La dynamique de disparition est aisément visible sur un diagramme spatio-temporel (cf fig. 4.2)Des expériences préliminaires montrent que le temps de disparition peut varier d'un facteur 10 d'une expériencè a l'autre. Nous allonsétudierallonsétudier l'influence de quelques paramètres afin d'indiquer des pistes de réflexion pour la compréhension du comportement d'une goutte d'eau sur un gel d' agar. Si deséchellesdeséchelles de temps différentes semblent exister, le processus de disparition présente des caractéristiques communes dans tous les cas de figure : lors du dépôt une déformation est visible de part et d'autre de la ligne de contact (cf fig. 4.1 et fig. 4.2) ; et avec le temps la goutte s'affaisse, puis lorsque la ligne triple atteint l'angle limite de rétraction, elle recule jusqu'` a disparitioncompì ete du liquide. Si le phénomène physiquè a l'origine de la disparition de la goutte est la diffusion, il n'est pasévidentpasévident, expérimentalement de savoir s'il s'agit de diffusion dans le gel ou bien de diffusion du liquide dans l'air ambiant, c'est-` a-dire d'´ evaporation. Les deux phénomènes sont envisageables : la situation d'une goutte de liquide en mouillage partiel sur un substrat poreux est en partie analoguè a celle d'une goutte d'encre sur du papier qui a ´ eté largementétudiéelargementétudiée pour les besoins de l'industrie de l'´ editionimprégnation se fait par capillarité : il s'agit d'unécoulementunécoulement dans un poreux dont l'efficacité dépend ,
Dans le cas de la diffusion de solvant dans le papier [17], une variation de la taille du pore d'un facteur 2 ou 4 modifie significativement la vitesse de résorption des gouttes dans le substrat Pour les gels d'agar, dans la gamme de concentration en agarose testée, il ne semble pas y avoir de manifestation distincte d'une influence sur le temps de disparition d'une goutte d'eau ou d'une goutte de solution eau/glycerol. Le temps moyen mesuré pour une goutte de 1 µL d'eau est relativement constant d'une concentrationàconcentrationà l'autre (cf fig. 4.21) Comme précédemment pour 0,5 %, 1 % et 2 %, les temps de disparition de gouttes de solution sont légèrement plusélevésplusélevés mais très proches de ceux d'une goutte d'eau de même volume ,
Unstable spreading of aqueous anionic surfactant solutions on liquid films. part2. sparingly soluble surfactant, Langmuir, vol.19, pp.703-708, 2003. ,
Dewetting behavior of aqueous cationic surfactant solutions on liquid films, Langmuir, vol.20, pp.7575-7582, 2004. ,
Surface characterization of poly(hydroxyethyl methacrylate) and related polymers. I. Contact angle methods in water, Journal of Polymer Science: Polymer Symposia, vol.12, issue.2, p.313, 1979. ,
DOI : 10.1002/polc.5070660130
Water and food quality, chapter 7 : Gel structure and food biopolymers, 1989. ,
Adaptive self-organization during growth of bacterial colonies, Physica A: Statistical Mechanics and its Applications, vol.187, issue.3-4, pp.378-424, 1992. ,
DOI : 10.1016/0378-4371(92)90002-8
Generic modelling of cooperative growth patterns in bacterial colonies, Nature, vol.368, issue.6466, pp.46-49, 1994. ,
DOI : 10.1038/368046a0
Evaporation-induced flow near a contact line: Consequences on coating and contact angle, EPL (Europhysics Letters), vol.83, issue.1, p.14003, 2008. ,
DOI : 10.1209/0295-5075/83/14003
URL : https://hal.archives-ouvertes.fr/hal-00292117
THE ZONATION PHENOMENON AND STRUCTURE OF THE SWARM COLONY IN PROTEUS MIRABILIS, Journal of Medical Microbiology, vol.6, issue.4, pp.429-433, 1973. ,
DOI : 10.1099/00222615-6-4-429
