Abstract
The influence of the yield stress of Carbopol® gel dispersions on the behaviour of quasi-static bubbles was investigated. Many fluids, from many different industrial fields, have yield stress behaviour. Most of them contain gas bubbles. To study bubble behaviour in such suspensions, a transparent model fluid (dispersion of Carbopol® in water) was used. The experimental device allowed to quasi-statically increase bubble internal pressure with small pressure step to reach a maximum target internal pressure and the pressure setpoint was inverted to return to the initial pressure. Hysterical behaviour of the bubbles was highlighted as they did not regain their initial shape because of yield stress. We show that the rheological behaviour is related to the internal pressure, bubble geometry and yield stress in quasi-static conditions. A modification of the Laplace law depending on the yield stress of the fluid and bubble sphericity was proposed and validated.
References
Ahonguio F, Jossic L, Magnin A (2014) Influence of surface properties on the flow of a yield stress fluid around spheres. J Non-Newton Fluid Mech 206:57–70. doi:10.1016/j.jnnfm.2014.03.002
Atapattu DD, Chhabra RP, Uhlherr PHT (1990) Wall effect for spheres falling at small Reynolds number in a viscoplastic medium. J Non-Newton Fluid Mech 38:31–42. doi:10.1016/0377-0257(90)85031-S
Beris AN, Tsamopoulos JA, Armstrong RC, Brown RA (1985) Creeping motion of a sphere through a Bingham plastic. J Fluid Mech 158:219–244. doi:10.1017/S0022112085002622
Bhavaraju SM, Mashelkar RA, Blanch HW (1978) Bubble motion and mass transfer in non-Newtonian fluids: part I. Single bubble in power law and Bingham fluids. AICHE J 24:1063–1070. doi:10.1002/aic.690240618
Boujlel J, Coussot P (2013) Measuring the surface tension of yield stress fluids. Soft Matter 9:5898–5908. doi:10.1039/c3sm50551k
Chadwick P (1963) Compression of a spherical shell of work-hardening material. Int J Mech Sci 5:165–182. doi:10.1016/0020-7403(63)90020-1
Clift R, Grace JR, Weber ME (2005) Bubbles, drops, and particles. Dover Publications, New York
Coussot P (2005) Rheometry of pastes, suspensions, and granular materials. In: Rheometry of pastes, suspensions, and granular materials. John Wiley & Sons, Inc., p 280
Coussot P (2014) Yield stress fluid flows: a review of experimental data. J Non-Newton Fluid Mech 211:31–49. doi:10.1016/j.jnnfm.2014.05.006
Coussot P, Tocquer L, Lanos C, Ovarlez G (2009) Macroscopic vs. local rheology of yield stress fluids. J Non-Newton Fluid Mech 158:85–90
Cyr M, Pouhet R (2015) The frost resistance of alkali-activated cement-based binders. In: Handbook of alkali-activated cements, Mortars and Concretes. Elsevier, pp 293–318
Dubash N, Frigaard I (2004) Conditions for static bubbles in viscoplastic fluids. Phys Fluids 16:4319–4330. doi:10.1063/1.1803391
Dubash N, Frigaard IA (2007) Propagation and stopping of air bubbles in Carbopol solutions. J Non-Newton Fluid Mech 142:123–134. doi:10.1016/j.jnnfm.2006.06.006
Gamer U (1988) The expansion of the elastic-plastic spherical shell with nonlinear hardening. Int J Mech Sci 30:415–426. doi:10.1016/0020-7403(88)90015-X
Gheissary G, van den Brule BHAA (1996) Unexpected phenomena observed in particle settling in non-Newtonian media. J Non-Newton Fluid Mech 67:1–18. doi:10.1016/S0377-0257(96)01436-X
Hariharaputhiran M, Subramanian RS, Campbell GA, Chhabra RP (1998) The settling of spheres in a viscoplastic fluid. J Non-Newton Fluid Mech 79:87–97. doi:10.1016/S0377-0257(98)00084-6
Hashemnejad SM, Kundu S (2015) Nonlinear elasticity and cavitation of a triblock copolymer gel. Soft Matter 11:4315–4325. doi:10.1039/C5SM00330J
