`drop.optimize.theory`¶

Module Contents¶

drop.optimize.theory.young_laplace_diff_equation(space, variables, bond_number)¶

Return the derivatives corresponding to the Young-Laplace equation.

Parameters:	space : 1D-array Space variable. variables : tuple (phi, r_tilde, z_tilde) bond_number : scalar Bond number.
Returns:	derivatives : tuple (d phi / d s_tilde, d r_tilde / d s_tilde, d z_tilde / d s_tilde )

Notes

tilde means non-dimensionalized by the tip radius.

References

[1]	Del Rıo, O. I., and A. W. Neumann. “Axisymmetric drop shape analysis: computational methods for the measurement of interfacial properties from the shape and dimensions of pendant and sessile drops.” Journal of colloid and interface science 196.2 (1997): 136-147. DOI:10.1006/jcis.1997.5214

drop.optimize.theory.theoretical_contour(bond_number, num_points=1000.0, s_max=10)¶

Compute a theoretical contour from the Young-Laplace differential equation.

Parameters:	bond_number : scalar Bond number. num_points : scalar, optional Number of points used to compute the profile. These points are evenly spaces from s=0 to s=s_max. s_max : scalar, optional Maximum value for the curvilinear coordinate.
Returns:	(R, Z) : tuple R and Z coordinates.

Notes

The profile is non-dimensionalized by the tip radius. The resolution is achieved with scipy.integrate.solve_ivp

drop.optimize.theory.rotate_lines(R, Z, center, theta)¶

Rotate with specific angle conversion for our images.

Parameters:	R : array Radial coordinates. Z : array Vertical coordinates. center : tuple Rotation center coordinates. theta : scalar Rotation angle.