) and longitude (L) must be as little as possible to increase the value of diffusivity. Also, as more reactants enter the liposome, the concentration increases so the difference in concentration between this and the concentration outside the membrane is lower as time pases. This reduces significantly the diffusivity of the reactants into the liposome as time goes on. It can be implied by the mathematical expressions previously described that by developing smaller liposomes in large quantities would result in a faster and more extended diffusion process, allowing the reactants to enter the lipidic membrane in more efficient way. <hr size="10px" width=100% align="center"/> <h2>References:</h2>

[N1] http://www.news-medical.net/health/What-is-a-Liposome.aspx [N2] “Bioprocess Engineering Basic Concepts ” Michael L. Shuler, Fikret Kargi. Pearson Education Limited 2nd Edition USA 1992 ISBN 1292025999 [N3] “Transport Phenomena” R. Byron Bird, Warren E. Steward, Edwin N. Lightfoot. John Wiley & Sons 2nd Edition USA 2007 ISBN 0470115394

[N4] “Diffusion-Mass Transfer in Fluid Systems” E.L. Culler. Cambridge  University Press.                England 1984 1st Edition ISBN 978-0-521-87121-1

   </div>

</div>

 </div>

 $('#navigation a, #fixedbar a').on('click', function(e) {
   e.preventDefault();
 });
 
 $(window).on('scroll',function() {
   var scrolltop = $(this).scrollTop();

   if(scrolltop >= 215) {
     $('#fixedbar').fadeIn(250);
   }
   
   else if(scrolltop <= 210) {
     $('#fixedbar').fadeOut(250);
   }
 });

}); </script>

</body> </html>

Biomod/2014/UANL/DiffusionModel

Navigation menu

Page actions

Page actions

Personal tools

Navigation

Search

research

Tools