Skip to main content
SpringerLink
Log in

Influence of surfactant upon air entrainment hysteresis in curtain coating

  • Research Article
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

The onset of air entrainment for curtain coating onto a pre-wetted substrate was studied experimentally in similar parameter regimes to commercial coating (Re = ρQ/μ = O(1), We = ρQ u c /σ = O(10), Ca = μU/σ = O(1)). Impingement speed and viscosity were previously shown to be critical parameters in correlating air entrainment data with three qualitatively different regimes of hydrodynamic assist identified (Marston et al. in Exp Fluids 42(3):483–488, 2007a). The interaction of the impinging curtain with the pre-existing film also led to a significant hysteretic effect throughout the flow rate-substrate speed parameter space. For the first time, results considering the influence of surfactants are presented in attempt to elucidate the relative importance of surface tension in this inertia-dominated system. The results show quantitative and qualitative differences to previous results with much more complex hysteretic behaviour which has only been reported previously for rough surfaces.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Abbreviations

g :

gravitational constant (ms−2)

h :

curtain height (cm)

Q :

curtain flow rate (cm2 s−1)

U :

substrate speed (ms−1)

u c :

curtain impingement speed (ms−1)

c :

film thickness (m)

P l :

pressure load (Nm−2)

t r :

curtain residence time (s)

w :

curtain width (μm)

μ:

viscosity (mPa s)

σ:

surface tension (m Nm−1)

ρ:

density (kg m−3)

max:

maximum

References

  • Blake TD, Clarke A, Ruschak KJ (1994) Hydrodynamic assist of dynamic wetting. AIChE J 40(2):229–242

    Article  Google Scholar 

  • Blake TD, Bracke M, Shikhmurzaev YD (1999) Experimental evidence of nonlocal hydrodynamic influence on the dynamic contact angle. Phys Fluids 11:1995–2007

    Article  MATH  Google Scholar 

  • Blake TD, Dobson RA, Ruschak KJ (2004) Wetting at high capillary numbers. J Colloid Interface Sci 279:198–205

    Article  Google Scholar 

  • Clarke A (2002) Coating on a rough surface. AIChE J 48:2149–2156

    Article  Google Scholar 

  • Clarke A, Stattersfield E (2006) Direct evidence supporting nonlocal hydrodynamic influence on the dynamic contact angle. Phys Fluids 18:048106

    Article  Google Scholar 

  • Cohu O, Benkreira H (1998) Air Entrainment in angled dip coating. Chem Eng Sci 53(3):533–540

    Article  Google Scholar 

  • Fainerman VB, Miller R (2004) Maximum bubble pressure tensiometry—an analysis of experimental constraints. Adv Colloid Interface Sci 108–109:287–301

    Article  Google Scholar 

  • Fainerman VB, Makievski AV, Miller R (1993) The measurement of dynamic surface tensions of highly viscous liquids by the maximum bubble pressure method. Colloids Surf A 75:229–235

    Article  Google Scholar 

  • Fainerman VB, Mys VD, Makievski AV, Miller R (2004) Correction for the aerodynamic resistance and viscosity in maximum bubble pressure tensiometry. Langmuir 20:1721–1723

    Article  Google Scholar 

  • Lin SP, Roberts G (1981) Waves in a viscous liquid curtain. J Fluid Mech 112:443-458

    Article  Google Scholar 

  • Marston JO (2008) PhD Thesis, The University of Birmingham

  • Marston JO, Simmons MJH, Decent SP, Kirk SP (2006a) Influence of the flow field in curtain coating onto a pre-wet substrate. Phys Fluids 18:112102

    Article  Google Scholar 

  • Marston JO, Decent SP, Simmons MJH (2006b) Hysteresis and non-uniqueness in the speed of onset of instability in curtain coating. J Fluid Mech 569:349–363

    Article  MATH  Google Scholar 

  • Marston JO, Simmons MJH, Decent SP (2007a) Influence of viscosity and impingement speed on intense hydrodynamic assist in curtain coating. Exp Fluids 42(3):483–488

    Article  Google Scholar 

  • Marston JO, Decent SP, Simmons MJH (2007b) Experimental evidence of non-unique solutions to a steady non-linear coating flow. IMA J Appl Math. doi:10.1093/imamat/hxm062

  • Meissner J, Kragel J, Frese C, Ruppert S, Fainerman VB, Makievski AV, Miller R (2004) Comparative studies of dynamic surface tensions of C12EO6 solutions measured by different maximum bubble pressure tensiometers. SOFW J 130:41–46

    Google Scholar 

  • Yamamura M, Suematsu S, Toshihisa K, Adachi K (1999) Experimental investigation of air entrainment in a vertical liquid jet flowing down onto a rotating roll. Chem Eng Sci 55:931–942

    Article  Google Scholar 

  • Yamamura M, Matsunaga A, Matawari Y, Adachi K, Kage H (2006) Particle-assisted dynamic wetting in a suspension liquid jet impinged onto a moving substrate at different flow rates. Chem Eng Sci 61(16):5421–5426

    Article  Google Scholar 

Download references

Author information

Author notes

  1. J. O. Marston

    Present address: A-STAR Institute of Chemical and Engineering Sciences, 1 Pesek Road, Jurong Island, Singapore, 627833, Singapore

Authors and Affiliations

  1. School of Chemical Engineering, University of Birmingham, Edgbaston, Birmingham, UK

    J. O. Marston, V. Hawkins & M. J. H. Simmons

  2. School of Mathematics, University of Birmingham, Edgbaston, Birmingham, UK

    S. P. Decent

Authors
  1. J. O. Marston
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. Hawkins
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. P. Decent
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. J. H. Simmons
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. O. Marston.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Marston, J.O., Hawkins, V., Decent, S.P. et al. Influence of surfactant upon air entrainment hysteresis in curtain coating. Exp Fluids 46, 549–558 (2009). https://doi.org/10.1007/s00348-008-0580-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00348-008-0580-7

Keywords

Search

Navigation