K. Wichterle

Calibration of electrodiffusion friction probes using a voltage-step transient

Voltage-step transient experiments are used to calibrate electrodiffusion (ED) friction probes. The approach is demonstrated on the probes in high-speed rotating impellers. This calibration has shown that shear rates as high as 106s-1 can be measured reliably using 0.5mm Pt working electrodes in ferro/ferricyanide aqueous solutions. The complete transient calibration experiment provides sufficient information about the dynamics of ED friction probes.

SHEAR RATES ON TURBINE IMPELLER BLADES

Shear rates on the front side of a turbine impeller blade have been measured by an electrochemical method. The values obtained for water, CMC solutions and a kaoline suspension have been found to be in general higher than assumed so far. The data agree (for ReM > 10) satisfactorily with the predictions from the laminar boundary layer solutions for the flow of power-law fluids around rotating disks

Conditions for suspension of solids in agitated vessels

Abstract Though much has been done in the examination of the critical impeller speed, NJS, just necessary for suspension of solid particles, any theory available does not fit well the data for a wide range of variables. An attempt is made to develop a theoretical model of the process based on the comparison of the terminal velocity of a particle and the characteristic velocity of the agitated liquid round the particle at the bottom. The velocity field near the bottom is deduced from the values of local shear rates as estimated before by an electrodiffusion method. Literature data on NJS indicate that the model is acceptable even under extreme conditions. The dependence of the normalized critical impeller speed, NJS*, on the normalized particle diameter, dp*, is NJS* = {(BJS/Amin)[dp*/(18 + 0.6dp*3/2)]}2/3 where Amin is a constant assumed to be dependent on geometrical simplexes of the mixing equipment only. BJS is a constant which may depend on the particle shape. The model even explains effects of other variables such as impeller and tank diameters, liquid viscosity, and densities. Some of these effects cannot be interpreted by a single-power function valid for a wide range of dp* covering industrially important problems of the solid suspension.

Drop breakup by impellers

Abstract Drop breakup in agitated vessels is one of the most important processes taking place in agitation of immiscible liquids. Suitability of a particular mixing equipment for liquid dispersion is usually studied in systems with very low fraction of the dispersed phase. Under such circumstances, the drops do not affect significantly the flow of the continuous phase, and interactions of individual drops occur rarely. In this paper, we estimate the forces acting on an isolated drop in agitated liquids from a hydrodynamic point of view. Actual shear rates in the impeller region predicted theoretically from the boundary layer theory and checked by a direct measurement are assumed to control the process. A new scaling procedure for predicting the equilibrium drop diameter is developed, and its results are confronted with existing experimental data.

SHEAR STRESSES ON THE WALLS OF AGITATED VESSELS

Abstract Characteristics of flow near the walls of baffled vessels equipped with a six blade Rushton type turbine were measured by an electrochemical method. A directionally sensitive probe was used for determination of velocity gradient vector fields. It was found that the flow conditions near the wall could be described by a meridional profile of the friction coefficient. An extensive set of experimental data obtained by the limiting current technique showed that the profile depends on the Reynolds number, on the flow index of the (power-law) fluids and on the d/D simplex. The maximum values of the friction coefficient characterizing flow near the impeller plane can be correlated by a simple relation of the laminar boundary layer type.

Breakup of Bubbles Rising in Liquids of Low and Moderate Viscosity

ABSTRACT The breakup rate of bubbles was studied by observing them rising in water and in glycerol solutions with μ = 1–32 mPas. A levitating technique was applied with bubbles seized in the downstream liquid flow of a diverging channel. Bubbles with volumes V B = 0.2–0.8 cm3 are generally spheroid but their shape pulsates. As they wobble they have a tendency to split. The exponential decay of the number of unbroken bubbles was found, which has been characterized quantitatively by a half-life, t 1/2. The rate of breakup increased significantly with the original size of the bubble. By regression of experimental data, the proportionality t 1/2 ∼ V B −4 has been determined. There is a significant effect of surface tension, while the effect of viscosity on the process appeared to be negligible in the bubble Reynolds number range of 60–3000 that was investigated.

