Wrinkling instability in the Near-Threshold regime 

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Modelling of capsule membrane

A microcapsule generally has a finite membrane thickness, h. Compared to the size of capsules, the thickness is quite small (h R). For simplicity, the membrane can be considered as 2D, neglecting the bending resistance due to the thin thickness [53], in which the global deformation of capsule can be described well. However, if the membrane is thick or non homogeneous, the bending moments due to the curvature of capsule deformation play important roles [54]. The bending resistance then has to be taken into account.

2D membrane

In the absence of bending resistance, the transverse shear stress vanishes across the membrane. The stress tension can be replaced by the tension T at the middle plane of the membrane (defined as force per unit arc length). When stretched or compressed, the membrane only undergoes in-membrane deformation, with surface shear elastic modulus Gs and area dilation modulus Ks [13]. The tension T can be decomposed into two principal direction, T1 and T2.

3D membrane

For a thick membrane, the transverse shear forces across the membrane can not be con-sidered as homogeneous. The produced tangential bending moments are not negligi-ble [66, 67]. The developing of bending moments make the 3D membrane with flexural stiffness, which is correlated to the bending modulus, B. Although the bending modu-lus has a few orders of magnitude smaller than the surface shear modulus, the bending resistance is believed to play central roles in determining the curved configuration at equilibrium for soft particles, for example biconcave RBCs [22].
As illustrated in Figure 1.3, when the membrane is bent, it produces the in-plane tension which requires n = 0. In the circumferential direction, the tensor can be described as s and . The transverse shear tension is described as a vector q, acting on the cross section of the membrane. The bending moment tensor is named as m. Like elastic tension, the transverse shear tensions and bending moments are required to have no normal component, lying in the tangential plane, namely q n = 0 and m n = 0. Thus, the full tension tensor, including the tangential and transverse shear tensions, can be written as T = + qn (1.7).
where the transverse shear tensor is expressed as q = (r m) (I nn). The bending moment tensor is related to the local curvature and the bending modulus. The detailed formulations can be found in reference [67]. To close the problem, constitutive laws in 3D is required. Strain-energy function is useful to deduce the tension tensor [67, 68].
A membrane without bending resistance might form corned shape, showing no curvature. In contrast, with the presence of bending resistance, the membrane has a reasonable curvature, after achieving the minimum energy. In this case, the final shape is the competition result of in-plane stress tension, bending resistance and external forces.

Capsules in flows

Soft particles exhibit spatiotemporal deformation when they are exposed to external stress field, for example in a hydrodynamics flow field. Since the flow generally has low Reynolds number (Re < 1), it is governed by the Stokes equation. Flow stress im-poses traction on the membranes to deform the particles. Meanwhile, complex dynam-ics might be coupled. In the past decades, an extensive number of studies have been carried out on RBCs [18, 33], vesicles [22, 69] and artificial capsules [5, 11, 57, 70, 71] in flows, via both experiments and numerics. In this section, we review the flow-structure interaction induced deformation and the general dynamics of capsules in shear and ex-tensional flow.

Liquid cores formation

The first step is the droplets formation using different immiscible phases. Conventional approaches (Figure 1.12(a)), for example static mixing [1, 107], high-pressure valve homogenizing [108] and electrospray [109, 110], are expected to have high efficiency in generation of droplets, which can meet the industrial requirement. However, the size of droplets is polydisperse due to exposure of produced droplets into the nonuniform shear or pressure field that might break a large droplet into several daughter droplets [111]. Recently, the emulsification of injecting a disperse phase into a continuous phase through a membrane where there exist micropores with a certain spacing array, provides a high production rate for droplets formation with size dispersity CV = 10-20% [112, 113] ( Figure 1.12(b)).

