Dispensing of rheologically complex fluids: The map of misery

Rheological effects may complicate the dispensing of complex fluids, when compared to their Newtonian counterparts. In this work, fluids with tailored rheological properties have been studied using high-speed video-microscopy. The level of viscosity, the degree of shear thinning, and the elasticity have been varied independently. At low-flow rates, droplets are formed that pinch off. The drop volumes, breakup mechanisms, and times have been identified. At higher-flow rates, a continuous jet is observed, with the transition depending on the rheology of the dispensed fluid. The relevant nondimensional groups are the Ohnesorge, Deborah, and elasto-capillary number, for when viscosity, inertia, or elastic forces dominate flow. In each of these cases, the transition between dripping and jetting dispensing occurs, controlled by a critical Weber, capillary, and Weissenberg number, respectively. This set of six nondimensional groups can be used to construct an operating space and map out areas of potential problems. © 2011 American Institute of Chemical Engineers AIChE J, 58: 3242–3255, 2012

[1]  H. Stone,et al.  CAPILLARY BREAKUP OF A VISCOUS THREAD SURROUNDED BY ANOTHER VISCOUS FLUID , 1998 .

[2]  D. Papageorgiou.  ON THE BREAKUP OF VISCOUS LIQUID THREADS , 1995 .

[3]  Gareth H. McKinley,et al.  Elasto-capillary thinning and breakup of model elastic liquids , 2001 .

[4]  Oliver G. Harlen,et al.  Viscoelasticity in inkjet printing , 2010 .

[5]  S. Middleman,et al.  Newtonian jet stability , 1966 .

[6]  W. Kulicke,et al.  Influence of the Molar Mass Distribution on the Elongational Behaviour of Polymer Solutions in Capillary Breakup , 2005 .

[7]  Christophe Clanet,et al.  Transition from dripping to jetting , 1999, Journal of Fluid Mechanics.

[8]  Diane M. Henderson,et al.  On the pinch-off of a pendant drop of viscous fluid , 1997 .

[9]  L. G. Leal,et al.  Extensional Rheometry of Entangled Solutions , 2002 .

[10]  T. Kowalewski,et al.  On the separation of droplets from a liquid jet , 1996 .

[11]  G. McKinley,et al.  How to extract the Newtonian viscosity from capillary breakup measurements in a filament rheometer , 2000 .

[12]  Xiongbiao Chen,et al.  Modeling and control of fluid dispensing processes: a state-of-the-art review , 2009 .

[13]  Alvin U. Chen,et al.  Computational and experimental analysis of pinch-off and scaling. , 2002, Physical review letters.

[14]  H. Buggisch,et al.  Stability of initially slow viscous jets driven by gravity , 2005, Journal of Fluid Mechanics.

[15]  Ichiro Matsubara,et al.  Monitoring of dispensed fluid with the quartz crystal microbalance (QCM) for the better control of inkjet or dispenser machine( Global Innovation in Advanced Ceramics) , 2008 .

[16]  M. Brenner,et al.  Pinching threads, singularities and the number 0.0304... , 1996 .

[17]  B. Derby.  Inkjet Printing of Functional and Structural Materials: Fluid Property Requirements, Feature Stability, and Resolution , 2010 .

[18]  Gareth H. McKinley,et al.  Formation of beads-on-a-string structures during break-up of viscoelastic filaments , 2010 .

[19]  G. McKinley,et al.  Nonlinear Shear and Extensional Flow Dynamics of Wormlike Surfactant Solutions , 2006 .

[20]  C. Pozrikidis.  Capillary instability and breakup of a viscous thread , 1999 .

[21]  Z. Dogic,et al.  Development of model colloidal liquid crystals and the kinetics of the isotropic–smectic transition , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[22]  O. Basaran,et al.  Dynamics of formation and dripping of drops of deformation-rate-thinning and -thickening liquids from capillary tubes , 2006 .

