Coiling rigid microfibers inside liquid droplets Paul Grandgeorge Arnaud Antkowiak Sébastien Neukirch 1 Sorbonne Université, UPMC Paris 06, CNRS, Institut Jean Le Rond d'Alembert, UMR 7190, Paris Liquid wires
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Coiling rigid microfibers inside liquid droplets
Paul GrandgeorgeArnaud Antkowiak
Sébastien Neukirch
1
Sorbonne Université, UPMC Paris 06, CNRS, Institut Jean Le Rond d'Alembert, UMR 7190, Paris
Liquid wires
Nephila golden orb weaver
Biological inspiration
Interesting properties of its capture silk
2
Liquid wires?
1 mm
Nephila spider capture silk thread coated with small water droplets. Throughout the compression, the fiber does not sag,
it remains under tension. Video credit: Hervé Elettro
3
Nephila capture silkIts highly compressible property
Real TimeH. Elettro et al.
PNAS - 2016
50μm
4
During the compression, the thread spools inside the water droplets.
Nephila capture silkA closer look inside the droplets
5
Elastocapillary in-drop spoolingThe movie
Silicone oil droplet on a RTV (silicone polymer) fiber. The system is immersed in a water bath.
Fiber: radius a≈35 μm, Young's modulus E≈1 Mpa. Droplet : radius R=1.5 mm, Δ𝛾≈40 mN/m.
3 mmReal Time
6
VA = PL1�sv + PL2�sl + L21
2
EI
R2+ P�l�sv
VB = PL1�sv + PL2�sl + L21
2
EI
R2+ P�l�sl +�l
1
2
EI
R2
Elastocapillary in-drop spoolingThe energetic approach
Solid-vapor interface energy
Solid-vapor interface energy
Solid-liquid interface energy
Bendingenergy
Solid-liquid interface energy
Bendingenergy
7
Circular cross section fiber of
radius : P = 2⇡a
I =⇡a4
4
a
Typical values (spider silk):
If it is thin and elastic enough, a thread can coil inside a droplet!
R ⇠ 100µm
E ⇠ 10 MPa
⇠ 10µm
VA = PL1�sv + PL2�sl + L21
2
EI
R2+ P�l�sv
VB = PL1�sv + PL2�sl + L21
2
EI
R2+ P�l�sl +�l
1
2
EI
R2
�� ⇠ 50 mN/m
Elastocapillary in-drop spoolingThe energetic approach
T = ��V
�l=
✓P�� � 1
2
EI
R2
◆
�V = �l
✓1
2
EI
R2� P��
◆
T > 0 ?
2⇡a� � ⇡a4E
8R2> 0
a <
✓16�
E
◆1/3
R2/3
8
Elastocapillary in-drop spoolingThe pre-movie II
2 mm
Bear thermoplastic polyurethane microfiber with no droplet sitting on it. Fiber: radius a=3.3 μm, Young's modulus E=20 Mpa.
Real Time
9
Elastocapillary in-drop spooling
Silicone oil droplets on said thermoplastic polyurethane microfiber. An artificial ultra compressible/extensible device.
Fiber: radius a=3.3 μm, Young's modulus E=20 Mpa. Final droplet : radius R=106 μm, 𝛾=21 mN/m.
The movie II
2 mmReal Time
10
The coiling fibers
Phase diagram of coiling and non-coiling fibers Fiber: Considered Young's modulus E = 70 MPa.
Droplet : 𝛾≈21 mN/m.
Phase diagram
2⇡a� � ⇡a4E
8R2> 0
Capillary Elastic- > 0
11
Elastocapillary in-drop spooling
Big silicone oil droplet on a thermoplastic polyurethane microfiber. Gravity kicks in.
Fiber: radius a=3.4 μm, Young's modulus E=20 Mpa. Droplet : radius R=430 μm, 𝛾=20 mN/m.
