Statics: surface deformation and contact angle on elastic materials

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Principle and setup

Before setting out all the details of our quantitative Schlieren optics set-up, we will start with a simple description of the principle of the Schlieren technique.
When a camera is targeting at a transparent object with the surface deformation with a uniform surface slope at certain region under the natural illumination (Figure 2.1(a)), a picture with homogeneous light intensity will be acquired. Equivalently, nothing will be observed on the acquired picture. The amount of light received by the CCD or CMOS sensors inside the camera from the deformed part and flat part is the same because the natural light is of all directions thus the overall sum of light beams that go to the camera from any point on the surface is almost the same. However, if the illumination light beam is collimated (Figure 2.1(b)), there are two changes compared to the case under the natural illumination: first, only a small part of the object is visible to the camera because the light beam, after passing through the part outside the yellow region (Figure 2.1(b)), is out of the camera lens’ range; second, if the transparent object is flat, only the part that is right in front of the camera, as is drawn in red line, can be sensed. However, the deformed region deflects light beams, leading them with a new path into the camera’s range, blue line in Figure 2.1(b). With the parallel light beam, the surface slope of the deformed part can be calculated through Snell’s law once the distance between the camera and the object, and the size of the camera lens are known.

Wetting velocity measurement

As part of this thesis is to investigate the spreading dynamics of liquids on soft materials, two sets of elastowetting dynamics are designed: droplet deflation, and droplet sliding and drifting on a titled substrate. We describe now how the contact line velocity is extracted with a subpixel precision. The experimental setup for droplet deflation, Figure 2.11(a), is part of the quantitative Schlieren system (Figure 2.3(a)) so that not only the contact line velocity/angle can be measured by a side view camera, which is equivalently shown as SC in Figure 2.3(a) and the camera in Figure 2.11(a), but also the simultaneous surface deformation is monitored by the Schlieren camera. Liquid spreads on a horizontal, flat soft layer that is coated on the rigid glass slide. The side view camera is mounted in perpendicular to the parallel light beam plane and is on the same altitude to the soft substrate surface. The spreading velocity is tuned by the flux rate of a pump.

Thickness control of soft films

Liquid droplets sit or spread on soft films and the thickness of those films needs to be well controlled. In this thesis, we deal with three types of soft materials: polydimethylsiloxane (PDMS) gel, PVA hydrogel and SBS-paraffin gel. All those gels are prepared and crosslinked on the surface of glass slide. The preparation of those gels is very different and their thickness control should also be different. However, to investigate the elastowetting properties of soft materials, we pay most of our attention to the PDMS gel. For the PVA hydrogel and SBSparaffin gel, we only look at their contact angle hysteresis and spreading of liquid on very thick film. Consequently, thickness control technique concerns only the PDMS gel if it is not specifically specified. For the PDMS soft film, its thickness ranges from several microns to several millimeters. Two techniques are employed for the thin and thick film, respectively. The thickness is measured with a 3D profiler (Microsurf 3D, Fogal Nanotech, France) at a precision of nanometers with the white light scanning mode. For drifting experiments of sliding droplets, a soft film with thickness gradient is needed. Its preparation will be described in the third part and the thickness measurement is performed by a side view microscopic camera with a precision of 3.3 𝜇𝑚.
To obtain soft film with small thickness, we adopt the spin coating technique. The procedure and the setup are demonstrated in Figure 2.17. A glass slide is fixed onto the horizontal rotational plate of a home-made spin coater. The polymer melt, Sylgard 527, is deposited onto the glass slide as is shown in Figure 2.17(a). The angular speed, 𝜔, of the spin coater can be tuned from 0 𝑅𝑃𝑀 to 3640 𝑅𝑃𝑀. After a spinning time 𝑇, a homogeneous liquid film forms and its thickness ℎ is predicted from the centrifugal force and the viscous force as126,127: ℎ = 𝑘𝜔𝛼, where 𝑘 and 𝛼 are determined from experiments.

PDMS fabrication and its rheology

In order to prepare chemically crosslinked soft PDMS gel samples having controlled mechanical properties, we use two commercially available silicone elastomer kits (Sylgard 184 and Sylgard 527 from Dow Corning company). Their mechanical properties are tuned by controlling the mass ratio of the two Sylgard128, 𝛼 = 𝑚𝑆184⁄(𝑚𝑆184 + 𝑚𝑆527), where 𝑚𝑆184 and 𝑚𝑆527 are the mass of the Sylgard 184 and Sylgard 527, respectively. The two Sylgards are prepared according to the manufacturer’s guide: Sylgard 184 is obtained from mixing the base and curing agent with a mass ratio of 10:1; Sylgard 527 is achieved by mixing part A and part B at a mass ratio of 1:1. As a result, the stoichiometry of each is always kept the same even when the proportion of them is different for different stiffness.

