/* Surface tension, excess pressure and virtual-work identities. */
kill(all)$
display2d:false$

dA_film : 2*L*dx$
F_film : 2*gamma*L$
print("Two-sided film work residual (must be 0):",
  ratsimp(F_film*dx-gamma*dA_film))$

dV_sphere : 4*%pi*R^2*dR$
dA_sphere : 8*%pi*R*dR$
print("Spherical-drop work residual (must be 0):",
  ratsimp((2*gamma/R)*dV_sphere-gamma*dA_sphere))$
print("Soap-bubble work residual (must be 0):",
  ratsimp((4*gamma/R)*dV_sphere-2*gamma*dA_sphere))$

dV_cylinder : 2*%pi*R*L*dR$
dA_cylinder : 2*%pi*L*dR$
print("Cylindrical-interface work residual (must be 0):",
  ratsimp((gamma/R)*dV_cylinder-gamma*dA_cylinder))$

young_balance : gammaSV-gammaSL-gammaLV*cos(theta)$
print("Young contact-angle residual (must be 0):",
  ratsimp(ev(young_balance,
    gammaSV=gammaSL+gammaLV*cos(theta))))$

quit();