Rotation Rate Of Cylinder Research Articles

Stability and chaotic advection in the eccentric Taylor problem

Theoretically, Lagrangian chaos or chaotic advection can occur by forcing a steady, two-dimensional velocity field with a time-periodic perturbation. This idea has recently been confirmed experimentally by Chaiken et al.1 and Chien et al.2 In principle, chaotic advection should also occur in a three-dimensional steady flow. To investigate this problem we constructed an eccentric Taylor–Couette apparatus with a rotating inner cylinder and a stationary outer cylinder. We obtain a 3-D steady flow in the following way. We first create a 2-D velocity field at small rotation rates of the inner cylinder by imposing a sufficiently large ecccentricity to obtain separated flow. (That is, an eddy in the region of largest gap is created by the separation of the fluid from the outer boundary and its reattachment downstream.) The inner cylinder rotation rate is then increased until Taylor vortices appear. The Taylor vortices modify the separated flow but do not destroy it. It is in this mixed Taylor vortex-separated flow regime that we carry out our studies of chaotic advection. On account of mathematical difficulties there exist few theoretical or experimental studies of stability of the flows in the eccentric geometry. We have therefore conducted numerical and laboratory experiments to identify the regions of parameter space where 3-D steady flow exists and where a transition of time dependence (i.e., 4-D flows) occurs. In our numerical work we used a commercial computational fluid dynamics program and we will report on our assessment of its accuracy in predicting the three-dimensional flow features observed in the experiments and its potential for investigating chaotic advection. In particular, we use it to find the ‘‘skeleton’’ of the flow and the fluxes between the associated regions of different flow type that it defines, and compare these with experimental observations.

Onset of secondary flow in the modulated Taylor-Couette system.

The critical Reynolds number for the linear instability of primary flow is calculated for a Taylor-Couette system in which the rotation rate of either cylinder is modulated sinusoidally in time. The method used is based on that of Hall (J. Fluid Mech. 67, 29 (1975)) and is restricted to small amplitudes of modulation but allows for a finite gap. For the case of outer-cylinder modulation, we find that the critical Reynolds number is larger than that for the unmodulated system, while, if the inner cylinder is modulated, it is smaller.

Electrodeposition of Silver Alloy Powders on Rotating and Vibrating Cathodes

SummaryA detailed study of the manufacture of Ag-Sn and Ag-Sn-Cu powder deposits at rotating cylinder and vibrating cathodes is reported. The electrolyte used was a cyanide-stannate bath. The effects of cathode potential, mass transport (rotation rate of cylinder) and temperature were examined, as well as use of K+ in place of Na+ cations. It is shown that the silver deposition process is mass transport controlled, the tin activation controlled. There is no evidence to suggest that the various components of the bath interact with one another. The full range of Ag-Sn compositions can be formed as powders, and it appears that Cu in any proportion can be included in these powders. Powders having the composition of commercially available dental amalgam alloys (Ag-28% Sn, O-30% Cu) were prepared.

Excitation of a taylor vortex mode having resonant frequency dependence of coherence length

Our experiment refers to the time-periodic “wavy mode” of the Taylor vortex system and to inner cylinder rotation rates ω i too low for its stable occurrence. Exciting the wave mode by forced motion of the boundary with frequency ω b (which may differ from he eigen frequency ω 0 of the mode), we observethe coherence length to depend resonantly on ω b − ω 0. Interpretation of our results is proposed in terms of the order parameter concept and a complex Ginzburg-Landau equation.

