Sticking velocity

Figure C2.9.2 Shear force versus time during (a) sliding and (b) stick-slip motion. The motion of the surface beneath the sliding block of figure C2.9.1 is at constant velocity.

Imposition of no-slip velocity conditions at solid walls is based on the assumption that the shear stress at these surfaces always remains below a critical value to allow a complete welting of the wall by the fluid. This iraplie.s that the fluid is constantly sticking to the wall and is moving with a velocity exactly equal to the wall velocity. It is well known that in polymer flow processes the shear stress at the domain walls frequently surpasses the critical threshold and fluid slippage at the solid surfaces occurs. Wall-slip phenomenon is described by Navier s slip condition, which is a relationship between the tangential component of the momentum flux at the wall and the local slip velocity (Sillrman and Scriven, 1980). In a two-dimensional domain this relationship is expressed as... 

Limestone is pulverized to 80 to 90 percent through 200 mesh. Shiny concentrations of 5 to 40% have been checked in pilot plants. Liquid to gas ratios are 0.2 to 0.3 gaLMSCF. Flue gas enters at 149°C (300°F) at a velocity of 2.44 m/s (8 ft/s). Utilization of 80 percent of the solid reagent may be approached. Flow is in parallel downward. Residence times are 10 to 12 s. At the outlet the particles are made just diy enough to keep from sticking to the wall, and the gas is within 11 to 28°C (20 to 50°F) of saturation. The fine powder is recovered with fabric filters. 

A common cause of erosion is partial obstruction of tubes by foreign bodies. At the inlet end, for example, debris such as sticks, glass fragments, and wood chips may lodge in tube ends or be held against the tubes by water flow. The nominal velocity of the water past the obstruction increases according to the degree of obstruction. It can be shown... 

Perforated sheets are, however, much more vulnerable to uneven pressure distributions and tilted inflow of air, as illustrated in Fig, 8,26. The supply air entering horizontally alxive the perforated sheet partly maintains its horizontal velocity component when being discharged through the holes in the perforated sheet. Thus, it leaves the perforated sheet at an angle less than 90°. The suction between the small outflowing jets also makes the airflow stick to the perforated sheet and flow along the sheet instead of perpendicular to (t. 

Ruhr-fass, n. churn (J/ to/.) dolly tub. -form, /. form or shape of stirrer, -frischen, n. (Metal.) puddling. -geschwindigkeit, /. velocity of stirring. -tUikchen, n. small stirring hook, -haken, m. stirring implement, rake, rabble, poker, -holz, n. wooden stirrer, stirring stick, paddle. 

As demonstrated in Fig. 5.7, the result indicates that two-phase flow patterns observed in a 100 pm quartz tube are almost similar to those observed in a 25 pm silica capillary tube with several exceptions. One such exceptions is that in slug flow encountered at low velocities, small liquid droplets in a gas slug stick to the tube wall (Fig. 5.8). This fact is evidence that no liquid film exisfs befween fhe gas slug and the tube wall. 

Stick-slip motion is another issue that has been explored using SFA. It is found that the occurrence of stick-slip depends on the sliding velocity and the stiffness of the system, and the mechanism of the phenomenon can be interpreted in terms of periodic transition between liquid and solid states of the conhned lubricant [40],... 

The dependence of friction on sliding velocity is more complicated. Apparent stick-slip motions between SAM covered mica surfaces were observed at the low velocity region, which would disappear when the sliding velocity excesses a certain threshold [35]. In AFM experiments when the tip scanned over the monolayers at low speeds, friction force was reported to increase with the logarithm of the velocity, which is similar to that observed when the tip scans on smooth substrates. This is interpreted in terms of thermal activation that results in depinning of interfacial atoms in case that the potential barrier becomes small [36]. 

It has been recognized that the behavior of atomic friction, such as stick-slip, creep, and velocity dependence, can be understood in terms of the energy structure of multistable states and noise activated motion. Noises like thermal activities may cause the atom to jump even before AUq becomes zero, but the time when the atom is activated depends on sliding velocity in such a way that for a given energy barrier, AI/q the probability of activation increases with decreasing velocity. It has been demonstrated [14] that the mechanism of noise activation leads to "the velocity... 

So far we have compared the static friction with the stick-slip transition. In both cases the system has to choose between the states of rest and motion, depending on which one is more favorable to the energy minimization. On the other hand, the differences between the two processes deserve a discussion, too. In stick-slip, when the moving surface slides in an average velocity V, there is a characteristic time, t =d.Ql V, that defines how long the two surfaces can... 

At the beginning of sliding, the system is accelerated because the driven force must excess the resistance from lubricating film. For this reason, the system actually jumps from A to the point B, instead of B, to gain a shear stress lower than the critical value This phenomenon, so called velocity-weakening has been regarded widely in the literatures as the cause for instability and stick-slip motion in lubricated systems. 

As previously noted, if the Reynolds number in the tube is larger than about 2000, the flow will no longer be laminar. Because fluid elements in contact with a stationary solid boundary are also stationary (i.e., the fluid sticks to the wall), the velocity increases from zero at the boundary to a maximum value at some distance from the boundary. For uniform flow in a symmetrical duct, the maximum velocity occurs at the centerline of the duct. The region of flow over which the velocity varies with the distance from the boundary is called the boundary layer and is illustrated in Fig. 6-3. 

It is instructive to simplify the above picture somewhat and consider the coalescence or sticking of two particles schematically shown in Fig. 13. One can assume that due to shear forces in the mixer, a fluidized bed in the present case, the two particles posses a relative velocity U0 which ensures collision at some point on their trajectory and possible sticking under appropriate conditions. It is essential that some binder be present at the point of contact, as depicted in the figure. From this simplified picture, allmechanisms... 

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