HIPE droplet geometry

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Table of contents

1. Introduction
2. Literature review
2.1 High Internal-Phase-Ratio Emulsions (HIPEs)
2.1.1 The earliest HIPEs
2.1.2 The internal structure of a HIPE
2.1.2.1 How is space filled?
2.1.2.2 HIPE droplet geometry
2.1.3 Linking the macroscopic properties of a HIPE with its microscopic structure
2.1.3.1. Flow behaviour
2.1.3.2. HIPE stability
Coalescence
Dilution
2.1.4 The physical chemistry of HIPEs
2.1.5 Practical uses of a HIPE
2.1.5.1 Controlling the droplet-size distribution
2.1.5.2 Emulsifying viscous oils
2.1.6. Making a HIPE: choosing a surfactant
2.1.6.1 Non-ionic surfactants
2.1.6.2 Ionic surfactants
2.1.7 Current applications
2.1.7.1 Safety fuel
2.1.7.2 Oil recovery
2.1.7.3 Emulsion templating
2.1.8 Future explorations
Filling space with scale invariance
2.2 Apollonian packing of spheres
2.2.1 A timeless problem
2.2.2 Present-day research
2.2.3 Fractals
3. Materials and methods for HIPEs
3.1 Preparing HIPEs
3.1.1 Tools required
3.1.2 Protocol
3.1.3 Reproducibility of the protocol
3.1.3.1 Chemical properties of oil
Incompatibility with alkanes
Compatibility with silicone oil
3.1.3.2 Physical properties of oil
Viscosity
3.2 Characterizing HIPEs
3.2.1 Rheology
3.2.1.1 Selecting a shearing geometry
Shape
Surface roughness
3.2.1.2 Protocol
3.2.2 Measuring droplet-size distribution by Light Scattering
3.2.2.1 Protocol
3.2.2.2 Interpreting the results
Number density or volume density?
Revealing a power-law behaviour
3.2.3 Small-Angle X-ray Scattering (SAXS)
3.2.3.1 Protocol
3.2.3.2 Data treatment
Background subtraction
Calculating the experimental structure factor
Spectra fitting
3.2.4 Numerical simulations
3.2.4.1 Osculatory Random Apollonian Packing
3.2.4.2 Calculating the Apollonian structure factor
3.2.4.3 Smoluchowski coalescence algorithm
Coalescence in a monodisperse population
Coalescence in a polydisperse population
Protocol
4. Results and Discussion
4.1 Macroscopic behaviour of a HIPE vs. its composition
4.1.1 Increasing gel-like character with increasing surfactant concentration
4.1.2 Rheology
4.1.3 Different droplet geometries corresponding to each regime
4.1.4 Size distribution of each type of HIPE
4.1.4.1 How to judge polydispersity in power-law distributions
4.1.4.2 Coalescence and fragmentation in HIPEs
Coalescence provokes polydispersity
Fragmentation causes power-law size distributions in all HIPEs
A novel approach: simultaneous fragmentation and coalescence in liquid HIPEs
4.1.5 Link between a HIPE’s microstructure and its rheological behaviour
4.1.5.1 Rheological properties of solid and hybrid HIPEs
4.1.5.2 Measure of surfactant film thickness by SAXS
4.1.5.3 The Farris effect
4.1.5.4 Newtonian flow behaviour in liquid HIPE
4.2 Evolution of liquid HIPEs
4.2.1 Evolution towards an Apollonian exponent
4.2.2 Persistence of the Apollonian exponent
4.2.3 Proof of Apollonian droplet packing through SAXS
4.2.4 Confirming Light Scattering observations by SAXS
4.2.4.1 Evolving towards RAP after 1 week
4.2.4.2 Increasing surface area with time
4.2.5 Existence of swollen micelles observed by SAXS
4.2.5.1 Two populations of swollen micelles
4.2.5.2 Making swollen micelles by the PIT method
4.3 Discussions on Apollonian HIPEs
4.3.1 Creation of smaller droplets in a HIPE
4.3.1.1 How are smaller droplets created during coalescence?
4.3.1.2 Why are smaller droplets created during coalescence in a liquid HIPE?
Evicted surfactants cannot be evacuated by the continuous phase
Evicted surfactant molecules are confined locally
Free energy is reduced by creating small droplets rather than maintaining flat films
4.3.1.3 Summary on the coalescence-fragmentation mechanism
4.3.2 How is an Apollonian HIPE so metastable?
4.3.2.1 Measure of coalescence rate
4.3.2.2 The consequence of coalescence-fragmentation
4.3.2.3 Thermodynamic considerations
Δ􀜵 in an Apollonian structure
􀟂􀜷 in an Apollonian structure
Elastic energy
Surface energy
5. Suggestions for applications of Apollonian HIPEs
5.1 Solid material with space-filling structure and ultra-low porosity
5.2 Photon or electron trap
5.3 Controlled release of drugs
5.3.1 Drug release from a spherical carrier by diffusion
5.3.2 Drug release by the dissolution of a solid sphere
6. Conclusion
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