6 Operation
41
B-390
Operation Manual, Version E
6 .7
Theoretical background
Equ. 1:
When a laminar jet is mechanically disturbed at the frequency ƒ,
beads of uniform size are formed
1
. The optimal wavelength
λ
opt
for
breakup, according to Weber
2
is given by:
Equ. 2:
where:
D = nozzle diameter
η
= dynamic viscosity [Pa s]
ρ
= density [kg/m
3
]
(ca. 1000 kg/m
3
for alginate solutions)
σ
= surface tension [N/m]
(ca. 55×10
-3
N/m for alginate solutions)
λ
opt
is the optimal wavelength to get the best bead formation for the given nozzle diameter and the
viscosity of the encapsulation mixture. It is possible to change
λ
opt
by 30 % and still achieve a good
bead formation.
The diameter of a bead = d [m] can be calculated with the flow rate = V’ [m
3
/s] and the frequency of
the pulsation ƒaccording to:
Equ. 3:
The jet velocity = v [m/s] and the nozzle diameter = D [m] are correlated to the flow rate (V’) according
to:
Equ. 4:
Figure 6-4
shows the dependence of the flow rate to the jet velocity and the nozzle diameter as calcu-
lated by Equation 4. Because the liquid must flow laminarly the working range of the jet velocity will
normally lay between 1.5 and 2.5 m/s, depending on the liquid viscosity and the nozzle diameter.
1
Lord Rayleigh 1878. Proc. London Math. Soc. 10:4.
2
Weber C. 1936. Zeitschrift für angewandte Mathematik und Mechanik. 11:136.
