SherbyNet - /page/wikibook/entry.mu

Micron Document

<!DOCTYPE html>

<title>Streaming current</title>

</head>

Streaming current

</h1>

</header>

A streaming current and streaming potential are two interrelated <a href="Electrokinetic_phenomena" title="Electrokinetic phenomena">electrokinetic phenomena</a> studied in the areas of <a href="Surface_chemistry" class="mw-redirect" title="Surface chemistry">surface chemistry</a> and <a href="Electrochemistry" title="Electrochemistry">electrochemistry</a>. They are an <a href="Electric_current" title="Electric current">electric current</a> or <a href="Electric_potential" title="Electric potential">potential</a> which originates when an <a href="Electrolyte" title="Electrolyte">electrolyte</a> is driven by a pressure gradient through a channel or porous plug with charged walls.<a href="#cite_note-Lyklema-1">[1]</a><a href="#cite_note-Li-2">[2]</a><a href="#cite_note-Chang-3">[3]</a>

The first observation of the streaming potential is generally attributed to the German physicist <a href="Georg_Hermann_Quincke" title="Georg Hermann Quincke">Georg Hermann Quincke</a> in 1859.

<div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2></div>

Streaming currents in well-defined geometries are a sensitive method to characterize the <a href="Zeta_potential" title="Zeta potential">zeta potential</a> of surfaces, which is important in the fields of <a href="Colloid" title="Colloid">colloid</a> and <a href="Interface_(chemistry)" class="mw-redirect" title="Interface (chemistry)">interface science</a>.<a href="#cite_note-Lyklema-1">[1]</a> In geology, measurements of related <a href="Spontaneous_potential" title="Spontaneous potential">spontaneous potential</a> are used for evaluations of formations. Streaming potential has to be considered in design for flow of poorly conductive fluids (e.g., gasoline lines) because of the danger of buildup of high voltages. The streaming current monitor (SCM) is a fundamental tool for monitoring <a href="Coagulation" title="Coagulation">coagulation</a> in <a href="Wastewater_treatment_plant" class="mw-redirect" title="Wastewater treatment plant">wastewater treatment plants</a>. The degree of coagulation of raw water may be monitored by the use of an SCM to provide a positive feedback control of coagulant injection. As the streaming current of the wastewater increases, more coagulant agent is injected into the stream. The higher levels of coagulant agent cause the small colloidal particles to coagulate and sediment out of the stream. Since less colloid particles are in the wastewater stream, the streaming potential decreases. The SCM recognizes this and subsequently reduces the amount of coagulant agent injected into the wastewater stream. The implementation of SCM feedback control has led to a significant materials cost reduction, one that was not realized until the early 1980s.<a href="#cite_note-4">[4]</a> In addition to monitoring capabilities, the streaming current could, in theory, generate usable <a href="Electric_power" title="Electric power">electrical power</a>. This process, however, has yet to be applied as typical streaming potential mechanical to electrical <a href="Energy_conversion_efficiency" title="Energy conversion efficiency">efficiencies</a> are around 1%.<a href="#cite_note-5">[5]</a>

<div class="mw-heading mw-heading2"><h2 id="Origin">Origin</h2></div>

Adjacent to the channel walls, the charge-neutrality of the liquid is violated due to the presence of the <a href="Electrical_double_layer" class="mw-redirect" title="Electrical double layer">electrical double layer</a>: a thin layer of <a href="Counterion" title="Counterion">counterions</a> attracted by the charged surface.<a href="#cite_note-Lyklema-1">[1]</a><a href="#cite_note-Kirby-6">[6]</a>

The transport of counterions along with the pressure-driven fluid flow gives rise to a net charge transport: the streaming current. The reverse effect, generating a fluid flow by applying a potential difference, is called <a href="Electroosmotic_flow" class="mw-redirect" title="Electroosmotic flow">electroosmotic flow</a>.<a href="#cite_note-Kirby-6">[6]</a><a href="#cite_note-Bruus-7">[7]</a><a href="#cite_note-Karniadakis-8">[8]</a>

<div class="mw-heading mw-heading2"><h2 id="Measurement_method">Measurement method</h2></div>

A typical setup to measure streaming currents consists of two reversible <a href="Electrode" title="Electrode">electrodes</a> placed on either side of a fluidic geometry across which a known pressure difference is applied. When both electrodes are held at the same potential, the streaming current is measured directly as the electric current flowing through the electrodes. Alternatively, the electrodes can be left floating, allowing a streaming potential to build up between the two ends of the channel.

A streaming potential is defined as positive when the electric potential is higher on the high pressure end of the flow system than on the low pressure end.