Electrodiffusional flow diagnostics in a centrifugal pump

This paper presents electrodiffusional measurements of the wall shear rate at the impeller surface of a radial centrifugal pump. Twelve probes of different radii and at different positions along one blade were used in a pump with an open six bladed impeller. By means of throttling and speed control the operating point of the pump was adjusted and the influence on the wall shear rate was studied. The measurements were related to the analytical solution for a free rotating disc and the shear gradients were in the same order of magnitude.

Bestimmung der Parameter des Potenzansatzes nach Ostwald-de Waele aus rheometrischen Messungen an einem Viskosimeter mit schnellrotierender Scheibe

ZusammenfassungFür die Bestimmung der Parameter desOstwaldde Waeleschen Modells zeigte sich die AbhÄngigkeit zwischen dem Momentkriterium und derReynolds- Zahl bei der Rotation einer Scheibe in einer nicht-Newtonschen Flüssigkeit, die durch Lösung der entsprechenden Bewegungsgleichungen unter der Voraussetzung „Ähnlicher“ Geschwindigkeitsprofile gewonnen wurde, als geeignet.Der Gültigkeitsbereich dieser theoretisch berechneten AbhÄngigkeit wurde mit Hilfe experimenteller Daten bestimmt.Für die rasche Bearbeitung der aus Messungen mit einem Viskosimeter mit rotierender Scheibe gewonnenen Daten wurde eine graphische Methode für die Berechnung der rheologischen Parameter ausgearbeitet.

On bubble rising in countercurrent flow

A single bubble of typical volume 20 mm³ ≤ VB ≤ 400 mm³ was placed in downward conically diverging flow of low and moderate viscous liquids (aqueous solutions of glycerine and of electrolytes (NaCl, Na3PO4, MgSO4), and butanol). Experiments were performed over a range of Reynolds number 60≤Re≤2200, Weber number 1≤We≤14, Tadaki number 1≤Ta≤10, Eötvös number 1≤Eo≤22, and bubble aspect ratio 0.4≤b/a≤0.9. The bubble shape, bubble position and motion were investigated by direct observation of two plane projection of bubble by high speed camera. Typical sampling frequency was 150 fps. Relatively long records, (approximately 9000 frames per one bubble observation) allow us to get relevant statistics of treated data. Bubble aspect ratio has been determined from both projection planes. Dimensionless front area of observed bubble has been introduced as suitable parameter for correlation with Eötvös number. Model of static bubble and classical Wellek correlation were employed as asymptotes. Bubble rising velocity has been determined and tested for each single bubble with respect to liquid properties. Velocity data are plotted within the frame given by several theoretical predictions for pure and contaminated liquids. Dimensional analysis is used considering viscosity and surface tension effect. New simple correlation of bubble rising velocity separating the effects of viscosity and surface tension is presented.

Asymmetric deformation of bubble shape: cause or effect of vortex-shedding?

Two perpendicular projections of rising bubbles were observed in counter-current downstream diverging flow. Evidently, the bubbles did not enter the boundary layer at the channel wall and a plug liquid flow assumption was acceptable in our experimental equipment. This confirmed that the experiment was appropriate for simulation of bubble rises in a quiescent liquid column. Recent data obtained by a high-speed camera permitted recording over a period of 60 s. Image analysis by a tailor-made program provided a time-series of quantities related to the position, size, and shape of bubbles. In addition to determination of the aspect ratio of the equivalent oblate ellipsoid, deviation from this shape was investigated in respect of the difference between the bubble’s centre of mass and the geometrical centre of bubble projection. Autocorrelation of the data indicated that the bubble inclination oscillated harmonically with a frequency of 5–10 Hz; cross correlation showed that the horizontal shift of the centre of mass, as well as the horizontal velocity, increased with increasing bubble inclination, and the vertical shift of the centre of mass increased with an increases in the absolute value of the bubble inclination. There is no significant phase shift in the oscillation of these quantities. The bulky bottom side of the bubbles is in accordance with the model of bubble oscillation induced by instability of the equilibrium of gravity and surface tension forces. The oscillation frequency dependence on surface forces (Eötvös number) is evident, while viscosity does not play a significant role in low-viscosity liquids. Therefore, vortex-shedding is more likely to be an effect of the oscillation and not its cause.