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Lecture

Diffusion: Fick's Law and Einstein's Demonstration

In course

PHYS-106(a): General physics : thermodynamics

Le but du cours de Physique générale est de fournir les notions de base nécessaires à la compréhension des phénomènes physiques. L'objectif est atteint lorsqu'il est possible de prévoir quantitativement les conséquences de ces phénomènes avec des outils th ...

Description

This lecture covers Fick's law, a phenomenological law establishing a proportionality relationship between current density vector and concentration gradient. It also delves into the second law of Fick, the resolution of the diffusion equation, and practical applications in daily life.

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Instructors (2)

Romuald Houdré

Curriculum Vitae CV 2011 Appointed as Adjunct Professor 2006 Appointed as Maitre d'Enseignement et de Recherche 2004 Joins the "Laboratory of Quantum Electronics" led by Prof. B. Deveaud-Plédran 2001-2004 Appointed as "Adjoint Scientifique" at the Institute for Quantum Photonics and Electronics (previously Institute for Micro and Optoelectronics led by Prof. M. Ilegems) 1998 Habilitation, University Pierre et Marie Curie, Paris 6 (France) 1997 Invited researcher at NTT, Optoelectronics Department (Atsugi, Japan) 1988-2000 "Collaborateur scientifique" at the Institut for Micro and Optoelectronics with Prof. M.Ilegems at the Swiss Federal Institut of Technology in Lausanne (Switzerland). In charge of the Molecular Beam Epitaxy (1988-1996) and the research on optical microcavities (1996-2000) 1987-1988 Laboratoire de Physique de la Matière Condensée at Ecole Polytechnique (France). 1986-1987 Postdoctoral fellow at the University of Illinois at Urbana-Champaign (U.S.A.) with Prof. H.Morkoç in the molecular beam epitaxy group 1983-1985 Ph.D. thesis on the photoemission from quantum wells and superlattices under negative electron affinity at Laboratoire de Physique de la Matière Condensée, Ecole Polytechnique (France), G.Lampel and C.Hermann as advisors

Cécile Hébert

Cécile Hébert was born in France in 1970. She obtained her Ingeneer degree (physics) and her PhD degree (design of a new energy filter for transmission electron microscopy, under the direction of Prof. B. Jouffrey) at the Ecole Centrale in Paris. As a post doc with Prof. P. Schattschneider, she was working on the calculation of the fine structure of ionisation edges in EELS. As a research assistant at the Vienna University of Technology, she was one of the main participant to the CHIRALTEM project dealing with the measurement of magnetic circular dichroism in the electron microscope.

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Related concepts (29)

Fick's laws of diffusion

Fick's laws of diffusion describe diffusion and were first posited by Adolf Fick in 1855 on the basis of largely experimental results. They can be used to solve for the diffusion coefficient, D. Fick's first law can be used to derive his second law which in turn is identical to the diffusion equation. A diffusion process that obeys Fick's laws is called normal or Fickian diffusion; otherwise, it is called anomalous diffusion or non-Fickian diffusion.

Diffusion

Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical potential. It is possible to diffuse "uphill" from a region of lower concentration to a region of higher concentration, like in spinodal decomposition. Diffusion is a stochastic process due to the inherent randomness of the diffusing entity and can be used to model many real-life stochastic scenarios.

Convection–diffusion equation

The convection–diffusion equation is a combination of the diffusion and convection (advection) equations, and describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection. Depending on context, the same equation can be called the advection–diffusion equation, drift–diffusion equation, or (generic) scalar transport equation.

Diffusion equation

The diffusion equation is a parabolic partial differential equation. In physics, it describes the macroscopic behavior of many micro-particles in Brownian motion, resulting from the random movements and collisions of the particles (see Fick's laws of diffusion). In mathematics, it is related to Markov processes, such as random walks, and applied in many other fields, such as materials science, information theory, and biophysics. The diffusion equation is a special case of the convection–diffusion equation, when bulk velocity is zero.

Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it - for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it - for example, both a latitude and longitude are required to locate a point on the surface of a sphere.

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