By S. Kalliadasis, C. Ruyer-Quil, B. Scheid, M. G. Velarde
Falling Liquid Films supplies a close assessment of cutting-edge theoretical, analytical and numerical methodologies, for the research of dissipative wave dynamics and trend formation at the floor of a movie falling down a planar prone substrate. This prototype is an open-flow hydrodynamic instability, that represents a very good paradigm for the learn of complexity in lively nonlinear media with strength offer, dissipation and dispersion. it is going to even be of use for a extra normal realizing of particular occasions characterizing the transition to spatio-temporal chaos and weak/dissipative turbulence. specific emphasis is given to low-dimensional approximations for such flows via a hierarchy of modeling techniques, together with equations of the boundary-layer kind, averaged formulations in accordance with weighted residuals ways and long-wave expansions. each time attainable the hyperlink among thought and scan is illustrated, and, as an additional bridge among the 2, the improvement of order-of-magnitude estimates and scaling arguments is used to facilitate the certainty of easy, underlying physics.
This monograph will attract complicated graduate scholars in utilized arithmetic, technological know-how or engineering project examine on interfacial fluid mechanics or learning fluid mechanics as a part of their software. it is going to even be of use to researchers engaged on either utilized, primary theoretical and experimental points of skinny movie flows, in addition to engineers and technologists facing methods regarding isothermal or heated motion pictures. This monograph is basically self-contained and no heritage on interfacial fluid mechanics is thought.
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Extra resources for Falling liquid films
2, and Bi and Biw both scale with the thermal conductivity of the liquid, in general Bi < Biw . As also pointed out in Appendix. 2 this situation can be reversed by insulating the solid, in which case Bi > Biw (increasing the thermal conductivity of the liquid does increase Bi but it cannot really lead to Bi > Biw ). 36) the control parameter that determines the Nusselt flat film thickness h¯ N in experiments. 35) is merely the dimensionless flow rate based on the viscous gravity scales, qN = u¯ N h¯ N /[(lν /tν )lν ] ≡ q¯N /ν.
These equations are the basis for subsequent modeling. In Chaps. 5 and 6 we develop in detail the different methodologies and models used to analyze film flows. We also offer a critical assessment of their domain of validity and discuss their limitations. In Chaps. 7, 8 and 9 we use the models developed earlier and we present results on wave evolution on an isothermal and heated falling film. We critically compare the theory, numerics and experimental results (whenever possible). 4 Structure and Contents of the Monograph 17 More specifically: In Chap.
We introduce a Cartesian coordinate system (x, y, z) where x is the streamwise coordinate in the direction of flow, y is the outward-pointing coordinate normal to the plate and z is the spanwise coordinate. The plate is then located at y = 0 and the interface at y = h(x, z, t), a single-valued function of x, z and time t . The main hypotheses are: H1: The density ρ of the liquid is constant, or, equivalently the liquid remains incompressible. , [27, 58]. We examine this assumption S. 1007/978-1-84882-367-9_2, © Springer-Verlag London Limited 2012 21 22 2 Flow and Heat Transfer: Formulation Fig.