Slurry flow speed

When the slurry flow speed is low, the bed thickens. As the fluid above the bed tries to move the solids by entrainment, they tend to roll and tumble. The particles with the lowest settling speed move as an asymmetric suspension, whereas the coarser particles build up the bed. As the speed drops even further, the pressure to maintain the flow becomes quite high and eventually the pipe blocks up. 

Figure 6-2 A typical casting head and a casting head for stabilizing sheet thickness. Manufacturing parameters (Vx Slurry flow speed, T Slurry thickness immediately after passing the blade, T Green sheet thickness after drying).

Runnels and Eyman [41] report a tribological analysis of CMP in which a fluid-flow-induced stress distribution across the entire wafer surface is examined. Fundamentally, the model seeks to determine if hydroplaning of the wafer occurs by consideration of the fluid film between wafer and pad, in this case on a wafer scale. The thickness of the (slurry) fluid film is a key parameter, and depends on wafer curvature, slurry viscosity, and rotation speed. The traditional Preston equation R = KPV, where R is removal rate, P is pressure, and V is relative velocity, is modified to R = k ar, where a and T are the magnitudes of normal and shear stress, respectively. Fluid mechanic calculations are undertaken to determine contributions to these stresses based on how the slurry flows macroscopically, and how pressure is distributed across the entire wafer. Navier-Stokes equations for incompressible Newtonian flow (constant viscosity) are solved on a three-dimensional mesh ... 

The slurry flows continuously into the first gas-phase reactor (GPR) (3). Reactor gas is circulated at high speed by a centrifugal compressor through a distribution grid. A cooler on the circulation gas... 

FIGURE 2.7 ICIOOO pad surface temperature profiles during the polishing of 200-mm and 300-mm blanket oxide wafers using silica-based slurry under 6 psi downforce and 200 ml/min slurry flow rate and with two different table/carrier speeds (Strasbaugh n-Hance Polisher). 

FIGURE 7.20 Removal rate versus downforce on 8" Cu blanket test wafers polished at 75/65 rpm table/carrier speed and 200ml/min slurry flow rate on Strasbaugh u-Hance polisher. Diamond data points indicate the removal rate values with the organic particles, and square data points denote removal rate values for silica particles, both polished under identical formulation and abrasive concentration (from Ref. 110). 

A set of thermal oxide wafers are polished using a silica-based slurry (Cabot SC-112) on an IPEC polisher equipped with an ICIOOO pad (Rohm Hass). The polishing time is set at 30 s with a slurry flow rate of 150ml/min and downpressure of 9 psi with 2 psi backpressure. The rotational speeds of the wafer and the pad are 25 rpm and 13rpm, respectively. After polishing, the wafers are dried and then taken to the clean room where the STEAG bench is located. 

CMP slurry delivery system employing filtration for LPC eontrol should consider slurry characteristics including—abrasive type(s) and composition, LPC, PSD, wt% solids, viscosity, chemical composition and the distribution system characteristics—specific pump type and the pumping effects on slurry abrasive, pump size and speed, global distribution loop backpressure, slurry usage and replenishment cycles, slurry turnover rate and typical turnovers before consumption, filter ratings for various locations, allowable pressure drop for filters, and the slurry flow and temperature consistency needs. 

Polishing experiments were also carried out on a Strasbaugh 6CA polisher. The polisher parameters were set at 40 rpm rotational speed of table and quill, 2.76 x lO" Nm downward pressure and 4 ml s slurry flow rate for all the polishing experiments. The slurry in the supply tank was continuously stirred using a magnetic stirrer. The alumina particle loading in the slurry... 

In the case of slurry flow in a rotary drum, turbulent suspension of the solids can occur due to the axial liquid velocity coupled with the radial liquid velocity due to the drum rotation and mixing action created by the drum internals. Typically, the peripheral drum velocity is much higher than the slurry axial velocity, and, consequently, the drum rotational speed becomes very important for solids turbulent suspension and, hence, transport. 

Figure 35 shows the variation of the percent slurry hold-up and hold-up slurry concentration for the case of 80 pm silica sand at a slurry flow rate of 0.02 kg/s. The working liquid was water at 23°C. Figure 35a shows that the percent slurry hold-up in the drum decreased with the drum speed. For the cases of 10 to 30% feed solids concentration, the asymptotic hold-up value was about 20%, which was slightly higher than the minimum hold-up of 16.2%. However, for the case of a feed solids concentration of 40%, the asymptotic percent slurry hold-up was higher. 

