Entrainment threshold

Figure 4. Evolution of the air entrainment threshold velocity U as a fnnction of the static contact angle 0(, of the impacting spheres on a water-air interface. The sphere diameters are 25.4 mm ( ), 20 mm (v), 15 mm (O) and 7 mm (A). The dashed line, in the hydrophobic domain, is the theoretical evolution predicted by expression (6).

To understand this dramatic, yet unexpected, evolution of the air entrainment threshold velocity with the different parameters, we first focus on the behavior of the liquid close to the solid surface. During the sphere impact, a thin liquid film develops and rises along the sphere, as can be seen in Fig. 6 which shows a series of chronophotographs of the impact phenomenon. This film either closes up at the... 

Figure 5. Evolution of the air entrainment threshold velocity U with the liquid properties, for a fixed wettability ( o <10°) and bead diameter (25.4 mm). U evolves linearly with the ratio ylyIwhich indicates that the air entrainment during impact is a capillary-number-controlled phenomenon.

Figure 6. Zoomed-in chronophotographs of the impact region, when a hydrophobic sphere (static contact angle 6>q 115°) is falling on an air-water interface at different impact velocities compared with the air entrainment threshold f/ (a) U = 2.4 m/s < f/ and (b) U = 5.0 m/s > f/. The thin liquid film that develops and rises along the sphere in both cases either gathers at the pole to encapsulate the sphere (low velocity), or is ejected from the sphere thus creating an air cavity behind it (high velocity).

GNB were found on the unwashed botanical trash than on the unwashed clean lint (Table VII). Both the botanical trash and the cleaned lint from the washed sample had levels of entrained GNB < the threshold limit of sensitivity (100 GN3/g) detectable in our laboratory. 

V 15% in the number of cells killed by the drug. This jump is not observed in the absence of entrainment (data not shown). Entrainment by the circadian clock further enhances the synchronization of cells and protects them from the drug, as long as V remains relatively small, i.e. V 10%. Therefore, circadian entrainment magnifies the consequences of cell cycle variability, as it introduces a threshold in the effect of this parameter. 

The effect of variability on drug cytotoxicity markedly depends on the temporal pattern of 5-FU delivery. When the peak in the circadian delivery of 5-FU occurs at 4 p.m., i.e. when the circadian schedule of 5-FU administration is most toxic to the cells, whether in the absence or presence of entrainment by the circadian clock, cytotoxicity increases as the degree of variability decreases. The effect is more marked in the conditions of entrainment a threshold in cytotoxicity then exists between... 

The T dependence of (ib) was unexpected as it implies that there are strong attractive forces acting between 02(A ) and I at relatively large internuclear separations. To explore this phenomena in more detail, and to test the reliability of Eqs. (20) and (21), we examined reaction (lb) at a temperature of 150 K. ° These measurements were carried out using a Laval nozzle to provide low temperature gas flows. Traces of I2 were entrained in He/02 mixtures, and pulsed laser photolysis was used to generate I by exciting just above the 12(B) dissociation limit. Near threshold photodissociation was used to ensure that I was produced with a translational temperature in equilibrium with the local conditions. I decay kinetics were... 

The rapid increase in crater depth above the threshold irradiance for phase explosion correlates with a significant increase in signal intensity. The ratio of crater volume to signal intensity, which represents the entrainment efficiency, remains the lowest at laser irradiances slightly above the phase explosion threshold. Such a ratio, however, increases at irradiances well above the threshold (> 10" W/cm ). 

In order to better quantify what affects the liquid response upon impact, Duez et al. [47] systematically measured the threshold velocity U associated with the onset of air entrainment as a function of the numerous experimental parameters sphere wettability, sphere diameter, liquid characteristics (dynamic viscosity, surface tension) or gas characteristics (nature, pressure)— We concentrate first on the role of surface wettability. Figure 4 shows the evolution off/ with the static contact angle 9q on the sphere. As already mentioned, U strongly depends on 9q, particularly in the non-wethng domain 9q > 90°) where U starts from around 7 m/s to become vanishingly small for superhydrophobic surfaces with 9q 180°. In this last case, an air cavity is always created during impact, whatever the sphere velocity. 

For atmospheric pressure or vacuum distillations, the vapor flow rate is limited by the loss of normal separation efficiency due to entrainment of liquid upward in the vapor phase. The amount of entrainment increases rapidly above a threshold value for the particular system. As the vapor flow rate is increased further, the mass of entrained liquid becomes sufficient to reduce the concentration profile established in the column. The maximum operational Cs has been defined as the greatest vapor flow rate attained before loss of normal separation efficiency. Figures 7-6 and 7-7 give a prediction of the maximum capacity for IMTP random packings and Intalox structured packings, respectively, as limited by liquid entrainment. 

The occurrence of wind erosion mainly depends on the wind velocity, the grain size distribution of the fill and the structure of the soil preventing particle detachment. The minimum wind velocity required to cause entrainment in the erosional agent of wind is known as the threshold velocity. The threshold velocity is strongly related to the size of the grains, but also to the vegetation, surface roughness, soil structure (surface crust), precipitation and humidity, surface soil moisture content, etc. 

Gust, G. and M.J. Morris. 1989. Erosion thresholds and entrainment rates of undisturbed in situ sediments. Journal of Coastal Research, 5 87-99. 

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