Electrohydrodynamic Waves Research Articles

Simple electrohydrodynamic waves

The conditions for the existence and tilting of simple electrohydrodynamic waves are investigated.

A proposal on the function of unsaturated fatty acids and ionic lipids: the role of potential compaction in biological membranes

Unsaturated fatty acids are constituents of nearly all biological membranes. They are always present in membranes which possess transmembrane potentials. Two completely different biosynthetic routes have evolved (aerobic and anaerobic) for placing cis double bonds in the 9 position on the fatty acids of membrane lipids. Bacterial membranes contain primarily monounsaturated fatty acids, whereas eukaryote membranes contain a significant fraction of polyunsaturated fatty acids. The polyunsaturated fatty acids are concentrated in organelles, such as chloroplasts and mitochondria that are known to manipulate transmembrane potentials. I propose that the function of the unsaturated fatty acids is to facilitate the transmission of a local compaction of the membrane (in response to a transmembrane potential) laterally through the membrane. The role of the cis double bond at position 9 is twofold: first to create a kink in the chains of a large fraction of membrane fatty acids enhancing the separation of two regions in the membrane and second to enhance the rigidity of the membrane in the region between the head group and the 9 double bond. This ordered region contains those carbons proximal to the 9 carbon and which are in a regular array of trans conformations. The presence of a reasonable proportion of cis double bonds at position 9 will tend to maintain these trans conformations utilizing pi-pi (van der Waals) interactions between adjacent hydrocarbon chains at position 9. The disordered region contains the carbons distal to the 9 carbon. These have greater degrees of freedom and considerable gauche conformations. The role of the double bonds in the polyunsaturated fatty acids distal to carbon 9 is to facilitate trans bilayer pi-pi (van der Waals) interactions enhancing compaction of the bilayer during the electrostriction. I further propose that it is the function of the ionic headgroups to form an interlocking polyionic network which constitutes an elastic sheet. These ionic interactions would serve as the restoring force converting the compaction into a wave. The facilitation of the compaction of the bilayer together with the polyionic restoring force permits the membrane to transmit conformational changes from one transmembrane protein to another. Since transmembrane potentials are created and responded to by proteins each in a single location, it is thus proposed that a potential compaction wave emanates from the first protein in all directions in the plane of the membrane. The proposed wave would have both physical and electrical components. The electrohydrodynamic wave would require that the compaction oscillations be coupled to an oscillating electrical field. These proposals are applied to mitochondrial oxidative phosphorylation, and to transport across biological membranes.

Propagation of electrohydrodynamic surface waves in a conducting fluid

A comprehensive study is made of the electrohydrodynamic surface wave phenomena in an inviscid, incompressible conducting fluid in the presence of an external steady electric field due to an arbitrary periodic surface pressure distribution. The initial value wave problem has been solved by the Laplace and the generalized Fourier transforms in conjunction with asymptotic techniques — as advanced in a previous work ofDebnath andRosenblat [12]. An explicit steady state solution related to short and long wave approximations is found. The asymptotic behaviour of the transient solution for large time is demonstrated. It is shown that there are two surface wave-trains propagating in the conducting medium, one of which corresponds to the classical surface wave train and the other is originated entirely due to the interactions of the electric field with gravity. The simultaneous effects of the electric field and surface tension on the propagation of small amplitude surface waves are analyzed. The implications of the wave solutions related to very deep and shallow fluids are explored. A discussion of the electrohydrodynamic wave motions with their characteristic features is presented.

ELECTROHYDRODYNAMIC WAVES AND RELATED PHENOMENA

1. Preliminary Discussion.-Magnetohydrodynamic (m.h.) waves were a great success. The possibility of such waves was first and brilliantly established by Alfv6n in 1942. Essentially, they assume a prevalent uniform magnetic field Ho which penetrates an incompressible inviscid fluid of infinite conductivity, initially at rest. Displacement current and accumulations of charge are ignored. Then it can be shown that the oscillations of the velocity and magnetic field (induced), about the equilibrium state, are propagated along Ho at the Alfven velocity Ao = (hlo/po)l/2Ho (in meter-kilogram-second-coulomb system). Considerable development by various writers followed Alfv6n's pioneer efforts. A bibliography on the subject, which is voluminous, cannot be given here. In this note, I shall open a discussion about what I call electrohydrodynamic (e.h.) waves. As this term implies, an externially impressed uniform electric field Eo is now prevalent, and we may expect to have, under conditions to be determined, coupled electric and hydrodynamic waves propagated along Eo. The fluid to be tested must be endowed with such properties as to preserve an electric field, just as the Alfv6n fluid preserves a magnetic field. There lies precisely the difficulty and attraction of the new problem, and perhaps this explains why the waves in question have not yet been discovered. Now, recent research by this writer1 has revealed the possible existence of superpermeable fluids. The latter may be regarded as analogous to superconducting fluids (shortly called superfluids), although there are notable differences between the two. There is no question that in order to preserve an electric field in a material, one must first have a = 0 (a, electrical conductivity); however, this is not enlough. A far more stringent condition is to be imposed upon the fluid to bring it to the superpermeable state, aind this is , -c (I,, magnetic permeability). The two conditions a -0, IA -o define a superpermeable fluid. Unider the first condition (a = 0), the ratio of charge density Pe to material density p is preserved.2 3 When both conditions are fulfilled, the electric displacement (excitation) D adheres to the individual fluid particle and moves alonig with it as shown by the author in an earlier paper.' If now the electric mass polarization P can be neglected, then the electric field itself is frozen into the fluid. However, the importance of this result appears in its full brightness only when one couples the electromagnetic and motion equations. Thereby, a difficulty arises: the trouble is that the equation of motion, as generally used in magnetohydrodynamics, is not adequate for the desired coupling; some useful terms have been omitted in the magnetohydrodynamic equations. Hence, one must first reexamine these equations. This will appear below. When, once again, charge accumulations can be neglected, then the e.h. waves become apparent: two sets of waves travel along the field Eo with the velocity Co = (eo/po)'/2Eo. These are the counterpart of the m.h. waves and offer singular possibilities.

Electrohydrodynamic and Magnetohydrodynamic Nonlinear Surface Waves

A nonlinear formulation of electrohydrodynamic and magnetohydrodynamic surface interactions is developed which, in the absence of magnetic or electric fields, becomes the classical ``long'' gravity-wave theory. The results are valid for a shallow highly conducting fluid that interacts strongly with a rigid highly conducting plate in such a way as to either conserve an electric potential difference or a magnetic flux. The growth of surface discontinuities from compression and depression waves is discussed, with transition electrohydrodynamic waves originating from timelike data given to illustrate waves that are partly controlled by gravity and partly by the electric field. Waves initiated from spacelike data are also described, and the integral jump conditions derived.