Waves and Ripples

It is well known that many types of waves and ripples can be damped by interfacial films of surface-active materials, as shown theoretically by Levich (L6, L7). There have been a number of investigations into the effects of surface-active additives on the flow of wavy films (E4, H2, H20, 12, Jl, L15, M7, Sll, S12, T3). In addition, surface-active materials have also been used in various studies of mass and heat transfer to films, and some of these results throw light on the flow behavior of the films, e.g. (H13, Mil, Rl, T9, T10, Til, T12). 

Nusselt s film condensation theory presumes an even increase in the thickness of the film due to further condensation. However experiments, among others [4.4] to [4.6], have shown that even in a flow that is clearly laminar, waves can develop at the film surface. These types of waves were not only observed on rough but also on polished surfaces. Obviously this means that the disturbances in the velocity that are always present in a stream are not damped under certain conditions, and so waves form. They lead to an improvement in the heat transfer of 10 to 25 % compared to the predictions from Nusselt s theory. According to Grimley [4.7], waves and ripples appear above a critical Reynolds number... 

Annular flow The liquid travels partly as an annular film on the wall of the tube and partly as small drops distributed in the gas which flows in the center of the tube. The interface is disturbed by high frequency waves and ripples. 

Hydrodynamics of Interfaces Thin Films, Waves, and Ripples... 

FIGURE 7.16. (a) Laser beam deflection technique used to measure the profile z x) of the film during wetting (b) profile in the regime Fr < I, when shock waves and ripples are absent (c) profile for four different thicknesses 8 cm away from the nucleation point in the regime FV > 1 the ripples are the signature of shock waves (courtesy A. Buguin). 

Another approach to measurement of surface tension, density, and viscosity is the analysis of capillary waves or ripples whose properties are governed by surface tension rather than gravity. Space limitations prevent more than a summary presentation here readers are referred to several articles [123,124]. 

If > 20, surface waves and rates increase. An approximate solution can be used. Ripples are suppressed with a wetting agent good to Nrs = 1200. 

Taylod205 also conducted mathematical analysis of the generation of ripples by wind blowing over a viscous fluid. Using a relationship between the growth of the amplitude of disturbance waves and the surface stress, Taylor derived a criterion for the instability of waves. In Taylor s instability theory, the disintegration of a liquid sheet/film is visualized as a process in which droplets are detached from the liquid surface with a wave of optimum amplitude. The diameter of the most frequent droplets is then formulated as a function of air velocity over the liquid surface, liquid density, surface tension and viscosity, as well as air density. 

In upward or climbing-film flow, waves or ripples are always present. At low gas rates and low liquid rates, films are thin, wave amplitude and entrainment may be relatively small, and straightforward hydrodynamic... 

Some amounts of sand riverine sediments are transported in channels in the form of sand ripples, waves and dunes formed on the river bed under the influence of the near-bottom currents. This sediment load (called bedload) usually comprises about 10% of the suspended sediment load. Taking into account this fact, we find that the total river sediment input to the Black Sea may range up to 84 x 106 tyear-1. 

A. Laminar, vertical wetted wall column W -3.41- L Ofilm (first term of infinite series) Sfiim — f —) — film thickness Wpg/ — <2° tv x [T] Low rates M.T. Use with log mean concentration difference. Parabolic velocity distribution in films. w = film width (circumference in column) Derived for flat plates, used for tubes if / pg y2 ttube > 3.0. a = surface tension 2o/ If Aj fiim > 20, surface waves and rates increase. An approximate solution Dapparent can be used. Ripples are suppressed with a wetting agent good to Afe = 1200. [138] p. 78 [141] p. 137 [152] p. 50... 

Entrainment and Mechanical Disintegration Gas can be entrained into a liquid by a solid or a stream of liquid falling from the gas phase into the liquicl, by surface ripples or waves, and by the vertical swirl of a mass of agitated hquid about the axis of a rotating agita-... 

Although scientists talk about the dual wave and particle properties of electrons, many nonscientists still believe that electrons are only tiny particles. Rooted as we are in the macroscopic world, it can be difficult for some to picture a particle as also being a wave. One look at the accompanying picture, however, should help change that. What looks like ripples surrounding two barely submerged pebbles in a pool of water is really the surface of a copper crystal. 

Henceforth we shall use the term capillary waves, or capillary ripples for waves that are so small that interfacial tension contributes significantly to their properties. Two types of such waves can be distinguished spontaneous, or thermal waves and those externally applied. The former type is always present they are caused by spontaneous fluctuations cind have a stochastic nature. In secs. 1.10 and 1.15 it was shown how from these fluctuations interfacial tensions and bending moduli could be obtained. Now the second type will be considered. Transverse or longitudinal perturbations can be applied to the interface, for example by bringing in a mechanically driven oscillator (see sec. 3.7). Such waves are damped, meaning that the amplitude Is attenuated. Damping takes place by viscous friction in the... 

The Schmidt numbers were varied from 0.60 to 2.5, and over this narrow range the difference between the exponents of 0,44 in Eq. (21.54) and 0.33 in Eq. (21,51) has only a small effect on the coefficient. The difference in exponents may have fundamental significance, since transfer to a liquid surface, which can have waves or ripples, should differ somewhat from transfer to a smooth rigid surface. 

Capillary Ripples Surface or interfacial waves caused by perturbations of an interface. When the perturbations are caused by mechanical means (e.g., barrier motion), the transverse waves are known as capillary ripples or Laplace waves, and the longitudinal waves are known as Marangoni waves. The characteristics of these waves depend on the surface tension and the surface elasticity. This property forms the basis for the capillary wave method of determining surface or interfacial tension. 

Armbruster and Mitrovic [62] observed that liquid falls from tube to tube in three patterns discrete droplets, jets or columns, and sheets, depending on the flow rate (i.e., film Reynolds number) and fluid properties. In addition, depending on the tube arrangement and spacing, the condensate may cause ripples, waves, and turbulence to occur in the film splashing may occur, as well as nonuniform rivulet runoff of condensate because of tube inclination or local vapor velocity effects. As a result, it is impossible to arrive at an analytical expression to describe these complex bundle phenomena. In general, the effect of inundation may be accounted for using... 

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