Cylinders rotation

If a fluid is placed between two concentric cylinders, and the inner cylinder rotated, a complex fluid dynamical motion known as Taylor-Couette flow is established. Mass transport is then by exchange between eddy vortices which can, under some conditions, be imagmed as a substantially enlranced diflfiisivity (typically with effective diflfiision coefficients several orders of magnitude above molecular difhision coefficients) that can be altered by varying the rotation rate, and with all species having the same diffusivity. Studies of the BZ and CIMA/CDIMA systems in such a Couette reactor [45] have revealed bifiircation tlirough a complex sequence of front patterns, see figure A3.14.16. 

Coaxial (Concentric Cylinder) Viscometer, The eadiest and most common type of rotational viscometer is the coaxial or concentric cylinder instmment. It consists of two cylinders, one within the other (cup and bob), keeping the specimen between them, as shown in Figure 27. The first practical rotational viscometer consisted of a rotating cup with an inner cylinder supported by a torsion wire. In variations of this design the inner cylinder rotates. Instmments of both types ate useful for a variety of apphcations. 

The mathematical model chosen for this analysis is that of a cylinder rotating about its axis (Fig. 2). Suitable end caps are assumed. The Hquid phase is introduced continuously at one end so that its angular velocity is identical everywhere with that of the cylinder. The dow is assumed to be uniform in the axial direction, forming a layer bound outwardly by the cylinder and inwardly by a free air—Hquid surface. Initially the continuous Hquid phase contains uniformly distributed spherical particles of a given size. The concentration of these particles is sufftcientiy low that thein interaction during sedimentation is neglected. 

The second type of thin-film evaporator, termed a wiped-film evaporator, introduces feed material on a heated waU of a cylinder. Rotating wiper blades continuously spread the feed along the inner waU of the cylinder to maintain uniformity of thickness and to ensure contact with the heated surface. The volatile components are driven off and coUected on an internal chilled condenser surface. The condensate or distUlate is removed continuously. At the end of the process, the residual becomes dry and heavy and drops to the bottom of the unit for removal. The wiped-film evaporator is best suited for treatment of viscous or high-solids content feed. 

Viscosity also is measured with a rotational viscometer. The mud is placed between two concentric cylinders. One cylinder rotates with constant velocity. The other cylinder is connected with a spring. The torque on this cylinder results in a deviation of the position from rest, which may serve as a measure of viscosity. 

Fig. 4.5.11 Measured TOF and phase encoding velocity profiles from the lower, vertical center line and corresponding fits using Eq. (4.5.8). Outer cylinder rotation speed is ...

Fig. 4.5.12 The dimensionless parameter f plotted against outer cylinder rotation speed V. Values off were fit from the lower ( ) or upper (o) vertical center line (see Figure 4.5.3) velocity profile.

Fig. 2. Mixing in the vortex mixing flow with increasing periods of flow (P). The flow is time periodic with each cylinder rotating alternately for a fixed time period (Jana, Metcalfe and Ottino, 1994).

Fig. 38. Variation of polydispersity with average cluster size at short times in a journal bearing flow. The symbols are from simulations and the lines are fits from Eq. (82). The regular flow is the journal bearing flow with only the inner cylinder rotating (Hansen and Ottino, 1996b).

However, flow generated by a cylinder rotating at high speed was subsequently used by others, and in particular by King and co-workers (K3, K4a), to demonstrate that dissolution and electrochemical corrosion may both be transport limited. The dependence of the mass-transfer coefficient on the rotation rate and on the diffusivity of the dissolving species was established by correlation of experimental data (see Table VII, System 43). 

A computer-controlled rheology laboratory has been constructed to study and optimize fluids used in hydraulic fracturing applications. Instruments consist of both pressurized capillary viscometers and concentric cylinder rotational viscometers. Computer control, data acquisition and analysis are accomplished by two Hewlett Packard 1000 computers. Custom software provides menu-driven programs for Instrument control, data retrieval and data analysis. 

In an earlier phase of this work [9] the intensities of axial and circumferential components of velocity fluctuation were measured in the TC annulus, using Laser Doppler Velocimetry (LDV), for a wide range of cylinder rotation speeds. On average, the intensities of axial velocity fluctuations were found to be within 25% of the intensities of circumferential velocity fluctuations [9]. As in Ronney et al. [5], turbulence intensities were found to be nearly homogeneous along the axial direction and over most of the annulus width, and to be linearly proportional... 

Hanni et al. (1976) described a continuous fluidized bed drier using the centrifugal principle. It consisted of a perforated horizontal cylinder rotating inside a plenum with hot air blown across the outside of the cylinder and perpendicular to the axis of rotation (Figure 1.20). Vanes placed in the air inlet allowed the incident angle of the air flow to be varied from 0° to 45° to the perpendicular. Particles were fluidized inside the Teflon-coated stainless steel cylinder which could be tilted by up to 6° in order to control particle residence time. The cylinder, of... 

C3, 12, J2, M3, S8). The amplitude of angular oscillations decreases as E increases, and a very long cylinder falls steadily to high Rey(I2, J2). If Re > 3500 (S8), motion also occurs in a horizontal plane. For relatively low y, the cylinder oscillates about a vertical axis (12, S8), while for dense particles in liquids or particles in gases the cylinder rotates continuously about a vertical axis (C3,12). A cylinder with E = 1 follows a trajectory inclined to the vertical, and tumbles in the direction of horizontal travel (12). For F < 1, the axis oscillates and rotates about a vertical line, so that the secondary motion resembles the final stages of motion of a coin spinning on a flat surface (12). 

This device contains a refractory-lined cylinder, rotating around its axis. Roasting and calcination are achieved by burning gases entering at one end of the cylinder and moving counter-current to crude material entering at the other end of the cylinder... 

Fig. 4.12 A long cylinder rotates within an outer cylindrical shell. The inner cylinder suddenly begins rotating with angular velocity Q, with the fluid in the annulus initially at rest. Also shown is a control volume illustrating the pressure and shear stresses...

One type is shown in Figure 12.2(a). They are perforated cylinders rotating at 15-20 rpm, below the critical velocity. The different-... 

It is also possible to calculate the flow path in a Couette apparatus for non-Newtonian liquids (flowing between rotating cylinders Fig. 31) (see page 56). If an inner cylinder rotates at an angular velocity co and a shear deformation takes place in the gap between the internal and external cylinder (R — i a) we observe a torque M ... 

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