Modeling foam drainage

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Table of contents

Introduction
Notations
I Foam drainage control by Marangoni stresses in a 2D-microchamber
1 Foam drainage
1.1 The Foam: a multiscale physical and physicochemical system
1.1.1 At the scale of a gas/liquid interface
Surface tension and the Young-Laplace law
Surfactants
From interface to film: the role of surfactants and disjoining pressure
1.1.2 At the scale of a film
Minimal surfaces
From film to bubble
1.1.3 At the scale of a bubble
Bubbles, films and Plateau borders
From bubble to foam
1.1.4 At the scale of a foam
Foam under gravity
Quantity of interface
1.2 Geometry of a 2D microfoam
1.3 Foam Ageing
Drainage
Coarsening
Coalescence
Our positioning/strategy regarding foam ageing
1.4 Foam drainage and Marangoni effect
1.4.1 Modelling the permeability of a porous medium
At the scale of the pore
At the scale of the porous medium: Darcy’s law
A special porous medium: the foam – Importance of surface mobility
1.4.2 Drainage equation
1.4.3 Marangoni effect: a pathway to control drainage ?
Definition & proof of concept: the tears of wine
Context
Our approach
2 Building the experimental setup
2.1 General framework – experimental setup
2.2 Foam generation
2.2.1 Manufacturing a Silicon Master
Mask design
Silicon Master
2.2.2 Manufacturing a Polydimethylsiloxane (PDMS) system
2.2.3 Generating bubbles in microfluidics
2.3 Materials & Methods
2.3.1 Gas/liquid phases & Stabilization
2.3.2 Dependence in temperature: @ /@T
2.4 Integrating heating resistors to a Hele-Shaw cell & temperature characterization .
2.4.1 Temperature control in microfluidics: context and applications
2.4.2 Manufacturing heating resistors
Gold layer
Chromium layer
2.4.3 Integration of heating resistors
2.4.4 Temperature characterisation
Materials & Observation
Temperature calibration
Reference image –
Power dissipated by the resistors –
Measuring a temperature gradient & dependence with electric power –
Advection Vs Diffusion : thermal Péclet number –
2.5 Thermocapillary tangential stress
3 (Micro)foam drainage control using a thermocapillary stress in a 2D Hele-Shaw cell
3.1 Motivations
3.2 Gravity Vs. Thermocapillarity: on the way to control drainage
3.2.1 Physical chemistry
3.2.2 Time evolution & liquid fraction measurement
Time evolution
Liquid fraction measurement
3.2.3 Gravity drainage
3.2.4 Thermocapillary drainage
3.2.5 Coupling gravity and thermocapillarity to control foam drainage
3.2.6 Mass conservation within the Hele-Shaw cell
3.2.7 The role of the capillary pressure
3.3 Conclusion of Chapter 3
4 Surface Rheology: an insight into solutocapillarity
4.1 General concepts
4.1.1 Interfacial viscoelasticity
4.1.2 Response of an interface to expansion or compression
4.1.3 Response to shear
4.2 Investigating the combined effect of thermocapillarity, solutocapillarity and surface shear viscosity
4.2.1 A brief state of the art
4.2.2 The solutocapillary effect
4.2.3 Physico-chemical characterization
Gas/liquid phases
Langmuir-Von Szyszkowski isotherm
Elastic behaviour evidence
4.2.4 Measurements and results
Mass conservation approach
Linearity between the reponse of the system and the temperature gradient .
Evolution of r with the DOH bulk concentration
Evolution of r with geometrical parameters (e and R): possible surfactants’
transport mechanisms
4.3 Conclusion of Chapter 4
II Development of a thermomechanical actuation system for Labs-onachip
5 State-of-the-art & device microfabrication
5.1 A brief history of droplet handling in microfluidics
5.1.1 State-of-the-art & our positioning
5.1.2 Thermomechanical effect
5.2 Device microfabrication & PDMS dilation characterisation
5.2.1 Device microfabrication
PDMS system
Manufacturing and integrating heating resistors
Experimental environment
5.2.2 PDMS dilation characterisation
5.3 Materials & Methods
5.3.1 Bancroft rule & Hydrophilic-lipophilic balance (HLB)
5.3.2 Water/oil phases & stabilisation
Stabilizing oil-in-water droplets
Stabilizing water-in-oil droplets
Experimental setup
5.4 COMSOL simulations: temperature control
Geometry, mesh and materials
Physics at play and boundary conditions
Temperature profiles
Conclusion
6 A versatile technology for droplet-based microfluidics: thermomechanical actuation
6.1 Propelling droplets without an external flow
Proof of concept in 1D-channels
2D counterpart
6.2 Directing droplets: stopping, sorting, rearranging
6.2.1 A thermomechanical valve
6.2.2 Sorting
6.2.3 Storage, release and sequence modification
6.3 Breaking up droplets: thermally-induced hydrodynamic pinching
6.3.1 Droplet breakup
6.3.2 Droplet production
6.4 Conclusion of Chapter 6
7 General Conclusion & Perspectives
7.1 Foam project
7.2 Thermomechanical actuation project
8 Value creation: publications and patents
8.1 Publications
8.2 Patents
12 Contents
A Liquid volume fraction measurement
Expressions of rA(z, ) and VA
Expressions of rB(z, ) and VB
Liquid volume fraction
B Why disregarding coarsening ?
Bibliography