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MIT10_626S11_lec23 - IV Transport Phenomena Lecture 23 Ion...

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IV. Transport Phenomena ± Lecture 23: Ion Concentration Polarization± MIT Student (and MZB) Ion concentration polarization in electrolytes refers to the additional voltage drop (or “internal resistance ) across the electrolyte associated with ion concentration gradients, which exists in addition to the Ohmic voltage drop associated with the mean conductivity. We focus on consider quasi-neutral “bulk” electrolytes. 1. Nernst-Plank equations Assume there is no convective transport ( General Nernst-Plank equations: ). , where , (Einstein relation) For dilute solution (with neglecting electrostatic correlations):± Then, Nernst-Plank equation goes to ± To determine , we can use electroneutrality/charge conservation. (Condition of “quasi-electroneutrallity”)
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Lecture 23: Ion concentration polarization 10.626 (2011) Bazant 2. Dilute Binary Electrolyte From quasi-electroneutrality, for a binary salt, we can define salt concentration C via which satisfies a simple diffusion equation with a certain average or “ambipolar” diffusivity, as derived in the last lecture: For dilute binary electrolyte, , the effective diffusivity goes to harmonic mean of the ion diffusivities, weighted by the charge of the opposite species( < > denotes the harmonic mean). Generally, the effective diffusivity for ambipolar electrolyte is an average of and giving more weight to smaller diffusivity D and smaller charge z . The diffusion is dominated by the smaller mobility. As an analogy, consider “teacher” with a small “student” traversing a room. Even though the student has the tendency to move much faster than his/her accompanying teacher, he/she is limited in the extent of this mobility by the teacher’s speed and position. That is, highly mobile “student” ions could not stray far from its less mobile “teacher” ion to be maintained electroneutrality of bulk electrolyte. It is the reason why the equation of effective diffusivity expresses the coupling of the positive and negative species. It is noted that this equation is only effective at describing bulk solution, which satisfy electroneutrality assumption. The equation no longer valid when the electroneutrality assumption breaks down, such as near charged surfaces. Fig 1. Interpretation of the effective ambipolar diffusivity of a dilute binary electrolyte where the anions are the “students” (or children) and the cations are the “teachers”, who strive to maintain a fixed “teacher-student ratio” consistent with electroneutrality. The ambipolar diffusivity gives more weight to the slower/larger ion with smaller charge (the teacher) since other ion (the student) responds more quickly to electric fields, not only the applied external electric field (which attracts students to different boundaries, as below), but also the internal “diffusion field” which helps the ions to maintain electroeutrality when their diffusivities are different.
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