Microcapsules synthesis

Microfluidics is a well-established technique to control liquid droplets size, which is recently adapted for microcapsules fabrication. However, it is contradictory between the capsules production rate and polymerization time at interfaces, when the size adjustment and membrane growth are coupled in the microchannels. If it works at high production rate of producing capsules, the membrane growth will be weakened, due to shortening the residence time of capsules in the microchannels. Reversely, long residence time prolongs the membrane growth, but simultaneously it lowers significantly the production rate.
To overcome this, and to tune capsule membrane growth in a wide range, we thus decoupled the interface emulsion from drop generation in the microfluidic chip, which is more cost-effective. First, we fabricated monodisperse drop templates by using a microfluidic chip. Then, these templates were transferred into an oil solution with presence of surfactant or cross-linker, where we can control the membrane growth easily by varying the concentrations and reaction time.

Stability of capsules during membrane assembly

Although the decoupling interface emulsification allows us to assemble microcapsules with tunable mechanical properties, it is still a challenge to control the morphology and stability of capsules during the membrane formation. In water-in-oil (W/O) emulsion system, the most-likely medium that might transfer out of capsules through membrane is water content, due to their small molecular weight and high motility [136, 139]. As a result, the membrane collapse occurs (Figure 2.5(a)), which is referred to as buckling.
Generally, surface of capsule with low stiffness is found to have multiple dimples. In contrast, smaller number of dimples appear on the capsule with larger stiffness. This buckling, indeed, is a nuisance that we have to avoid in the investigation of capsules deformation in flows. Interestingly, with presence of surfactant, for example PFacidYN in oil phase, capsules start to buckle at a critical size in a long time membrane reaction, 20 minutes, for concentration of PFacidYN 3.3% w/w (Figure 2.5(b)). For capsules size larger than the critical value, their surface show well. As the amphiphilic surfactant molecules mainly play a role of water carrier in the emulsion [131], and there exists a big step of chemical potential for water inside and outside the capsules, one of the strategies to prevent the buckling is adding a few microliters of water in the bulk phase before transferring CHT or HSA droplet templates into. To achieve a balance, we thus vibrated the bulk strongly, and then let it at rest 10 minutes. The difference of capsules diameter before and after membrane emulsion in this way is less than 3% which is within the standard deviation of size distribution in microfluidics. Another strategy is to increase the osmotic pressure inside capsules by adding some salts in the encapsulated medium, for example Ca2+ and Mg2+.

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Stability of capsules in suspending fluids

After microcapsule synthesis, for characterizing the membrane elasticity we thus need to suspend them in a suspending fluid. Oil-based fluids would be the first choice as the suspending fluids for W/O microcapsules. Similar to the process of capsules preparation, capsules should be stable in such suspending fluids, for example no buckling. In this section, we discuss water-based microcapsules stability in some common oils, and further discuss the means to control the pre-stress on membrane in suspending fluids.

Qualitative observation of capsules stability in common oils

First, different types of oils were selected and added into closed reservoirs with a fixed volume of 5 mL (see Table A.5 in Appendix A for detailed properties of the oils). Then, we immersed different volumes of capsules (no glycerol enclosed) in these oils, and observed the status of capsules in 12 hours. Figure 2.7(a) shows that increasing the fraction of capsules in a type of oil can inhibit buckling. Saturating the oils with water, for example MCT oil and silicone oil, efficiently vanishes buckling even for the low fraction of capsules. Mineral oil exhibits good features to stabilize capsules.
Increasing the fraction of glycerol that enclosed inside the capsules is also helpful to slow down the buckling for a given volume fraction of capsules in oils (Figure 2.7(b)). Similarly, MCT oil and silicone oil with water treatment, and mineral oil show good performance to prevent buckling. In this context, we chose silicone oil with water saturation treatment as suspending fluid for capsules characterization. In contrast to mineral oil, silicone oil has high viscosity that produces relatively large viscous stress to deform the capsules.

