Capillary Rise in a Taylor-Hauksbee Cell with a Tilted Edge - Selected Topics of Computational and Experimental Fluid Mechanics - page 514

Fig. 2 Left hand side picture of the experimental equilibrium profile (rectangular hyperbola) for

ʲ =

0rad. Right hand side theoretical profile ( curve ) and experimental data ( symbols )

In this case the pressure jump across the surface is approximately

2 ˃ cos ʸ

p =

ʲ ,

(4)

ʱ

s cos

meanwhile the equilibrium profile is determined by the balance

p = ˁg Y s cos ʲ. (5)

This balance gives the hyperbola

˃ ʸ

2 cos

Y s =

ʲ ,

(6)

s cos 2

ˁgʱ

Another way to get the profile is by using the vertical length H s ( but it is more

complex because for some values of s could exist two values of H s and for other
ones, none. Thus, it is better to compute s

s )

( H s ) (an injective function) given by

2 ˃ cos ʸ

S =

H s +

H s tan ʲ. (7)

ˁgʱ cos ʲ

Consequently, the equilibrium profile can be plotted by using Eqs. ( 6 )or( 7 ).
To make sure that our model is correct in the prediction of the equilibrium profiles
in Fig. 3 we show the actual equilibrium profile in a Taylor-Hauskbee cell having
ʲ = 30 ◦ ) 0.523 rad ( and ʱ = 0.0092 rad. The liquid of work was again silicone oil

of μ = 100 cP. In Fig. 4 we give an example of Fig. 3 showing other details.