type used for wavelengths were possible, one could determine Unfortunately, insufficient theory prevents tAe former, and the inability of experiments to separate you prevents the latter. From experimental data on air-water systems, where X, ps exactly.
and u can be theoretically determined,
Am.
1s
found to be of the
YO
order of 20. Thus. for the liquid-liquid systems treated, y o cm. This is the order of magnishould be of the order of tude of wall roughness, If .yo is due to wall roughness alone, it should be independent of the fluid pairs used. Thus, yo should be obtainable from careful air-water experiments. O n e could then calculate u for liquid-liquid systems and proceed along the lines used in the treatment of wavelengths.
= Re(t) = time =
= = = = = = =
= =
lower (upper) phase small-disturbance velocity in v direction lower (upper) phase small-disturbance velocity in y direction Cartesian coordinate amplitude of waves a t time t original small-disturbance amplitude 3 1 s = rate of propagation of waves of length X growth angle lower (upper) phase boundary layer thickness displacement of interface from its undisturbed position dimensionless lower (upper phase viscosity number,
p_
7“