A calculation of the viscosity and the sedimentation constant for solutions of large chain molecules taking into account the hampered flow of the solvent through these molecules, Physica, vol.13, issue.8, p.447, 1947. ,
DOI : 10.1016/0031-8914(47)90030-X
Liquides : Solutions, dispersions, ´ emulsions, gels, 2003. ,
URL : https://hal.archives-ouvertes.fr/hal-00530545
Contact-line instabilities in liquids spreading on solid substrates, Physica A: Statistical Mechanics and its Applications, vol.329, issue.1-2, pp.7-13, 2003. ,
DOI : 10.1016/S0378-4371(03)00612-5
Freinage viscoélastique de l'´ etalement d'une goutte The concentration dependance of biopolymer gel modulus, C.R. Acad. Sci. Paris Brit. Polym. J, vol.317, issue.17, pp.1153-1158164, 1985. ,
Spreading and Imbibition of Liquid Droplets on Porous Surfaces, Langmuir, vol.18, issue.8, pp.2980-2984, 2002. ,
DOI : 10.1021/la0117810
Advancing contact lines on chemically patterned surfaces, Journal of Colloid and Interface Science, vol.269, issue.1, p.171, 2004. ,
DOI : 10.1016/j.jcis.2003.08.008
Instabilities in Droplets Spreading on Gels, Physical Review Letters, vol.99, issue.12, p.99, 2007. ,
DOI : 10.1103/PhysRevLett.99.124501
Spreading and imbibition of viscous liquid on a porous base, Physics of Fluids, vol.11, issue.1, pp.48-57, 1999. ,
DOI : 10.1063/1.869901
Dynamics of wetting, Current Opinion in Colloid & Interface Science, vol.6, issue.1, p.49, 2001. ,
DOI : 10.1016/S1359-0294(00)00087-X
Wetting: statics and dynamics, Reviews of Modern Physics, vol.57, issue.3, p.827, 1985. ,
DOI : 10.1103/RevModPhys.57.827
Gouttes, bulles, perles et ondes, pp.42-47, 2005. ,
In situ localisation and quantification of surfactins in a Bacillus subtilis swarming community by imaging mass spectrometry, PROTEOMICS, vol.32, issue.18, pp.3682-3691, 2008. ,
DOI : 10.1002/pmic.200701025
URL : https://hal.archives-ouvertes.fr/hal-00326299
Capillary flow as the cause of ring stains from dried liquid drops, Nature, issue.389, 1997. ,
On the Spreading of Liquids on Solid Surfaces: Static and Dynamic Contact Lines, Annual Review of Fluid Mechanics, vol.11, issue.1, pp.371-400, 1979. ,
DOI : 10.1146/annurev.fl.11.010179.002103
Prevention of neonatal respiratory distress syndrome by tracheal instillation of surfactant; a randomized clinical trial, Journal of Critical Care, vol.2, issue.1, 1985. ,
DOI : 10.1016/0883-9441(87)90128-6
Contact Angles and Hysteresis on Soft Surfaces, Journal of Colloid and Interface Science, vol.184, issue.1, 1996. ,
DOI : 10.1006/jcis.1996.0611
Origins of the Complex Motion of Advancing Surfactant Solutions, Langmuir, vol.11, issue.1, p.87, 1995. ,
DOI : 10.1021/la00001a018
The dynamics of a localized surfactant on a thin film, J. Fluid Mech, vol.213, pp.127-148, 1989. ,
Synthesis of hydrogels with extremely low surface friction, Journal of the American Chemical Society, vol.123, issue.23, pp.5582-5583, 2001. ,
Gel friction : A model based on surface repulsion and adsorption, The Journal of Chemical Physics, vol.109, issue.18, pp.8062-8068, 1998. ,
Spatiotemporal analysis of flagellin gene expression defines a specific subpopulation of cells at the onset of swarming in Bacillus subtilis that spearheads the tips of elongating dendrites ,
Identification of genes required for different stages of dendritic swarming in Bacillus subtilis, with a novel role for phrC. Microbiology, pp.398-412, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00594195
Water and Food quality, pp.251-273, 1989. ,
Dimorphic transition in Escherichia coli and Salmonella typhimurium: surface-induced differentiation into hyperflagellate swarmer cells., Proc Natl Acad Sci U S A, pp.8631-8636, 1991. ,