Sleep-deprivation: Effects on sleep and EEG in the rat

1. The vigilance states (waking, rapid eye movement (REM) sleep, and non-REM (NREM) sleep), motor activity, food intake and water intake were continuously recorded by telemetry in unrestrained rats. In addition, an amplitude measure and a frequency measure (number of zero-crossings (ZCR) per 10 s) of the telemetered EEG-signal was obtained. The animals were recorded during a control day, then subjected to 12-h or 24-h sleep-deprivation (SD) by means of a slowly rotating cylinder, and subsequently recorded for further 1–2 days. The EEG-parameters were recorded also during SD. 2. On the control day, the EEG-amplitude of NREM-sleep exhibited a decreasing trend in the 12-h light-phase (Figs. 3, 4). The occurence of slow wave sleep (SWS; defined as the NREM-sleep fraction with less than 40 ZCR/10 s) was practically limited to the first part of the light-phase (Figs. 2, 4). Cumulative plots of the zero-crossing bands (Fig. 2) revealed a prominent daily rhythm in the EEG-frequency distributionwithin NREM-sleep. 3. The percentage of NREM-sleep and REM-sleep was little affected by the 12-h SD, but the amount of SWS and the EEG-amplitude of NREM-sleep were increased (Figs. 4, 6). After a 24-h SD period terminating before light-onset, NREM-sleep was reduced and REM-sleep was markedly enhanced (Figs. 4, 6; Table 1). Both the duration and frequency of REM-sleep episodes were increased, and episodes of total sleep prolonged (Table 2). The amount of SWS was significantly more increased after 24-h SD than after 12-h SD, whereas the EEG-amplitude of NREM-sleep was enhanced to a similar extent after both SD-schedules (Tables 1, 3 Fig. 6). 4. After a 24-h SD period terminating before dark-onset, sleep (particularly REM-sleep) was enhanced in the first hours of the dark-phase, yet the usual high activity bouts prevailed in the later part of the dark-phase (Figs. 7, 8; Table 1). The extent and time-course of REM-sleep rebound was similar after the two 24-SD schedules, whereas SWS-rebound was different: SWS exhibited a one-stage rebound when recovery started in the light-phase, and a two-stage rebound when recovery started in the dark-phase (Fig. 9). 5. A comparison of the effects of 12-h SD performed with the usual and with the double cylinder rotation rate, showed only small differences, indicating that forced locomotion was a minor factor in comparison to sleep-deprivation (Fig. 10; Table 1). 6. The daily pattern of SWS on control days, and the marked increase of SWS after SD correspond to the results from other animal and human studies. It is proposed that due to the existence of an intensity dimension, NREM-sleep is finely regulated around its baseline level, and thus may be readily and accurately adjusted to current ‘needs’, whereas REM-sleep, lacking an apparent intensity gradient, is regulated around a level which is considerably below baseline. Thus, in contrast to NREM-sleep, REM-sleep compensation can occur only by an increase in the time devoted to this state, thereby curtailing the time available for other activities.

An experimental and analytical investigation of angular momentum exchange in a rotating fluid

Stimulated by considerations of the shear structure of the tropospheric jet stream, we have performed a series of experiments in a rotating vessel (using water, barotropic model) to study the angular momentum exchange in a rotating fluid. In the experiments, a cylinder was fitted in the centre of a cylindrical vessel (of large diameter) rotating around the vertical axis and could rotate independently around the same axis in both directions. The experimental results are as follows. (i) For constant relative rotation with the inner cylinder acting as a source (sink) of angular momentum, the momentum exchange becomes stationary, the bottom of the vessel being a sink (source) of momentum. The zone for this exchange is confined to a relatively small area around the inner cylinder. Beyond this zone, the ‘friction’ zone, no relative motion can be observed. Essentially the radial extent b of the ‘friction’ zone depends on the dimensionless parameter ε = Δω/ω (Δω = relative rotation rate of inner cylinder, ω = rotation rate of vessel): b(|ε|) > b(–|ε|). (ii) The velocity field shows a strong tendency to be two-dimensional, the radial and vertical components being about one to two orders of magnitude smaller than the zonal component, whose absolute value decreases monotonically from the inner cylinder to the outer limit of the ‘friction’ zone. Elementary analytical considerations indicate that inertial stability seems to be the key for the understanding of these results.

Low Reynolds number shear flow past a rotating circular cylinder. Part 1. Momentum transfer

The two-dimensional flow of an incompressible viscous fluid past a circular cylinder, symmetrically placed in a uniform shear field, is considered both theoretically and experimentally for small values of the shear Reynolds number. A series of angular rotational speeds is covered, each giving rise to a fundamentally different flow pattern. It is shown first that the Stokes solution to this problem is not entirely consistent everywhere with the linear shear boundary condition which presumably exists far from the body. Using the method of inner and outer expansions, this solution is then improved by properly taking into account the first-order effects of the inertia terms, but, surprisingly, the streamline structure in the outer region is still found to depart from that of the uniform shear sufficiently far away from the object. In spite of the somewhat bizarre nature of the theoretical solution far from the cylinder, experimental studies clearly show, however, that it accurately represents the actual flow within the inner region over a wide range of cylinder rotation rates.