[23]  John R. Lister,et al.  SELF-SIMILAR CAPILLARY PINCHOFF OF AN INVISCID FLUID , 1997 .

[24]  E. Hinch,et al.  Effect of a spectrum of relaxation times on the capillary thinning of a filament of elastic liquid , 1997 .

[25]  G. McKinley,et al.  Extensional stress growth and stress relaxation in entangled polymer solutions , 2003 .

[26]  D. Bousfield,et al.  Nonlinear analysis of the surface tension driven breakup of viscoelastic filaments , 1986 .

[27]  O. Basaran,et al.  Analysis of the drop weight method , 2005 .

[28]  N. Willenbacher,et al.  Capillary breakup extensional rheometry (CaBER) on semi-dilute and concentrated polyethyleneoxide (PEO) solutions , 2010 .

[29]  Osman A. Basaran,et al.  Small‐scale free surface flows with breakup: Drop formation and emerging applications , 2002 .

[30]  Patrick K. Notz,et al.  Satellite drops: Unexpected dynamics and change of scaling during pinch-off , 2001 .

[31]  O. Basaran,et al.  Local dynamics during pinch-off of liquid threads of power law fluids: Scaling analysis and self-similarity , 2006 .

[32]  E. Villermaux,et al.  Physics of liquid jets , 2008 .

[33]  Shi,et al.  Iterated instabilities during droplet fission. , 1994, Physical review letters.

[34]  William D. Harkins,et al.  THE DETERMINATION OF SURFACE TENSION (FREE SURFACE ENERGY), AND THE WEIGHT OF FALLING DROPS: THE SURFACE TENSION OF WATER AND BENZENE BY THE CAPILLARY HEIGHT METHOD. , 1919 .

[35]  S. Middleman,et al.  Viscoelastic jet stability , 1969 .

[36]  L. Campo-Deaño,et al.  The slow retraction method (SRM) for the determination of ultra-short relaxation times in capillary , 2010 .

[37]  J. Rothstein,et al.  The effect of step-stretch parameters on capillary breakup extensional rheology (CaBER) measurements , 2009 .

[38]  Diane M. Henderson,et al.  The motion of a falling liquid filament , 2000 .

[39]  L. Walker,et al.  Surface tension driven jet break up of strain-hardening polymer solutions , 2001 .

[40]  G. McKinley,et al.  ‘Gobbling drops’: the jetting–dripping transition in flows of polymer solutions , 2009, Journal of Fluid Mechanics.

[41]  C. Macosko,et al.  How dilute are dilute solutions in extensional flows , 2006 .

[42]  D. V. Boger,et al.  The effects of polymer concentration and molecular weight on the breakup of laminar capillary jets , 1998 .

[43]  A. Rothert,et al.  Transition from symmetric to asymmetric scaling function before drop pinch-off. , 2001, Physical review letters.

[44]  Daniel R. Lester,et al.  Drop formation dynamics of constant low-viscosity, elastic fluids , 2002 .

[45]  L. Walker,et al.  Effect of fluid relaxation time of dilute polymer solutions on jet breakup due to a forced disturbance , 2002 .

[46]  J. Eggers,et al.  Blistering pattern and formation of nanofibers in capillary thinning of polymer solutions. , 2008, Physical review letters.

[47]  Xiongbiao Chen,et al.  Evaluation of fluid dispensing systems using axiomatic design principles , 2007 .

[48]  Hariprasad J. Subramani,et al.  Dripping-jetting transitions in a dripping faucet. , 2004, Physical review letters.

[49]  R. Shinnar,et al.  Breakup of a laminar capillary jet of a viscoelastic fluid , 1969, Journal of Fluid Mechanics.

[50]  O. Basaran,et al.  Scaling in pinch-off of generalized Newtonian fluids , 2003 .

[51]  J. Eggers,et al.  Universal pinching of 3D axisymmetric free-surface flow. , 1993, Physical review letters.