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SBS-paraffin gel fabrication and its rheology

SBS-paraffin gel is developed from mixing the commercial SBS powder (Styrene Butadiene Styrene; G1682, Kraton Polymers, USA) with paraffin liquid (Norpar15, ExxonMobil, USA) at different concentrations. SBS powder is dissolved into the paraffin oil under stirring at 90°𝐶 for 2 hours. After the full mixing of the two, the solution is poured onto a glass slide at ambient temperature (~25°𝐶) in a fashion as described in section 2.5.
The rheological properties of SBS-paraffin gels are measured by T. Kajiya at fixed temperature of 25°𝐶 by a strain-controlled rheometer (Physica MCR 500; Anton Paar, Austria)68,69. The rheological response is that of entangled polymer solution: the loss modulus dominates at very low frequency thus the gel flows at a long-time scale, while at high frequency the storage modulus dominates and the system is elastic due to the entanglement of the chain.

Hydrogel fabrication and its rheology

Hydrogels are synthesized from a commercially available photocrosslinkable polymer (PVA_SbQ, Poly (vinyl alcohol), N-methyl-4 (4’-formylstyryl) pyridinium methosulfate acetal, Polysciences, Inc, USA) and a crosslinker GA (Glutaraldehyde solution, Grade II, 25% in H2O, Sigma-Aldrich Co, USA). The preparation procedures are in the following: Firstly, the PVA SbQ solution, GA, distilled water (Milli-Q Integral; Millipore, USA) and acid HCl are mixed with the designed stoichiometry at the ambient temperature. HCl is used as catalyst of the PVAGA crosslinking reaction. The reaction rate depends on the HCl concentration: we use 0.03 𝑚𝑜𝑙/𝐿 for gelation time about several hours. The mixture solution is placed under the UV light (VL-206.BLB, 2 × 6 𝑊 – 365 𝑛𝑚 Tube, France) at a distance of 9 𝑐𝑚 for 18 ℎ𝑜𝑢𝑟𝑠 to ensure the completion of the gelation. The sample is enclosed with a specifically designed chamber saturated with water to avoid drying during the crosslinking reactions. Figure 2.24 shows the crosslinking reactions during the UV light exposure. Not only is the PVA_SbQ polymer itself crosslinked (reaction in Figure 2.24(a)), but also they are crosslinked by the GA crosslinker through the hydroxyl group (reaction in Figure 2.24(b)).

Table of contents :

Chapter 1 State of the ART
1.1 Introduction
1.2 Wetting fundamentals: from Young to Neumann
1.2.1 Rigid wetting: Young’s equation
1.2.2 Wetting of a liquid on another immiscible liquid: Neumann’s triangle
1.2.3 Wetting of a liquid on a compliant substrate: elastowetting
1.3 Statics in elastowetting
1.3.1 Static contact angle and its hysteresis
1.3.2 Deformation at the contact line
1.4 Dynamics in elastowetting
1.4.1 Dissipation in rigid wetting
1.4.2 Dissipation in elastowetting
1.5 Open questions and the structure
Chapter 2 Experimental techniques and materials
2.1 General review of experiments
2.2 Quantitative Schlieren optics
2.2.1 Principle and setup
2.2.2 Calibration and validation
2.3 Contact angle detection
2.4 Wetting velocity measurement
2.5 Thickness control of soft films
2.6 Materials
2.6.1 PDMS fabrication and its rheology
2.6.2 SBS-paraffin gel fabrication and its rheology
2.6.3 Hydrogel fabrication and its rheology
Chapter 3 Statics: surface deformation and contact angle on elastic materials ..
3.1 Introduction
3.2 Measurements of the surface deformation
3.2.1 Thickness effect
3.2.2 Droplet size effect
3.2.3 Rigidity effect
3.3 Model from the linear elastic theory
3.4 Results
3.5 Discussions
3.5.1 Contributions from two contact lines and the Laplace pressure
3.5.2 Tangential force
3.6 Modifying contact angle hysteresis with a resting droplet
3.7 Summaries and conclusions
3.7.1 Surface deformation
3.7.2 Resting time effect on the contact angle hysteresis
3.8 Perspectives
Chapter 4 Dynamics: moving contact line on viscoelastic materials
4.1 Introduction
4.2 Experiments and observation
4.2.1 Hydrodynamics fails
4.2.2 Thickness matters
4.3 Rationalization with the theory of linear viscoelasticity
4.3.1 Modeling
4.3.2 Results
4.3.3 Discussion
4.4 Summaries and conclusions
4.5 Perspectives
Chapter 5 Sliding and drifting of droplets on soft films
5.1 Introduction
5.2 Droplets sliding on viscoelastic films
5.2.1 Droplet size effect
5.2.2 Thickness effect
5.3 Drifting droplets with thickness gradient
5.3.1 Experimental setup
5.3.2 Drifting
5.3.3 Results
5.4 Conclusions and perspectives
Chapter 6 General conclusions and perspectives
6.1 Conclusions
6.2 Perspectives
6.2.1 Contact angle hysteresis on SBS-paraffin gels
6.2.2 Elastowetting on hydrogels
Appendix A: Deflection of the parallel light beam
Appendix B: Scaling for the thickness effect at small thickness limit
Bibliography

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