Shear rate rotor-stator

The monodisperse materials described hereafter were obtained with the Couette type cell designed by Bibette et al. [ 150,159]. It consists of two concentric cylinders (rotor and stator) separated by a very narrow gap (100 pm), allowing application of spatially homogeneous shear rates over a very wide range (from 0 to 14280 s ), with shearing durations of the order of 10 s. 

The drive system of a rotational rheometer is likely to be optimized in one of two ways depending upon its preferred mode of operation. The most common form of rheometer is a controlled-rate (controlled-speed) device. This configuration is also used in most viscometers and has been around for decades. A shear rate is applied to a rotor by the motor controlling the viscometer s speed. The rotor is normally a flat plate or cylindrical cup. The stator is thus a cone or plate for the first two geometries or a cylindrical bob for the third (Figure HI. 1.1). The stator is linked to the rotor via the sample, which acts to couple the input signal like an automobile transmission. Thus, the torque on the stator when measured by a transducer is used to derive the shear stress in the sample. 

The shear created between the rotor and stator is a function of the tip speed and the gap thickness. The shear rate is given by ... 

Colloid Mills. Colloid mills are another form of rotor stator mill. A colloid mill is composed of a conical rotor rotating in a conical stator (Fig. 8.5). The surface of the rotor and stator can be smooth, rough, or slotted. The spacing between the rotor and stator is adjustable by varying the axial location of the rotor to the stator. The gap can be as little as a few hundred microns to a couple of millimeters.18 Varying the gap varies not only the shear imparted to the particles but also the mill residence time and the power density applied. Particle size is affected by adjusting the gap and the rotation rate. It is possible to produce particles in the 1-10 pm size range. 

Under high(6)the binodal is transformed to the curve for the gel-forming system. It can testify about the change of the mechanism of the phase separation of solutions. At the high shear rate the macromolecules can form the adsorbt.ion-entanglement layers on the surface of the rotor and stator [21 that can lead to the formation of the gel-like particles and, finally to the phase separation. 

Rotor/stator gap (gap width) Smaller gap increases shear forces, increases milling rate, and produces smaller particles. 

For the toothed rotor/stator mills, there are localized areas of high shear where the most energy is imparted to the particles, and breakage is believed to occur, through a combination of shear and collision. Therefore, useful parameters that quantify mill performance will reflect these effects. Three typical parameters used in rotor-stator mill scale up are tip speed (rotation rate of rotor x rotor circumference), shear rate (tip speed/distance between rotor and stator), and shear frequency (rotation rate x number of slots on rotor x number of slots on stator).Rotor-stator types typically differ in the number of rows of teeth and the number of teeth in each row of rotor and stator, though other geometric differences are possible. When rotor-stators of different design are available for study, shear frequency appears to have... 

The cold crank simulator test, ASTM D2602/IP 383, measures the apparent viscosity of an oil sample at low temperatures and high shear rates, related to the cold starting characteristics of engine oils, which should be as low as possible. The oil sample fills the space between the rotor and the stator of an electric motor, and when the equipment has been cooled to the test temperature, the motor is started. The increased viscosity of the oil will reduce the speed of rotation of the motor and indicates the apparent viscosity of the oil. The test is comparative for different oil samples rather than an accurate prediction of the absolute performance of an oil in a specific engine. 

Traditional methods of emulsification include high-pressure homogenizers, rotor-stator systems, and ultrasound homogenizers [110, 111], The first two examples employ high mechanical shear rates to produce small droplets of the... 

The apparatus consists of a bell-shaped rotor and a stator which is thermostatted. Both filling the cell with polymer solution and running the experiment can be done under an atmosphere of nitrogen. Small samples may be taken directly above the gap with a syringe inserted through the septum. Control experiments analyzing the entire solution proved that correct results can be thus obtained. For Newtonian fluids the mean value of the shear rate y for the device shown in Fig. 1 may be calculated by ... 

The cell has two concentric rotating and fixed cylinders fitted with a syringe pump containing the premixed polydisperse emulsion. The inner cylinder is connected to a motor of variable speed and acts as the rotor, while the fixed outer cylinder is the stator. At high shear rates, the pre-mix emulsion pushed through the system by the syringe pump is converted to narrow size distribution emulsions. 

Because of the problem of sealing at both ends, this so-called ribbon viscometer can only be realized for materials of extremely high viscosity. The properties of a ribbon viscometer are shown to a good approximation by a rotation viscometer of the Couette type (see Section 9.5.2). In Couette viscometers, a rotor revolves around a stator (or vice versa). The viscous liquid lies between the rotor and the stator. If the space between them is sirfficiently narrow, the shear rate is constant across the whole distance between rotor and stator (Figure 7-4). 

