Digital, Two-Phase, and Droplet Microfluidics - Microfluidics for Biotechnology - page 192

Figure 4.74 In a homothetic scaling-up, the boundaries of the dripping droplet regime are similar
for the depths 50, 100 and 200 m m. The close square symbols, the open triangular symbols, and the
stars, respectively, represent the depths of 50 m m, 100 m m, and 200 m m.

2

ρ V R

i i thread

(4.113)

We = < We

c

γ

where r i , and R thread are respectively the density of the alginate phase and the ra-
dius of the alginate thread. This dimensionless number characterizes the balance
between inertial forces and interfacial tension on the alginate phase.
The second condition is

η V

e e

(4.114)

Ca = < Ca

c

γ

This capillary number scales the viscous forces with the interfacial tension for
the oil phase. Equations (4.113) and (4.114) yield

We

γ

c

Q Q dw < =

(4.115) i ic i

ρ R

i thread

and

dw Ca γ

η

e c

Q Q < =

(4.116)

e ec

e

Assuming that R thread is always approximately of the order of magnitude (~a
few tenth of microns) at break-up, (4.115) and (4.116) imply that the critical flow