Enhanced Capillary Rise of Wetting Liquids in Reduced Gravitational Shielding Under Microgravity Conditions

We study the capillary rise of wetting in liquids by slightly modifying Ponomarenko’s result, a recently derived and observed t1/3 law, without omitting the corresponding gravity term and therefore we find hnew (t)≅0.9085hPon (t) instead, which corresponds to a 9% difference. Furthermore, in order to examine the effect of corrected gravity, we extend the result on the surface of a planetary body by correcting the gravitational acceleration for its oblateness coefficient and rotation. We find that experiments that take place on the equator result in highest capillary heights, than those at mid latitudes and the poles. Similarly, analyzing the effect of reduced gravitational shielding on the capillary rise under conditions of microgravity in experiments aboard orbiting spacecraft, we find that equatorial circular orbits exhibit the highest capillary heights, where equatorial elliptical orbits of large eccentricities exhibit the smallest capillary heights. Finally, we calculate the rate of change of the meniscus height in the time domain, for the different laboratory conditions on the surface of the Earth and in space and as example. As an example we say that laboratory sites at the equator will exhibit larges time rates of change for the meniscus height. Similarly, for experiments above a spacecraft we find that circular equatorial orbits exhibit the highest time rates of change, where elliptical orbits exhibit smaller time rates that reduce as the eccentricity increases

Modulus of surface families and the radial stretch in the Heisenberg group

We develop a modulus method for surface families inside a domain in the Heisenberg group and we prove that the stretch map between two Heisenberg spherical rings is a minimiser for the mean distortion among the class of contact quasiconformal maps between these rings which satisfy certain boundary conditions.Comment: 24 pages, typos correcte