Gravity
2 mmReal Time
12
Elastocapillary in-drop spoolingGravity
P�� � 1
2
EI
R2>
mg
2
2⇡a� � ⇡a4E
8R2>
4
3
⇡⇢gR3
2
P = 2⇡a
I =⇡a4
4� < ⇡/2
13
The coilable fibers
Phase diagram of coilable and non-coilable fibers Fiber: Considered Young's modulus E = 70 MPa.
Droplet : 𝛾=21 mN/m.
Phase diagram
2⇡a� � ⇡a4E
8R2>
4
3
⇡⇢gR3
2
2⇡a� � ⇡a4E
8R2> 0
14
The coiling fibers
Phase diagram of coiling and non-coiling fibers with gravity. Fiber: Considered Young's modulus E = 70 MPa.
Droplet : 𝛾=21 mN/m, 𝜌g = 9600 N/m3.
Phase diagram
2⇡a� � ⇡a4E
8R2>
4
3
⇡⇢gR3
2
amax
= c(⇢g, �) · E�3/7
Capillary Elastic- > 1/2 Weight
15
The coiling fibersPhase diagram
Phase diagram of coilable and non-coilable fibers. Droplet : 𝛾=21 mN/m, 𝜌g = 9600 N/m3.
amax
= c(⇢g, �) · E�3/7
16
Biggest coilable fibreGravity
P = 2⇡a
I =⇡a4
4
P�� � 1
2
EI
R2>
mg
2
2⇡a� � ⇡a4E
8R2>
4
3
⇡⇢gR3
2
� < ⇡/2
17
Biggest coilable fibreThe tutor
I =⇡a4
4
P = 2⇡a+ Psoft
' Psoft
Psoft
� � ⇡a4E/4 + Esoft
Isoft
2R2
>4
3
⇡⇢gR3
2
P�� � 1
2
EI
R2>
mg
2
18
Biggest coilable fibreThe tutor
Phase diagram of coiling and non-coiling fibers with gravity. Rigid fiber: Considered Young's modulus E = 70 MPa.
Soft fiber : Young's modulus Esoft=200 kPa, width w = 180 μm, height h = 50 μm. Droplet : 𝛾=21 mN/m, 𝜌g = 9600 N/m3.
Psoft
� � ⇡a4E/4 + Esoft
Isoft
2R2
>4
3
⇡⇢gR3
2
amax
= C(⇢g, Psoft
�, Esoft
Isoft
) · E�1/4
19
The coiling fibersPhase diagram
Phase diagram of coilable and non-coilable fibers. Droplet : 𝛾=21 mN/m.
am
a
x =c · E �
3/7
amax
= C(⇢g, Psoft
�, Esoft
Isoft
) · E�1/4
20
Coiling the uncoilableThe tutor
Phase diagram of coilable and non-coilable fibers with tutor. Soft fiber : Young's modulus Esoft=200 kPa, width w = 180μm, height h = 50μm.
Droplet : 𝛾=21 mN/m, 𝜌g = 9600 N/m3.
am
a
x = C · E �1/
4
amax
= C(⇢g, Psoft
�, Esoft
Isoft
) · E�1/4
am
a
x =c · E �
3/7
21
2 mm
Coiling the uncoilableUncoilable
Silicone oil droplet on a poly-actif acid (PLA) microfiber. Fiber: radius a=4.1 μm, Young's modulus E=2.7 GPa.
Droplet : radius R=256 μm, Δ𝛾≈20 mN/m.
Real Time
22
Coiling the uncoilable
Silicone oil droplet on a composite poly-actif acid (PLA) microfiber + polyvinyl siloxane (PVS) tutor fiber.
PLA fiber: radius a=4.1 μm, Young's modulus E=2.7 GPa. PVS fiber: width w=100 μm, height h = 35 μm, Young's modulus E=200 kPa,
Droplet: radius R=430 μm, Δ𝛾≈20 mN/m.
The coilabe composite fiber
2 mmReal Time
23200 μm
Coiling the uncoilableCoiled!
24
Thank you!
0.5 mmReal Time
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