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Dynamics of contact line motion and wettability is essential in many industrial applications such as liquid coating, lubrication, printing, painting, condensation, etc. However, the wettability of surfaces depends not only on liquid–solid chemical properties but also can be strongly affected by surface roughness. As a practical application of controlled wettability, we can mention the self‐cleaning surfaces, protective clothing, microfluidics devices, electro wetting, etc. In this article, we experimentally investigate the spreading of droplets deposited onto rough surfaces. Anisotropic surfaces were prepared by abrasive polishing on the following materials: aluminium alloy AA7064, titanium alloy Ti‐6Al‐4V, steel AISI 8630, copper alloy UNS C17000, machinable glass ceramic, and poly‐methylmethacrylate. Topographical 2D parameters were calculated according to the following standards, defining Geometrical Product Specifications (GPS): ISO 4287, ISO 12085, ISO 13565, ISO 12780, and ISO 12181. The influence of topographical parameters on wettability and spreading phenomenon has been evaluated by statistical covariance analysis. The following parameters have strong influence on fluid spreading on rough surfaces: Rmris the relative material ratio of the roughness profile, Trcis the microgeometric material ratio, Pmris the relative material ratio of the raw profile, Kris the mean slope of the roughness motifs, RONtis the peak to valley roundness deviation, and Pskis the Skewness of the raw profile. The physical meaning of selected parameters is discussed, and Kr(the mean slope of the roughness motifs) is selected as the most important and physically meaningful parameter. It has been found that for all tested materials, fluid spreading shows increasing tendency when mean slope of the roughness motifs (Kr) increases. SCANNING 33: 370–377, 2011. © 2011 Wiley Periodicals, Inc.

Two-dimensional flow is considered in a fluid bead located in the gap between a pair of contra-rotating cylinders and bounded by two curved menisci. The stability of such bead flows with two inlet films, and hence no contact line, are analysed as the roll speed ratio S is increased. One of the inlet films can be regarded as an ‘input flux’ whilst the other is a ‘returning film’ whose thickness is specified as a fraction ζ of the outlet film on that roll. The flow is modelled via lubrication theory and for Ca ≪ 1, where Ca represents the capillary number, boundary conditions are formally developed that account for S ≠ 1 and the non-constant gap. It is shown that there is a qualitative difference in the results between the single and double inlet film models unless small correction terms to the pressure drops at the interfaces are taken into account. Futhermore, it is shown that the inclusion of these small terms produces an O(1) effect on the prediction of the critical value of S at which bead break occurs. When the limits of the returning film fraction are examined it is found that as ζ → 0 results are in good agreement with those for the single inlet film. Further it is shown for a fixed input flux that as ζ → 1 a transition from bead break to upstream flooding of the nip can occur and multiple two-dimensionally stable solutions exist. For a varying input flux and fixed and ‘sufficiently large’ values of ζ there is a critical input flux &λmacr;(ζ) such that as S is increased from zero: (i) bead break occurs for λ < &λmacr;; (ii) upstream flooding occurs for λ > &λmacr;; (iii) when λ = &λmacr; the flow becomes neutrally stable at a specific value of S beyond which there exist two steady solutions (two-dimensionally stable) leading to bead break and upstream flooding, respectively.

In multiple-roll coaters thin liquid films are transferred from roll to roll by means of liquid ‘beads’ which occupy the small gaps between adjacent rolls. Double-Film-Fed (DFF) beads are those which feature two ingoing films instead of the usual one, and arise in the intermediate stages of certain types of roll coater. One of the ingoing films, h1, is supplied from the previous inter-roll gap while the other, h2, ‘returns’ from the subsequent gap. Such a flow is investigated here under the conditions of low flow rate, small capillary number and negligible gravity and inertia, using lubrication theory and finite element analysis. The thickness of film h1 is fixed independently, while that of h2 is specified as a fraction, ζ, of the film output on the same roll. This simple approach allows a degree of feedback between the output and input of the bead, and enables one to simulate different conditions in the subsequent gap. Predictions of outgoing film thicknesses made using the two models agree extremely well and show that, for each value of ζ < 1, one outgoing film thickness decreases monotonically with speed ratio, S, while the other features a maximum. Good agreement is also seen in the pressure profiles, which are entirely sub-ambient in keeping with the small capillary number conditions. The finite element solutions reveal that in the ‘zero-flux’ case (when ζ = 1) the flow structures are very similar to those seen in an idealized cavity problem. In the more general (ζ < 1) situation, as in single-film-fed meniscus roll coating, several liquid transfer-jets occur by which liquid is conveyed through the bead from one roll to the other. The lubrication model is used to calculate several critical flow rates at which the flow is transformed, and it is shown that when the total dimensionless flow rate through the bead exceeds 1/3, the downstream flow structure is independent of the relative sizes of the ingoing films.