curvature

Examples of curvature in the following topics:

• Surface Tension

  • When all the forces are balanced, the curvature of the surface is a good measure of the surface tension, which is described by the Young-Laplace equation:
  • where $\Delta P$ is the pressure differential across the interface, $\gamma$ is the measured surface tension, and $R_1, R_2$ are the principal radii of curvature, which indicate the degree of curvature.
  • This equation describes the shape and curvature of water bubbles and puddles, the "footprints" of water-walking insects, and the phenomenon of a needle floating on the surface of water.
  • In imagining the shape of a liquid droplet or the curvature of the surface of a liquid, one must keep in mind that the molecules at the surface are at a different level of potential energy than are those of the interior.

• Fused Benzen Ring Compounds

  • If we extend the structure of corannulene by adding similar cycles of five benzene rings, the curvature of the resulting molecule should increase, and eventually close into a sphere of carbon atoms.
  • Strain introduced by the curvature of the surface may be responsible for the enhanced reactivity of C60.

• Capillary Action

  • The curvature of the surface at the top of a column of fluid in a narrow tube is caused by the relative strength of the forces responsible for the surface tension of the fluid (cohesive forces) and the adhesive forces to the walls of the container.

• The de Broglie Wavelength

  • As the amplitude increases above zero the curvature decreases, so the amplitude decreases again, and vice versa – the result is an alternating amplitude: a wave.

• Liquid to Gas Phase Transition

• Temperature

  • Upon heating or cooling, the two metals expand or contract at different rates, causing a bending or curvature to appear in the strip.