Supplemental Material
Microfluidic Fabrication of Polymeric Core-shell Microspheres for
Controlled Release Applications
T. T. Kongab, J. Wunc, KWK Yeungc MKTsun Toc, H. C. Shumad* and L. Q. Wangab*
a
b
Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong
Kong
HKU- Zhejiang Institute of Research and Innovation (HKU-ZIRI), 311100, Hangzhou, Zhejiang,
China
c
Department of Orthopaedics and Traumatology, Li Ka Shing Faculty of Medicine, HKU, HK,
China
d
HKU-Shenzhen Institute of Research and Innovation (HKU-SIRI), 518000, Shenzhen,
Guangdong, China
emmakong@hku.hk, miketto@hku.hk ashum@hku.hk, lqwang@hku.hk.
*corresponding author
Deduction of the model to predict sizes of the double emulsion droplets in a flowfocusing geometry assuming the break-up of the middle phase triggers the
formation of double emulsion droplets
In the dripping regime, when the capillary number Ca, which is the ratio of shear and
interfacial forces, reaches a critical value, typically on the order of 1, the droplet detaches
from the nozzle and flows towards downstream. The size of the generated emulsion
droplet can be predicted by solving the equation (1) [1].
(1)
Fshear: the shear force exerted on the dispersed phase by continuous phase
Fr: the pinning force caused by surface tension of the dispersed phase
For double emulsions, the middle jet is assumed to break up into droplets first,
containing the ruptured innermost droplets. By treating the middle jet containing the
inner phase as one dispersed phase,
(2)
(3)
F2,shear : shear force exerted on middle jet by outer phase
F2,ϒ : the pinning force caused by surface tension of middle jet
: viscosity of the outer phase fluid
: diameter of the injection capillary
: diameter of the jet thread formed in the co-flowing geometry
By mass balance assumptions
Dc : diameter of the collection capillary
Q1, Q2, Q3 : volumetric flow rate of the inner, middle, outer phase fluid
ϒ2,3 : interfacial tension between middle and outer fluid
v2 ,v3 : average velocity of middle, outer phase respectively, where
,
.
By solving eq. (1-3), eq. (4) regarding d2 can be obtained as following [1]
,
(4)
By mass balance assumption
(5)
Deduction of the model to predict sizes of the double emulsion droplets in a flowfocusing geometry assuming the break-up of the inner phase triggers the formation
of double emulsion droplets
If the inner phase is assumed to break up first, and its break-up forces middle phase to
pinch off before its critical capillary number is reached, then the inner droplet size d1
should satisfy the critical capillary number required.
(6)
(7)
: the viscosity of middle fluid
v1 ,v2 : average velocity of inner, middle phase respectively,
: diameter of the jet thread formed in the co-flowing geometry,
: diameter of the injection capillary
Dc : diameter of the collection capillary
ϒ1,2 : interfacial tension between inner and middle fluid
By solving equation (1), (6)-(7), the diameter of total droplet d1 is given by
(8)
By mass balance assumption
(9)
Reference:
1. R. M. Erb, D. Obrist, P. W. Chen, J. Studer and A. R. Studart, Soft Matter, 7, 8757
(2011)