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A silicalite-1 tubular membrane was prepared on the inner surface of a porous α-alumina support. Helium permeation at different feed volumetric flows (11–41 mL/min) with different sweep flow rates (9–90 mL/min) at STP conditions was measured. The molar fraction was obtained as a function of the residence time ratio. The influences of the geometric parameters of the tubular system and the feed flow rates on the permeation through the membrane were investigated. The dependence of the permeances with the residence time ratio was experimentally obtained and we propose that this dependence is a useful design criterion for tubular membrane permeation systems. The best results in this work were obtained for Q He,in /Q N2,in = 0.22 for V SS /V TS = 7.3. Also, the data showed that an appropriate combination of the flows and the area sections of the system resulted in an optimum value for the Peclet number of 0.3. The experimental data were reproduced by numerically solving the Maxwell–Stefan equations under the assumption that transport across the membrane can be modeled in terms of a Robin-type boundary condition.

In this paper the analysis of the classical dynamics of a charged particle is carried out without considering that the electromagnetic field necessarily goes to zero at infinity. A quite general non-linear equation of motion is obtained for an extended charged particle valid for any distribution of charge in the particle and for an electromagnetic field satisfying any boundary conditions. Some common approximations are analyzed with detail to determine how the usual difficulties arise.

The correct definition of electromagnetic momentum in matter, either Abraham's g A = (1/4πc) (E × H), or Minkowski's g M = (1/4πc) (D × B) has been a theme of controversy for a century. Therefore, we can find those who favor one or the other of these proposals. We present here an alternative view, considering that both of the aforementioned equations are equivalent since they pertain to different balance equations derived from the macroscopic Maxwell equations. This is done through their application to a device proposed by Lai in 1980, and recovering his results. Advanced undergraduate and graduate students can find in this work an introduction to a controversial issue and an alternative point of view about it.

The Dirac equation, with minimal coupling, is analysed in order to show that the Zitterbewegung (rapid oscillatory motion) also arises when a static and uniform magnetic field is taken into account. The corresponding equations of motion are solved in the Heisenberg picture with the weak-field approximation.

A proper handling of retarded quantities leads us to a systematic derivation of the Lorentz- Dirac equation. Our basic assumption is that the Lorentz force FΜΝυΝ,where FΜΝ is the electromagnetic field produced by the charge itself, is the radiation reaction force. We exhibit the contribution of each term of FΜΝ to the Lorentz-Dirac equation.

A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases using canonical transformations applied to Hamiltonians for a particle with variable mass. The Green's function is constructed and, from it, the motion of a Gaussian wave packet is studied in detail., Comment: 14 pages, 4 figures, misprints and figures corrected