2 results
Liquid transfer from single cavities to rotating rolls
- Diego M. Campana, Marcio S. Carvalho
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- Journal:
- Journal of Fluid Mechanics / Volume 747 / 25 May 2014
- Published online by Cambridge University Press:
- 23 April 2014, pp. 545-571
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In this work we study computationally the dynamics of a liquid bridge formed between a two-dimensional trapezoidal cavity, which represents an axisymmetric cell or a plane groove engraved in a roll, and a moving plate. The flow is a model of the liquid transfer process in gravure printing systems. The considered plate kinematics represents the actual motion of a roll-to-roll system, which includes extension, shear and rotation relative to the cavity. The fluid flow is modelled by solving the Stokes equations, discretized with the finite element method; the evolving free surfaces are accommodated by employing a pseudosolid mesh deforming algorithm. The results show that as the roll radius is reduced, thus increasing the lateral and rotational motions of the top plate relative to the cavity, a larger volume of liquid is transferred to the plate. However, due to lateral displacement of the contact lines, special care must be taken concerning the wettability properties of the substrate to avoid errors in the pattern fidelity. The predictions also show a strong nonlinear behaviour of the liquid fraction extracted from a cavity as a function of the capillary number. At high capillary numbers the fluid dynamics is mainly controlled by the extensional motion due to the strong contact line pinning. However, at low values of the capillary number, the contact lines have higher mobility and the liquid fraction primarily depends on the lateral and rotational plate velocity. These mechanisms tend to drag the fluid outside the cavity and increase the liquid fraction transferred to the plate, as has been observed in experiments.
Instability of a viscous liquid coating a cylindrical fibre
- ALEJANDRO G. GONZÁLEZ, JAVIER A. DIEZ, ROBERTO GRATTON, DIEGO M. CAMPANA, FERNANDO A. SAITA
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- Journal:
- Journal of Fluid Mechanics / Volume 651 / 25 May 2010
- Published online by Cambridge University Press:
- 22 March 2010, pp. 117-143
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The instability of a liquid layer coating the surface of a thin cylindrical wire is studied experimentally and numerically with negligible gravity effects. The initial uniform film is obtained as the residual of a sliding drop, and the thickness measurements are performed with an anamorphic optical system that compresses the vertical scale (allowing to observe several wavelengths) and widens the horizontal one (to follow in detail the evolution of local minima and maxima). Experimental timelines showing the growth and position of the maxima and minima are compared with linear theory and fully nonlinear simulations. A primary mode grows in the early stages of the instability, and its wavelength λ1 is not always in agreement with that corresponding to the maximum growth rate predicted by the linear theory λm. In later stages, a secondary mode appears, whose wavelength is half that of the primary mode. The behaviour of the secondary mode allows us to classify the experimental results into two cases, depending on whether it is linearly stable (case I) or unstable (case II). In case I, the amplitude of the secondary mode remains small compared with that of the primary one, while in case II both amplitudes may become very similar at the end. Thus, the distance between the final drops may be quite different from that seen between initial protuberances. The analysis of the experiments allows us to define a simple criterion based on the comparison between λ1 and λm. Contrary to the predictions of widely used previous quasi-static theories, experiments show that the relation between maximum and minimum of the primary mode is better approximated by a kinematic model based on the assumption that primary maxima increase as fast as the minima decrease. Numerical simulations confirm this hypothesis.