The value of streaming current observed in a <a href="Capillary" title="Capillary">capillary</a> is usually related to the <a href="Zeta_potential" title="Zeta potential">zeta potential</a> through the relation:<a href="#cite_note-9">[9]</a>

<msub>

</mrow>

</msub>

<mfrac>

<mrow>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

<msup>

</mrow>

</msup>

</mrow>

</mfrac>

</mrow>

<mfrac>

<mrow>

</mrow>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle I_{str}=-{\frac {\epsilon _{rs}\epsilon _{0}a^{2}\pi }{\eta }}{\frac {\Delta P}{L}}\zeta }</annotation>

</semantics>

</math><img src="./f7833df8e86a19da2116d6ccdd681862bcc69324.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:23.02ex; height:6.176ex;" alt="{\displaystyle I_{str}=-{\frac {\epsilon _{rs}\epsilon _{0}a^{2}\pi }{\eta }}{\frac {\Delta P}{L}}\zeta }" loading="lazy">.</dd></dl>

The <a href="Electrical_conduction" class="mw-redirect" title="Electrical conduction">conduction</a> current, which is equal in magnitude to the streaming current at steady state, is:

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

<msup>

</mrow>

</msup>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle I_{c}=K_{L}a^{2}\pi {\frac {U_{str}}{L}}}</annotation>

</semantics>

</math><img src="./4dfbb5320f7c74b38954aa2b2863a0975a9c93f4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:16.769ex; height:5.176ex;" alt="{\displaystyle I_{c}=K_{L}a^{2}\pi {\frac {U_{str}}{L}}}" loading="lazy"></dd></dl>

At steady state, the streaming potential built up across the flow system is given by:

<msub>

</mrow>

</msub>

<mfrac>

<mrow>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

</mrow>

<mrow>

<msub>

</mrow>

</msub>

</mrow>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle U_{str}={\frac {\epsilon _{rs}\epsilon _{0}\zeta }{\eta K_{L}}}\Delta P}</annotation>

</semantics>

</math><img src="./bb64073e0af4e20c747526b8108f321b2d15c870.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:17.324ex; height:5.843ex;" alt="{\displaystyle U_{str}={\frac {\epsilon _{rs}\epsilon _{0}\zeta }{\eta K_{L}}}\Delta P}" loading="lazy"></dd></dl>

Symbols:

<ul><li>Istr - streaming current under short-circuit conditions, A</li>

<li>Ustr - streaming potential at zero net current conditions, V</li>

<li>Ic - conduction current, A</li>

<li>εrs - <a href="Relative_permittivity" title="Relative permittivity">relative permittivity</a> of the liquid, dimensionless</li>

<li>ε0 - electrical <a href="Permittivity" title="Permittivity">permittivity</a> of vacuum, F·m−1</li>

<li>η - dynamic <a href="Viscosity" title="Viscosity">viscosity</a> of the liquid, kg·m−1·s−1</li>

<li>ζ - zeta potential, V</li>

<li>ΔP - pressure difference, Pa</li>

<li>L - capillary length, m</li>

<li>a - capillary radius, m</li>

<li>KL - specific conductivity of the bulk liquid, S·m−1</li></ul>

The equation above is usually referred to as the Helmholtz–Smoluchowski equation.

The above equations assume that:

<ul><li>the double layer is not too large compared to the pores or capillaries (i.e., <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \kappa a\gg 1}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \kappa a\gg 1}</annotation>

</semantics>

</math><img src="./7ca5ba4711473c97118eca3e2d7767a56c84bd43.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.345ex; height:2.176ex;" alt="{\displaystyle \kappa a\gg 1}" loading="lazy">), where κ is the reciprocal of the <a href="Debye_length" title="Debye length">Debye length</a></li>

<li>there is no surface conduction (which typically may become important when the zeta potential is large, e.g., |ζ| > 50 mV)</li>

<li>there is no electrical double layer polarization</li>

<li>the surface is homogeneous in properties<a href="#cite_note-10">[10]</a></li>

<li>there is no axial concentration gradient</li>

<li>the geometry is that of a capillary/tube.</li></ul>

<div class="mw-heading mw-heading2"><h2 id="Literature">Literature</h2></div>

<ol><li>J. Lyklema, Fundamentals of Interface and Colloid Science</li>

<li>F.H.J. van der Heyden et al., Phys. Rev. Lett. 95, 116104 (2005)</li>

<li>C. Werner et al., J. Colloid Interface Sci. 208, 329 (1998)</li>

<li>Mansouri et al. The Journal of Physical Chemistry C, 112(42), 16192 (2008)</li></ol>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