DOI : 10.1073/pnas.91.18.8631
spreading oil on sea, Annual Review of Fluid Mechanics, pp.341-368, 1972. ,
Measurement of Rates of Spread of Solutions of Surface Active Agents, Analytical Chemistry, vol.20, issue.11, p.1039, 1984. ,
DOI : 10.1021/ac60023a012
A biochemical oscillator explains several aspects of Myxococcus xanthus behavior during development, Proc Natl Acad Sci U S A, number 101, pp.15760-15765, 2004. ,
DOI : 10.1073/pnas.0407111101
Self???similar, surfactant???driven flows, Physics of Fluids, vol.6, issue.3, p.1084, 1994. ,
DOI : 10.1063/1.868280
Une analyse cytologique, génétique et physique du processus de " swarming " chez Bacilus subtilis, 2005. ,
Comparative Analysis of the Development of Swarming Communities of Bacillus subtilis 168 and a Natural Wild Type: Critical Effects of Surfactin and the Composition of the Medium, Journal of Bacteriology, vol.187, issue.1, p.1839, 2004. ,
DOI : 10.1128/JB.187.1.65-76.2005
Branched swarming patterns on a synthetic medium formed by wild-type Bacillus subtilis strain 3610: detection of different cellular morphologies and constellations of cells as the complex architecture develops, Proc Natl Acad Sci U S A, pp.1839-1849, 1979. ,
DOI : 10.1099/mic.0.27061-0
Kinetics of fluid spreading on viscoelastic substrates, Journal of Polymer Science Part B: Polymer Physics, vol.73, issue.5, p.562, 2005. ,
DOI : 10.1002/polb.20362
Totally Synthetic Polymer Gels Responding to External Glucose Concentration:?? Their Preparation and Application to On???Off Regulation of Insulin Release, Journal of the American Chemical Society, vol.120, issue.48, pp.12694-12695, 1998. ,
DOI : 10.1021/ja982975d
Modeling Spatio-Temporal Patterns Generated byBacillus subtilis, Journal of Theoretical Biology, vol.188, issue.2, pp.177-185, 1997. ,
DOI : 10.1006/jtbi.1997.0462
Capillary sorption in fibrous assemblies, Journal of Colloid and Interface Science, vol.83, issue.1, p.265, 1981. ,
DOI : 10.1016/0021-9797(81)90031-X
Swarming of Pseudomonas aeruginosa Is Dependent on Cell-to-Cell Signaling and Requires Flagella and Pili, Journal of Bacteriology, vol.182, issue.21, pp.5990-5996, 2000. ,
DOI : 10.1128/JB.182.21.5990-5996.2000
Hydrodynamics of bacterial colonies: A model, Physical Review E, vol.67, issue.3, 2003. ,
DOI : 10.1103/PhysRevE.67.031906
Equilibrium and spreading of liquids on solid surfaces, Advances in Colloid and Interface Science, vol.19, issue.1-2, p.75, 1983. ,
DOI : 10.1016/0001-8686(83)80004-9
THE SPREADING OF AQUEOUS SURFACTANT SOLUTIONS ON GLASS, Chemical Engineering Communications, vol.1, issue.13, p.133, 1981. ,
DOI : 10.1080/00986448108910901
The radial capillary, Journal of Colloid and Interface Science, vol.124, issue.1, p.301, 1988. ,
DOI : 10.1016/0021-9797(88)90351-7
Spreading of a surfactant monolayer on a thin liquid film : Onset and evolution of digitated structures, Chaos, vol.9, issue.1, pp.141-153, 1999. ,
Population morphogenesis by cooperative bacteria, Forma, vol.16, pp.307-326, 2001. ,
Contact Angle Hysteresis: a First Analysis of the Noise of the Creeping Motion of the Contact Line, Europhysics Letters (EPL), vol.11, issue.2, p.163, 1990. ,
DOI : 10.1209/0295-5075/11/2/012
Patterns of reporter gene expression in the phase diagram of Bacillus subtilis colony forms., Journal of Bacteriology, vol.178, issue.7, pp.1980-1989, 1996. ,
DOI : 10.1128/jb.178.7.1980-1989.1996
Prophylactic treatment of very premature infants with human surfactant, N. engl. j. med, issue.13, pp.315785-790, 1986. ,