Figure 36a is similar to Figure 35a, but for a slurry feed rate of 0.04 kg/s. The percent slurry hold-up behavior was similar to that for = 0.02 kg/s. The variation of the hold-up solids concentration ratio, C/Cp, is shown in Figure 36b. It is clear that for drum speeds > 2.62 s, all the curves for the various Cp values approached a limiting value of C/Cp = 1.0. This result is, once again, indicative that both the water and the solids move with the same axial velocity similar to a homogeneous slurry. The maximum deviation of C/Cp from unity occurs at low drum speeds, signifying a large relative velocity for the water and the solids. This case is that of a stratified slurry flow.

Figure 39 shows the mean residence time for the solids, water, X, and the ratio xJXf. As would be deduced from the variation of the hold-up solids concentration shown in Figures 35b and 36b, the mean residence time of the solids in the drum is higher than that of the water at low values of the drum speed. However, for N > 2.62 s , the ratio of xjx approached unity, indicating complete suspension of the solids. Figure 39c depicts that xjx was not sensitive to variation in the slurry feed rate. However, as would be expected, the individual values of the x and x, were affected by the slurry flow rate (Figures 39a and 39b). 

Figure 41. Effect of drum speed on normalized solids concentration for four different slurry flow rates, (p, = 1 mPa s).

The flow of slurry in a pipeline is much different from the flow of a single-phase liquid. Theoretically, a single-phase liquid of low absolute (or dynamic) viscosity can be allowed to flow at slow speeds from a laminar flow to a turbulent flow. However, a two-phase mixture, such as slurry, must overcome a deposition critical velocity or a viscous transition critical velocity. The analogy can be made here in terms of an airplane if the speed drops excessively, the airplane stalls and stops flying. If the slurry s speed of flow is not sufficiently high, the particles will not be maintained in suspension. On the other hand, in the case of highly viscous mixtures, if the shear rate in the pipeline is excessively low, the mixture will be too viscous and will resist flow. 

In Chapters 3, 4, and 5 the mechanics of solid suspensions are described in detail. An im portant parameter to introduce in this chapter is the critical velocity of a slurry flow. Figure 1-8 plots the pressure loss per unit length on the y-axis, versus the velocity Kof a slurry flow on the x-axis. Five points are shown for flow at a constant volume concentration. For this slurry of moderate viscosity, the flow is stationary and the solids clog the pipeline below point 1. There is insufficient speed to move the particles. As the flow is accelerated, the speed reaches point 1, which is called the deposition critical velocity Vp, or minimum speed to start the flow. Between points 1 and 2, the bed builds up, dunes form, and the different phases are well separated. Between points 2 and 3 the flow is streaking but... 

One fundamental aspect to the transportation of solids by a liquid is the resistance, called the drag force, that such solids wiU exert, and the ability of the Uquid to lift such solids, called the lift force. Both are complex functions of the speed of the flow, the shape of the solid particles, the degree of turbulence, and the interaction between particles and the pipe. One approach is to look at a vehicle that we have aU come to know—the airplane. This distraction from the complex world of slurry flows is justifiable. 

In the past, engineers have tried to simplify the complexity of slurry flows by defining certain transition velocities. With the use of modern research tools, there is an emerging approach of rejecting the concept of an abrupt change from one state of flow to another, and a tendency to consider such a change over a band of the speed. Different approaches have been developed to examine the mixture of coarse and fine particles from superimposed layers to two-layer models. 

As the flow speed increases, turbulence is sufficient to lift more solids. All particles move in an asymmetric pattern with the coarsest at the bottom of a horizontal pipe covered with superimposed layers of medium- and fine-sized particles. Many particles may strike the bottom of the pipe and rebound. Wear on the bottom of the pipe must be taken into account in maintenance schedules and the pipes must be rotated at intervals suggested by the slurry engineer in order to maintain an even wear pattern of the internal wall of the pipe. Although the flow is not symmetric, from the point of view of power consumption, this regime may be the most economical for transporting a certain mass of solids. 

Consider a 20" OD pipe with a wall thickness of 0.375", rubber lined with a rubber thickness of 14". The internal diameter of the pipe would be Dj= [20 - 2(0.375+0.25)] = 18.75" or 477 mm. The cross-sectional area of the pipe would be 0.178 m and the average flow speed of the slurry would be calculated as E= 0.453/0.178 = 2.55 m/s. Applying the Thomas-Einstein equation to the volumetric concentration of 8.7% gives an... 

A Bingham slurry with a concentration of 50% by weight is tested in a plastic-lined pipe with an inner diameter of 2.5 in. The tests indicate a yield stress of 1.5 Pa, a slurry mixture specific gravity of 1.54, and a coefficient of rigidity of 0.4 Pa s. Assuming a flow speed of 4 ft/s in a laminar regime, determine the friction factor by Buckingham s equation. 

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