Jørgensen L, Merrer ML, Delanoë-Ayari H, Barentin C (2015) Yield stress and elasticity influence on surface tension measurements. Soft Matter 11:5111–5121. doi:10.1039/c5sm00569h
Kundu S, Crosby AJ (2009) Cavitation and fracture behavior of polyacrylamide hydrogels. Soft Matter 5:3963. doi:10.1039/b909237d
Landeau P, Kosevich L (1986) Theory of elasticity, third edition: volume 7. Butterworth-Heinemann, Oxford
Łaźniewska-Piekarczyk B (2013) The frost resistance versus air voids parameters of high performance self compacting concrete modified by non-air-entrained admixtures. Constr Build Mater 48:1209–1220. doi:10.1016/j.conbuildmat.2013.07.080
Megahed MM (1991) Elastic-plastic behaviour of spherical shells with non-linear hardening properties. Int J Solids Struct 27:1499–1514. doi:10.1016/0020-7683(91)90074-P
Mougin N, Magnin A, Piau J-M (2012) The significant influence of internal stresses on the dynamics of bubbles in a yield stress fluid. J Non-Newton Fluid Mech 171-172:42–55. doi:10.1016/j.jnnfm.2012.01.003
Neville AM (2011) Properties of concrete, Edition: 5. Prentice Hall, Harlow, England; New York
Ovarlez G, Cohen-Addad S, Krishan K et al (2013) On the existence of a simple yield stress fluid behavior. J Non-Newton Fluid Mech 193:68–79. doi:10.1016/j.jnnfm.2012.06.009
Pierre A, Lanos C, Estellé P (2013) Extension of spread-slump formulae for yield stress evaluation. Appl Rheol 23:14. doi:10.3933/ApplRheol-23-63849
Pierre A, Lanos C, Estellé P, Perrot A (2015) Rheological properties of calcium sulfate suspensions. Cem Concr Res 76:70–81. doi:10.1016/j.cemconres.2015.05.017
Rasband W (2015) Freeware ImageJ
Samson G, Phelipot-Mardelé A, Lanos C (2016) Thermal and mechanical properties of gypsum-cement foam concrete: effects of surfactant. J Eur J Environ Civ Eng. doi: 10.1080/19648189.2016.1177601
Sikorski D, Tabuteau H, de Bruyn JR (2009) Motion and shape of bubbles rising through a yield-stress fluid. J Non-Newton Fluid Mech 159:10–16. doi:10.1016/j.jnnfm.2008.11.011
Snabre P, Magnifotcham F (1998) I. Formation and rise of a bubble stream in a viscous liquid. Eur Phys J B-Condens Matter Complex Syst 4:369–377. doi:10.1007/s100510050392
Terasaka K, Tsuge H (2001) Bubble formation at a nozzle submerged in viscous liquids having yield stress. Chem Eng Sci 56:3237–3245. doi:10.1016/S0009-2509(01)00002-1
Tokpavi DL, Jay P, Magnin A, Jossic L (2009) Experimental study of the very slow flow of a yield stress fluid around a circular cylinder. J Non-Newton Fluid Mech 164:35–44. doi:10.1016/j.jnnfm.2009.08.002
Vance K, Sant G, Neithalath N (2015) The rheology of cementitious suspensions: a closer look at experimental parameters and property determination using common rheological models. Cem Concr Compos 59:38–48. doi:10.1016/j.cemconcomp.2015.03.001
You LH, Zhang JJ, You XY (2005) Elastic analysis of internally pressurized thick-walled spherical pressure vessels of functionally graded materials. Int J Press Vessel Pip 82:347–354. doi:10.1016/j.ijpvp.2004.11.001
Zhang Z, Provis JL, Reid A, Wang H (2014) Geopolymer foam concrete: an emerging material for sustainable construction. Constr Build Mater 56:113–127. doi:10.1016/j.conbuildmat.2014.01.081
Zhu J, Li T, Cai S, Suo Z (2011) Snap-through expansion of a gas bubble in an elastomer. J Adhes 87:466–481. doi:10.1080/00218464.2011.575332
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Rights and permissions
About this article
Cite this article
Samson, G., Phelipot-Mardelé, A., Lanos, C. et al. Quasi-static bubble in a yield stress fluid: elasto-plastic model. Rheol Acta 56, 431–443 (2017). https://doi.org/10.1007/s00397-017-1007-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00397-017-1007-2