Modification of Fick鈥檚 First Law by Introducing the Time Delay

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by Introducing the Time Delay</title> <meta name="description" content="Modification of Fick鈥檚 First Law by Introducing the Time Delay"> <meta name="keywords" content="Fick's first law, flux, diffusion, time delay, modified Fick鈥檚 first law"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research 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Fick鈥檚 First Law by Introducing the Time Delay</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=H.%20Namazi">H. Namazi</a>, <a href="https://publications.waset.org/abstracts/search?q=H.%20T.%20N.%20Kuan"> H. T. N. Kuan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fick's first law relates the diffusive flux to the concentration field, by postulating that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative). It is clear that the diffusion of flux cannot be instantaneous and should be some time delay in this propagation. But Fick鈥檚 first law doesn鈥檛 consider this delay which results in some errors especially when there is a considerable time delay in the process. In this paper, we introduce a time delay to Fick鈥檚 first law. By this modification, we consider that the diffusion of flux cannot be instantaneous. In order to verify this claim an application sample in fluid diffusion is discussed and the results of modified Fick鈥檚 first law, Fick鈥檚 first law and the experimental results are compared. The results of this comparison stand for the accuracy of the modified model. The modified model can be used in any application where the time delay has considerable value and neglecting its effect reflects in undesirable results. <iframe src="https://publications.waset.org/abstracts/19767.pdf" style="width:100%; height:400px;" frameborder="0"></iframe> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fick%27s%20first%20law" title="Fick's first law">Fick's first law</a>, <a href="https://publications.waset.org/abstracts/search?q=flux" title=" flux"> flux</a>, <a href="https://publications.waset.org/abstracts/search?q=diffusion" title=" diffusion"> diffusion</a>, <a href="https://publications.waset.org/abstracts/search?q=time%20delay" title=" time delay"> time delay</a>, <a href="https://publications.waset.org/abstracts/search?q=modified%20Fick%E2%80%99s%20first%20law" title=" modified Fick鈥檚 first law"> modified Fick鈥檚 first law</a> </p> <a href="https://publications.waset.org/abstracts/19767/modification-of-ficks-first-law-by-introducing-the-time-delay" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/19767.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">408</span> </span> </div> </div> </div> </main> <footer> <div id="infolinks" class="pt-3 pb-2"> <div class="container"> <div style="background-color:#f5f5f5;" class="p-3"> <div class="row"> <div class="col-md-2"> <ul class="list-unstyled"> About <li><a href="https://waset.org/page/support">About Us</a></li> <li><a href="https://waset.org/page/support#legal-information">Legal</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/WASET-16th-foundational-anniversary.pdf">WASET celebrates its 16th foundational anniversary</a></li> </ul> </div> <div class="col-md-2"> <ul 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Modification of Fick鈥檚 First Law by Introducing the Time Delay