Table of contents :

Acknowledgements
Abstract
Résumé
List of publications
General introduction
1 State of the art: dynamics and synthesis of microcapsules 
1.1 Introduction
1.2 Basic concepts of microcapsules
1.2.1 Scales, configuration and properties
1.2.2 Applications
1.3 Modelling of capsule membrane
1.3.1 2D membrane
1.3.2 3D membrane
1.4 Capsules in flows
1.4.1 Deformation
1.4.2 Dynamics
1.5 Capsule wrinkling in flows
1.5.1 A brief review
1.5.2 Wrinkling energies
1.6 Capsule membrane breakup
1.7 Synthesis of microcapsules
1.7.1 Liquid cores formation
1.7.2 Membrane formation
1.7.3 Rheological properties
1.7.4 Morphology
1.7.5 Stability
1.8 Conclusion
2 Materials and methods 
2.1 Introduction
2.2 Chemicals and solutions
2.3 Microcapsules synthesis
2.3.1 Decoupling interface emulsion
Drop-templates generation
Membrane assembly
2.3.2 Stability of capsules during membrane assembly
2.3.3 Control route of physical properties
2.4 Stability of capsules in suspending fluids
2.4.1 Qualitative observation of capsules stability in common oils
2.4.2 Pre-stress control on membrane
2.5 Planar extensional flow
2.5.1 Visualization
Photography of capsules
Cross-slot chamber
2.5.2 Flow field and validation
2.6 Determination of membrane elasticity
2.7 Atomic force microscopy
2.8 Scanning electron microscopy
2.9 Discussion and conclusion
3 Interfacial rheology of microcapsules 
3.1 Introduction
3.2 Membrane shear elasticity
3.2.1 Effect of capsule size
3.2.2 Effect of reaction time
3.2.3 Effect of concentrations
3.2.4 Effect of pre-stress
3.3 Membrane thickness and elasticity
3.3.1 Membrane thickness
3.3.2 Shear modulus
3.4 Yield stress and plasticity
3.4.1 Yield deformation
3.4.2 Relaxation
3.5 Discussion and conclusion
4 Microcapsules breakup 
4.1 Introduction
4.2 Parameters definition
4.3 Comparison of drops and capsules
4.3.1 Overall observation
4.3.2 Interfaces deformation
4.3.3 Steady-state and time-dependent deformation
4.3.4 Critical breakup in various viscosity ratios
4.4 Breakup phase diagrams
4.5 Mechanism of breakup
4.5.1 Low Gs (< 0.1 N/m)
4.5.2 High Gs (> 0.1 N/m)
4.6 Post breakup
4.7 Discussion and conclusion
5 Wrinkling instability in the Near-Threshold regime 
5.1 Introduction
5.2 Wrinkling induced by flow
5.3 Wrinkling at threshold
5.3.1 Critical wrinkling stress
5.3.2 Onset and development
5.4 Phase diagram
5.5 Wavelength and wave number in NT
5.6 Discussion and conclusion
6 Wrinkling instability in the Far-from-Threshold regime 
6.1 Introduction
6.2 Relaxation of compression
6.3 Wrinkling length development
6.4 Wavelength
6.4.1 In the NT regime
6.4.2 In the FT regime
6.5 Phase diagram
6.6 Discussion and conclusion
7 Conclusions and perspectives
7.1 General conclusions
7.2 Perspectives
7.2.1 Interfacial rheology
7.2.2 Relaxation of elastic capsules
7.2.3 Wrinkles-to-folds transition
A Protocol of solutions preparation 
A.1 Chitosan solution (CHT)
A.2 Phosphatidic fatty acids solution (PFacidYN)
A.3 Human serum albumin solution (HSA)
A.4 Terephthaloyl chloride solution (TC)
A.5 Suspending fluids
A.6 Physico-chemical properties of the chemicals
A.7 Treatment of silicone oil
B Microfluidics system 
B.1 Configuration of T-junction chip
B.2 Flow rate controlled system
C Models of flow chambers 
C.1 Design of the flow chamber
D Dry membrane preparation 
D.1 Drying process
D.2 Membrane tailoring for SEM
D.2.1 Flat membrane
D.2.2 Capsule membrane
E Capsules breakup preparation 
E.1 Viscosity ratio adjustment
E.2 Particles decoration at water-oil interface
E.3 Capsules and droplets preparation
E.4 Fluorescent capsules preparation
E.5 Interfacial tension measurement
E.6 Interfacial rheology measurement
E.7 Fluorescent capsule Gs > 0.1 N/m during rupture
F Wrinkling instability of CHT/PFacidYN capsules
F.1 Estimation of wrinkles arc length
F.2 Estimation of wavelength w
Bibliography 167

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