Stability of an unsupported multi-layer surfactant laden liquid curtain under gravity
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The industrial process of curtain coating has long been an important method in coating applications, by which a thin liquid curtain is formed to impinge upon a moving substrate, due to its highly lucrative advantage of being able to coat multiple layers simultaneously. We investigate the linear stability of an unsupported two-layer liquid curtain, which has insoluble surfactants in both liquids, which are widely used in industry to increase the stability of the curtain. We formulate the governing equations, simplified by making a thin film approximation, from which we obtain equations describing the steady-state profiles. We then examine the response of the curtain to small perturbations about this steady state to identify conditions under which the curtain is unstable, finding the addition of surfactants stabilizes the curtain. Our results are then compared to experimental data, showing a favourable trend and thereby extending the works of Brown (J Fluid Mech 10:297–305, 1960) and Dyson et al. (J Eng Math 64:237–250, 2009).
KeywordsCurtain coating Multi-layer Stability Surfactants
Mathematics Subject Classification76E17 76D45 76T99
D.H. would like to thank the EPSRC for their financial support, and KAUST for funding the experimental work conducted whilst D.H. was on a research visit. The authors would also like to thank the anonymous reviewers who have contributed in improving this paper.
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