Since the effects of shear stress are particularly strong in the case of rodlike macromolecules, rotation viscometers are frequently used for measurements on substances such as deoxyribonucleic acid (Figure 9-23). With a sufficiently low rotational speed and a narrow gap between rotor and stator, a linear shear-rate gradient can be produced between the rotor and stator of a rotation viscometer. With such narrow gaps between rotor and stator, the centering of rotor in the stator (or, in some viscometers, vice versa) is particularly important. In rotation viscometers of the Couette type, centering is achieved by use of a mechanical axis. A much better centering system is used in the Zimm-Crothers viscometer. This utilizes... 

Rotational rheometer n. An instrument for measuring the viscosity of molten polymers (any many other fluid types) in which the sample is held at a controlled temperature between a stator and a rotor. From the torque on either element and the relative rotational speed, the viscosity can be inferred. The most satisfactory type for melts is the cone-and-plate geometry, in which the vertex of the cone almost touches the plate and the specimen is situated between the two elements. This provides a uniform shear rate throughout the specimen. It may be operated in steady rotation or in an oscillatory mode. 

Fig. 3.9 a-f. Zimm-Crothers viscosimeter for low shear rates and strongly shear thinning fluids a test fluid b stator with temperature control liquid c rotor d rotating magnet e photo diode f light source... 

The power density Py is the characteristic quantity of turbulent flow. It determines the size of the smallest eddies and the intensity of microturbulence. In addition, it is a measure of the shear intensity in laminar flows or the intensity of cavitation in ultrasonic fields (see above). The power input P in the dispersion zone can be derived from the pressure drop (e.g. in pipes and nozzles) or can be measured caloricafly (e.g. for rotor-stator systems and ultrasonication Pohl 2005 Kuntzsch 2004). Additionally, P can be roughly approximated by the electric power consumption of the dispersion machine (e.g. for ultrasonication Mandzy et al. 2005 Sauter et al. 2008), even though the real values may be lower by a factor of 2 to 5. A further source of uncertainty is the volume of the dispersion zone (Vdisp). since the stress intensities are not uniformly distributed in dispersion apparatuses. In particular, this applies to agitated vessels, where the highest dissipation rates are obtained in the vicinity of the stirring instmment (Henzler and Biedermann 1996),... 

Copredpitation Batch mode vs. continuous mode Flow rate Droplet size distribution Mixer design (shear and energy, e.g., stir bar, vortex, propeller, homogenizer, rotor-stator) Solvent to antisolvent ratio Temperature Processing times (scale dependent)... 

Crystallinity Impurity Solvate Incomplete dissolution pH Temp Amount Miscibility w/solvent Mixer type(high-shear in-line versus suspended mixer homogenizer) Mixer design Rotor/stator design and gap Tip speed S/AS flow rates and ratio Batch size Processing time Temperature Too slow Incomplete removal of solvent Temp. Time Air flow Humidity Shear/temp Milling mechanism... 

For turbulent flow through rotor-stator devices with teeth, the aforementioned velocity field results indicate that flow stagnation on the leading edge of the downstream stator teeth provides a major energy field for emulsification and dispersion. It is not clear from these results what role is played by flow in the shear gap. The simulations indicate that the flow in the rotor-stator gap is not a simple shear flow but is more like a classical turbulent shear flow. Use of nominal shear rate may not be useful in scale-up. 

Although rotor-stator mixers can pump to some extent, it is preferred to use a pump to control the feed rate to the mixer. This way, one does not need to vary the rotor speed to control the flow rate. Instead, the rotor speed can be varied to control the energy input, turbulent kinetic energy, and shear rates in the device, independent of the flow rate. To prevent equipment failure, it is also important to ensure that the unit is fully flooded and not starved during operation. 

Vendors often design and scale-up rotor-stator mixers based on equal rotor tip speed, Vtip = kND, where N is the rotational speed of the rotor and D is the rotor diameter. This criterion is equivalent to equal nominal shear rate in the rotor-stator gap, y- In niost industrial rotor-stator mixers, the shear gap width S, remains the same on scale-up, making the two criteria equivalent. 

The nominal shear rate in the rotor-stator gaps is calculated as follows ... 

It is important to recall from the discussion above that for turbulent flow the actual shear rate in the rotor-stator gap varies substantially from y. and that gap shear rate does not directly control power draw and dispersion. However, tip speed may control turbulence characteristics, especially if the spacing between stator elements (teeth or stator openings) as well as the shear gap width do not change on scale-np. 

---