By H. K. Kuiken (auth.), H. K. Kuiken (eds.)
This publication commemorates the looks 100 years in the past of a paper on gradual viscous movement, written via the physicist and Nobel laureate H.A. Lorentz. even supposing Lorentz isn't remembered through so much as a fluid dynamicist - certainly, his popularity rests totally on his contributions to the idea of electrons, electrodynamics and early advancements in relativity - his fluid-mechanics paper of 1896 comprises many rules that have remained very important in fluid mechanics to this very day. In that brief paper he recommend his reciprocal theorem (an integral-equation formula that is used broadly these days in boundary-element calculations) and his mirrored image theorem. moreover, he has to be credited with the discovery of the stokeslet.
The participants to this publication have all made their mark in gradual viscous circulation. each one of those authors highlights additional advancements of 1 of Lorentz's principles. There are purposes in sintering, micropolar fluids, bubbles, locomotion of microorganisms, non-Newtonian fluids, drag calculations, and so forth. different contributions are of a extra theoretical nature, resembling the stream because of an array of stokeslets, the interplay among a drop and a particle, the interplay of a particle and a vortex, the mirrored image theorem for different geometries, a disk relocating alongside a wall and a higher-order research.
Lorentz's paper of 1896 can be incorporated in an English translation. An introductory paper places Lorentz's paintings in fluid mechanics in a much wider point of view. His different nice enterprise in fluid mechanics - his theoretical modelling at the enclosure of the Zuyderzee - is additionally mentioned. The advent additionally provides a quick description of Lorentz's existence and occasions. It used to be Albert Einstein who acknowledged of Lorentz that he was once `...the maximum and noblest guy of our time'.
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Extra info for The Centenary of a Paper on Slow Viscous Flow by the Physicist H.A. Lorentz
C c âx ây âz If the state of motion M does not involve externa! forces and if we are allowed to disregard the second-order terms, then the expression on the right is reduced to the first two terms; it is then possible to determine the force acting on L, as long as the velocities u, v, w are known. on the surfaces :E and CT. One more term is involved when externa! forces X, Y, Zare present with the velocities still being infinitesimal, but, still, it is not necessary to know u, v and w at every point in space.
Accordingly, expression (17) is just that combination of the stokelet with a dipole of sţrength ( -a2 F / 6ţt) which appears in the classical motion of Stokes -here reinterpreted in terms of Lorentz's surface distribution of stokeslets. s~tisfying Eqs. (1) is that the circularmean C(a) ofu, taken around any circle ofradius a in the (y, z) plane, is equal to the value of (18) at its centre P. ) Such a locally two-dimensional field is generated by those stokeslets normal to the flagellar centreline whose strengths are designated in the basic theorem as fn( s) per unit length.
Both special features arise because a stokeslet field depends only on the relative position of singularity and field point. Accordingly, (a) the Lorentz field is effectively a circular mean of a curvilinear distribution of stokeslet fields, and thus equates to a stokeslet/dipole distribution as in the theorem; while, moreover, (b) the Lorentz distribution of stokeslet rings has values of inverse-first-power terms in its field on the fiagellar surface which, by standard properties ofharmonic functions, coincide with any interior value, including that centreline value which necessarily has the same cutoff distance as the surface field of a centreline distribution of stokeslets.
The Centenary of a Paper on Slow Viscous Flow by the Physicist H.A. Lorentz by H. K. Kuiken (auth.), H. K. Kuiken (eds.)