/* start https://en.wikipedia.org/ */

.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("./mw/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("./mw/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("./mw/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("./mw/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}

/* end https://en.wikipedia.org/ */

</style><cite id="CITEREFLyklema,_J.1995" class="citation book cs1">Lyklema, J. (1995). Fundamentals of Interface and Colloid Science. <a href="Academic_Press" title="Academic Press">Academic Press</a>.</cite>

</li>

<li id="cite_note-Li-2"><a href="#cite_ref-Li_2-0">^</a> <cite id="CITEREFLi,_D.2004" class="citation book cs1">Li, D. (2004). Electrokinetics in Microfluidics. <a href="Academic_Press" title="Academic Press">Academic Press</a>.</cite>

</li>

<li id="cite_note-Chang-3"><a href="#cite_ref-Chang_3-0">^</a> <cite id="CITEREFChang,_H.C.,_Yeo,_L.2009" class="citation book cs1">Chang, H.C., Yeo, L. (2009). Electrokinetically Driven Microfluidics and Nanofluidics. <a href="Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>.</cite><code class="cs1-code">{{cite book}}</code>: CS1 maint: multiple names: authors list (link)

</li>

<li id="cite_note-4"><a href="#cite_ref-4">^</a> <cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20160304095842/http://www.waterhouse-bc.ca/Theory%20of%20the%20Streaming%20Current%20Monitor.pdf">"Archived copy"</a> (PDF). Archived from <a rel="nofollow" class="external text" href="http://www.waterhouse-bc.ca/Theory%20of%20the%20Streaming%20Current%20Monitor.pdf">the original</a> (PDF) on 2016-03-04. Retrieved 2013-05-07.</cite><code class="cs1-code">{{cite web}}</code>: CS1 maint: archived copy as title (link)

</li>

<li id="cite_note-5"><a href="#cite_ref-5">^</a> <cite id="CITEREFOlthuisSchippersEijkelVan_Den_Berg2005" class="citation journal cs1 cs1-prop-long-vol">Olthuis, Wouter; Schippers, Bob; Eijkel, Jan; Van Den Berg, Albert (2005). "Energy from streaming current and potential". Sensors and Actuators B: Chemical. 111–112: 385–389. <a href="CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.590.7603">10.1.1.590.7603</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.snb.2005.03.039">10.1016/j.snb.2005.03.039</a>.</cite>

</li>

<li id="cite_note-Kirby-6">^ <a href="#cite_ref-Kirby_6-0">a</a> <a href="#cite_ref-Kirby_6-1">b</a> <cite id="CITEREFKirby,_B.J.2010" class="citation book cs1">Kirby, B.J. (2010). <a rel="nofollow" class="external text" href="http://www.kirbyresearch.com/textbook">Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices</a>. Cambridge University Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-521-11903-0</bdi>.</cite>

</li>

<li id="cite_note-Bruus-7"><a href="#cite_ref-Bruus_7-0">^</a> <cite id="CITEREFBruus,_H.2007" class="citation book cs1">Bruus, H. (2007). Theoretical Microfluidics. <a href="Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>.</cite>

</li>

<li id="cite_note-Karniadakis-8"><a href="#cite_ref-Karniadakis_8-0">^</a> <cite id="CITEREFKarniadakis,_G.M.,_Beskok,_A.,_Aluru,_N.2005" class="citation book cs1">Karniadakis, G.M., Beskok, A., Aluru, N. (2005). Microflows and Nanoflows. <a href="Springer_Verlag" class="mw-redirect" title="Springer Verlag">Springer Verlag</a>.</cite><code class="cs1-code">{{cite book}}</code>: CS1 maint: multiple names: authors list (link)

</li>

<li id="cite_note-9"><a href="#cite_ref-9">^</a> "Measurement and Interpretation of Electrokinetic Phenomena", International Union of Pure and Applied Chemistry, Technical Report, published in Pure Appl. Chem., vol 77, 10, pp. 1753–1805, 2005 <a rel="nofollow" class="external text" href="http://old.iupac.org/publications/pac/2005/pdf/7710x1753.pdf">(pdf)</a>.

</li>

<li id="cite_note-10"><a href="#cite_ref-10">^</a> Menachem Elimelech and Amy E. Childress, "Zeta Potential of Reverse Osmosis Membranes: Implications for Membrane Performance". U.S. Department of the Interior, Bureau of Reclamation, Denver Office. Water Treatment Technology Program Report No. 10. December 1996.

</li>

</ol></div></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2022-03-04" href="https://en.wikipedia.org/wiki/?title=Streaming_current&oldid=1075127683">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

</div>

</div></div>

</div>

</main>

</div>

</body></html>