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D. Badali, M. Chugunova, D.E. Pelinovsky, and S. Pollack

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Regularized shock solutions in coating flows with small surface tension

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Physics of Fluids 23, 093103-8 (2011)

**Abstract:**

We study the dynamics of thin liquid films on the surface of a rotating horizontal cylinder in the
presence of gravity in the small surface tension limit. Using dynamical system methods, we show
that the continuum of shock solutions increasing across the jump point persists in the small surface
tension limit, whereas the continuum of shock solutions decreasing across the jump point
terminates in the limit. Using delicate numerical computations, we show that the number of steady
states with equal mass increases as the surface tension parameter goes to zero. This corresponds to
an increase in the number of loops on the mass-flux bifurcation diagram. If n is the number of loops
in the mass-flux diagram with 2n+1 solution branches, we show that n+1 solution branches are
stable with respect to small perturbations in the time evolution of the liquid film

**Keywords**:

steady-state coating flows, bifurcation and stability, mass-flux diagram, singular perturbation theory