Level 3

Problem 1 (Scaling). One atomic mass unit (AMU) equals $1.6605 \times 10^{-27}$kg. Convert the density, surface tension and viscosity of liquid argon (listed in the Background section) to units of AMU per cubic Angstrom, AMU per square picosecond and AMU per Angstrom-picosecond. How long (picoseconds) did it take for the deformation to roughly level off in the Atomistic simulation from Example 1? Using Background equation (15) with the appropriate radius (in Angstroms) along with the viscosity and surface tension as described above, convert this to a dimensionless time. How well does this compare with the dimensionless time (approximately 6) required for the deformation to level off in the Continuum simulation from Level 1 Problem 3? These are different situations (gas versus liquid surrounding the droplet in the Atomistic versus Continuum simulations) but you would expect only a factor of 2 difference owing to Background equations (16) and (17).

Problem 2 (Numerical Artifact). In the Continuum simulation from Level 1 Problem 3, the deformation levels off, but then slowly increases again very slowly as dimenionless time goes on beyond 6. You will notice that, at these later times, the volume error has accumulated, so that the droplet's equivalent radius has decreaseed discernibly below its initial (dimensionless) value of unity. (This is due to numerical errors in the simulation, and is not a physical effect.) Can you rationalize the less severely deformed droplet shape with smaller radius?