CONTACT ANGLE RELATIONSHIPS ON SILICA AQUAGEL SURFACES, The Journal of Physical Chemistry, vol.66, issue.10, p.1790, 1962. ,
DOI : 10.1021/j100816a005
Reaction???diffusion modelling of bacterial colony patterns, Physica A: Statistical Mechanics and its Applications, vol.282, issue.1-2, pp.283-303, 2000. ,
DOI : 10.1016/S0378-4371(00)00085-6
Microstructure et propri??t??s hygro-m??caniques du gel d'agar, Journal de Physique III, vol.5, issue.7, pp.985-998, 1995. ,
DOI : 10.1051/jp3:1995172
Structure of the core and central channel of bacterial flagella, Nature, vol.342, issue.6250, pp.648-54, 1989. ,
DOI : 10.1038/342648a0
Wetting on heterogeneous surfaces: Experiments in an imperfect Hele-Shaw cell, Physical Review E, vol.51, issue.2, p.1291, 1995. ,
DOI : 10.1103/PhysRevE.51.1291
Contribution a l'´ etude des proprétés tensioactives des lipopeptides de Bacilus Subtilis, 1996. ,
Contact angle hysteresis on heterogeneous surfaces, Langmuir, vol.1, issue.2, p.219, 1985. ,
DOI : 10.1021/la00062a007
Dynamics of interface of gels undergoing volume phase transition, Journal de Physique II, vol.1, issue.9, p.1053, 1991. ,
DOI : 10.1051/jp2:1991200
URL : https://hal.archives-ouvertes.fr/jpa-00247574
Role of Mechanical Pressure in Permeation of a Solvent through Gels, Europhysics Letters (EPL), vol.27, issue.6, pp.445-450, 1994. ,
DOI : 10.1209/0295-5075/27/6/006
The influence of solid micro-deformation on contact angle equilibrium, Journal of Physics D: Applied Physics, vol.20, issue.7, p.945, 1987. ,
DOI : 10.1088/0022-3727/20/7/018
The spreading dynamics of a liquid drop on a viscoelastic solid, Journal of Physics D: Applied Physics, vol.21, issue.6, pp.981-985, 1998. ,
DOI : 10.1088/0022-3727/21/6/019
The two motility systems of Myxococcus xanthus show different selective advantages on various surfaces., Proc Natl Acad Sci U S A, pp.3378-82, 1993. ,
DOI : 10.1073/pnas.90.8.3378
Spreading of liquids on gel surfaces, The Journal of Chemical Physics, vol.113, issue.18, p.253, 2000. ,
DOI : 10.1063/1.1310664
The spreading of silicone oil drops on horizontal surfaces, Journal of Physics D: Applied Physics, vol.12, issue.9, p.1473, 1979. ,
DOI : 10.1088/0022-3727/12/9/009
Theory of elasticity, chapter 4, 1970. ,
Fingering instability in thin wetting films, Physical Review Letters, vol.62, issue.13, p.1496 ,
DOI : 10.1103/PhysRevLett.62.1496
Dynamics of surfactantdriven fracture of particle rafts Experimental investigation on the formation of dense-branchingmorphology-like colonies in bacteria, Phys. Rev. Lett. Journal of the Physical Society of Japan, vol.9683, issue.10, pp.178301-673630, 1198. ,
Gene expression patterns during swarming in Salmonella typhimurium: genes specific to surface growth and putative new motility and pathogenicity genes, Molecular Microbiology, vol.3, issue.1, pp.169-87, 2004. ,
DOI : 10.1111/j.1365-2958.2003.03977.x
Fingering phenomena associated with insoluble surfactant spreading on thin liquid films, Journal of Fluid Mechanics, vol.510, pp.169-200, 2004. ,
DOI : 10.1017/S0022112004009437
Rheological properties of agarose gels with different molecular weights, Rheologica Acta, vol.70, issue.6, pp.580-587, 1983. ,
DOI : 10.1007/BF01351404
Biomimetic Gel Exhibiting Self-Beating Motion in ATP Solution, Biomacromolecules, vol.6, issue.6, pp.2923-2926, 2005. ,
DOI : 10.1021/bm050398x
Surface tension and elasticity of gel studied with laser-induced surface-deformation spectroscopy, Physical Review E, vol.78, issue.4, 2008. ,
DOI : 10.1103/PhysRevE.78.041405
Contact angles on deformable solids, Journal of colloid and interface science, vol.110, issue.1, 1986. ,