Experiments in a parallel band apparatus and a transparent concentric cylinder device allow the observation of bubble deformation (shape and orientation) and breakup as a function of the viscosity ratio λ and the Capillary number Ca. For viscosity ratios between 3.1×10−7 and 6.7×10−8, critical Capillary numbers Ca c for bubble breakup between 29 and 45 are found. It is furthermore shown that in the given parameter space no clear distinction between tip breakup and fracture can be made for bubble

Dressler, Marco

Fischer, Peter

Müller-Fischer, Nadina

Tobler, Philip

Windhab, Erich

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Single bubble deformation and breakup in simple shear flow

ERRATUMSingle bubble deformation and breakup in simple shear flowNadina Mu¨ller-Fischer Æ Philip Tobler ÆMarco Dressler Æ Peter Fischer Æ Erich J. WindhabPublished online: 4 August 2009 Springer-Verlag 2009Erratum to: Exp Fluids (2008) 45:917–926DOI 10.1007/s00348-008-0509-1Unfortunately, a published article contains error in thebubble dimension data. The modified analysis for the errorwas given below.In the publication ‘Single bubble deformation andbreakup in simple shear flow’ (2008) we report on thebubble deformation and bubble breakup in simple shearflow. The obtained results were compared to the previousfindings by Canedo et al. (1993) and Rust and Manga(2002) (Figure 6 of Mu¨ller-Fischer et al. 2008). Thedeviations of the deformation parameters D and L/xBbetween our results and those by Canedo et al. and Rustand Manga were explained by ‘higher curvature effects dueto confinement and bound flow conditions, limitation inimage analysis, the influence of surfactants, and limitedvalidity of the used models’. Revisiting the original datafiles, however, leads to the conclusion that we used for thecalculation of the bubble deformation the diameter of thebubble and not the bubble radius. As a consequence, alldeformation data are corrupted by the factor of two.Equations 5 and 10 in (2008) have to be rewritten as:Laﬃ 3:45  Ca0:5 ð1ÞLa¼ 3:1  Ca0:43 ð2Þwith a as bubble radius (instead of xB as bubble diameter).Using the correct bubble dimensions Figure 6 of Mu¨ller-Fischer et al. (2008) can be redrawn as shown in Fig. 1showing the deformation parameter parameter L/a as afunction of the Capillary number Ca.Both models by Hinch and Acrivos (1980) (Eq. 1) andCanedo et al. (1993) (Eq. 2) are used to describe themeasured data. The model of Hinch and Acrivos is fittingthe experimental data well for Ca B 20 but fail at largebubble deformations. The same result has been indicated inThe online version of the original article can be found underdoi:10.1007/s00348-008-0509-1.N. Mu¨ller-Fischer  P. Tobler  M. Dressler  P. Fischer (&) E. J. WindhabInstitute of Food Science & Nutrition, ETH Zurich,8092 Zurich, Switzerlande-mail: peter.fischer@ilw.agrl.ethz.chN. Mu¨ller-FischerBu¨hler AG, 9240 Uzwil, Switzerlande-mail: nadina.mueller-fischer@buhlergroup.com1.010.0 6.393 10 1.878 10 1.292 10Hinch and Acrivos Canedo et al.-7-7-7L/a   [-] L /a  = 3.45·CaL /a  = 3.1·Ca100.00 5 10 15 20 25 30 35 40Ca [-]Fig. 1 Deformation parameter L/a as a function of the Capillarynumber Ca for bubbles in simple shear. Symbols represent measuredvalues, the solid line represents the model prediction by Hinch andAcrivos (1980), the dashed line the model for Canedo et al. (1993)123Exp Fluids (2009) 47:549–550DOI 10.1007/s00348-009-0722-6Rust and Manga (2002). On the other hand, i.e., aboveCa C 25, Eq. 2 by Canedo et al. (1993) can match theexperiment results well. The validity of both models in thedifferent Ca number regime is related to the assumptionsmade. Hinch and Acrivos (1980) take only circular bubblecross-section into account, which is not correct for largebubble deformations as shown by Canedo et al. (1993). Thelatter authors assume an ellipsoidal cross-section, which fitthe high deformation regime of our bubble deformationexperiments well. In conclusion, Eq. 1 can be used todescribe the bubble deformation for Capillary numberssmaller than 20 and Eq. 2 can be used when the Capillarynumbers are larger than 25 (k  1 and Re  1).Acknowledgments The authors would like to thank Malin Liu,Department of Chemical Engineering, Tsinghua University, Beijing100084, China for pointing out the mistake in the droplet dimensionanalysis.ReferencesCanedo E, Favelukis M, Tadmor Z, Talmon Y (1993) An experi-mental study of bubble deformation in viscous liquids in simpleshear flow. AIChE J 39:553Hinch E, Acrivos A (1980) Long slender drops in a simple shear flow.J Fluid Mech 98:305Mu¨ller-Fischer N, Tobler P, Dressler M, Fischer P, Windhab E (2008)Single bubble deformation and breakup in simple shear flow.Exp Fluids 45:917Rust A, Manga M (2002) Bubble shapes and orientation in low Resimple shear flow. J Colloid Interface Sci 249:476550 Exp Fluids (2009) 47:549–550123

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Single bubble deformation and breakup in simple shear flow

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