Helmholtz’s law

The jet-like or elongational flow field in these features can be understood as a local separation from the wall. An analysis of the vorticity field however poses a fundamental problem related to the non-slip condition at the wall since the Helmholtz laws are incompatible with this condition. One of Helmholtz s law states that a vortex line has to be closed or that it has to end at a boundary. Since at the wall (xy-plane) the velocities u and v parallel to the wall are identical zero, the same must hold for the vorticity component J normal to the wall. No vortex line can hence be attached to the wall. The main aspects of this problem are described by LIGHTHILL (1963). 

This method is based on Helmholtz s law, which specifies the variations of Gibbs energy with temperature ... 

On the theoretical side, it was Hermann von Helmholtz (Sidebar 3.4) who first presented a clear and comprehensive mathematical formulation of energy conservation as a principle of universal validity, applicable to all natural phenomena. Helmholtz s landmark paper of 1847, Uber die Erhaltung der Kraft, reflected some lingering ambiguities of the force (Kraft) concept, but exhibited the deep integration of the first law into analytical dynamics in a clear and modem way. Helmholtz deserves to be counted the scientist most responsible for rigorous mathematical formulation of the first law. 

It is known as the Helmholtz-Smoluchowski (limiting) law. after Helmholtz, who derived an expression similar to 14.3.41 but without e in it. and Smoluchowski who Improved Helmholtz s expression. 

All three derivations of the Clausius equation (3) are identical in principle, as they all make use of the second law of thermodynamics. In giving them all in detail we merely wished to show in what diverse ways the second law can be made to lead to concrete experimental results. The most diverse methods have been employed by various investigators in deriving such results. The choice of method depends partly on the nature of the problem and partly also on the task of the investigator. Van t Hoif, for example, generally used reversible cycles in his classical researches. Other physical chemists prefer Helmholtz s equation or the thermodynamic potential, while partial differential equations, as used in the first of the above derivations, are generally found in physical papers. 

There has been no shortage of attempts to estimate surface (Helmholtz-) energies from contact angles, by invoking some model. A controversial issue is Neumann s equation of state method ) which is based on the assumed validity of a second relationship between interfacial tensions, so that and y can be individually estimated. Another route starts by assuming [5.7.5] to be valid. For an apolar liquid on a solid S (y = y ), combination with Young s law gives... 

Wilhelm Carl Werner Otto Fritz Franz Wien (1864-1928) became an assistant to Hermann v. Helmholtz at the Physikalisch-Technische Reichsanstalt in Berlin in 1890. It was there that he discovered the displacement law in 1893, and also published an equation for M s in 1896, that only slightly differed from Planck s law. Wien became Professor of Physics at the TH in Aachen in 1896, moved in 1899 to become a professor in Wurzburg, and once again changed to the University of Munich in 1920. In 1911 he was awarded the Nobel prize for Physics as an acknowledgement of his work on thermal radiation. 

As already discussed in Section 3.2 the potential across a single solid-liquid interface cannot be measured. One can only measure the potential of an electrode vs. a reference electrode. It has already been shown in Section 3.2 that a certain potential is produced at a metal or semiconductor electrode upon the addition of a redox system, because the redox system equilibriates with the electrons in the electrode, i.e. the Fermi level on both sides of the interface must be equal under equilibrium. It should be emphasized here that the potential caused upon addition of a redox couple to the solution occurs in addition to that already formed by the specific adsorption of, for instance, hydroxyl ions. A variation in the relative concentrations of the oxidized and reduced species of the redox system leads to a corresponding change of the potential across the outer Helmholtz layer, as required by Nernst s law (see Eq. 3.47), which can be detected by measuring the electrode potential vs, a reference electrode. However, there still exists a potential across the inner Helmholtz layer which remains unknown. 

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