Sinusoidal fluid motion

Viscoelastic fluids that are more concentrated are characteri2ed with devices that are similar to the rotational viscometers described previously. However, instead of constant rotational motion in one direction, a sinusoidal oscillatory motion is provided. Some instmments allow both viscosity and viscoelastic measurements. 

Rheometric Scientific markets several devices designed for characterizing viscoelastic fluids. These instmments measure the response of a Hquid to sinusoidal oscillatory motion to determine dynamic viscosity as well as storage and loss moduH. The Rheometric Scientific line includes a fluids spectrometer (RFS-II), a dynamic spectrometer (RDS-7700 series II), and a mechanical spectrometer (RMS-800). The fluids spectrometer is designed for fairly low viscosity materials. The dynamic spectrometer can be used to test soHds, melts, and Hquids at frequencies from 10 to 500 rad/s and as a function of strain ampHtude and temperature. It is a stripped down version of the extremely versatile mechanical spectrometer, which is both a dynamic viscometer and a dynamic mechanical testing device. The RMS-800 can carry out measurements under rotational shear, oscillatory shear, torsional motion, and tension compression, as well as normal stress measurements. Step strain, creep, and creep recovery modes are also available. It is used on a wide range of materials, including adhesives, pastes, mbber, and plastics. 

Sinusoidal oscillations of the continuous phase cause levitation or countergravity motion much more readily for gas bubbles, due to changes in bubble volume which cause a steady component in the pressure gradient drag term (Jl, J2). If the fluid motion is given by Eq. (11-49), the pressure in the vicinity of the bubble also varies sinusoidally. For normal experimental conditions, the resulting volume oscillations are isothermal (P2), and given by (Jl) ... 

There is conflicting evidence regarding the extent to which imposed vibrations increase particle to fluid heat and mass transfer rates (G2), with some authors even claiming that transfer rates are decreased. For sinusoidal velocity variations superimposed on steady relative motion, enhancement of transfer depends on a scale ratio A/d and a velocity ratio Af /Uj (G3). These quantities are rather like the scale and intensity of turbulence (see Chapter 10). For Af /Uj < l/2n, the vibrations do not cause reversal in the relative motion and the enhancement of mass transfer has been correlated (G3) by... 

Because of the high amplitudes of particle motion in the fluid due to (1) and (2), nonlinear acoustic effects can be important. In particular, acoustic streaming can occur, so that a propagating sinusoidal wave produces a steady ( zero frequency ) force in the direction of wave propagation. This steady force causes fluids in contact with the membrane to move. 

The shear rate at the VSEP membrane is created by the inertial-induced relative motion of the fluid, and can be of the order 10 s The shear rate varies sinusoidally and increases proportionally with local membrane azimuthal displacement to radius. The maximum shear rate at the periphery can be related to the vibrating frequency (F) and the membrane displacement at the periphery (d) by the following equation [66] ... 

When the outer cylinder undergoes a very small sinusoidal oscillation in a tangential direction, this motion causes the inner cylinder, suspended by a torsion wire, to oscillate with the same frequency but with different amplitude and phase. The viscoelastic properties of the fluid can be determined by the expressions (Bird et al, 1987)... 

Aside from the simple shearing motion, the response of visco-elastic materials in a variety of other well-defined flow configmations including the cessation/initiation of flow, creep, small amplitude sinusoidal shearing, etc. also lies in between that of a perfectly viscous fluid and a perfectly elastic solid. Conversely, these tests may be used to infer a variety of rheological information about a material. Detailed discussions of the subject are available in a number of books, e.g. see Walters [1975] and Makowsko [1994]. 

The deep-channel viscometer could also be adapted for measurement of the nonlinear interfacial rheological behaviour of the film [52]. In this case several small tracer particles are placed on the fluid interface at different radial positions and the angular velocities are determined from measurements of the period of revolution. When used to measure viscoelastic properties, the deep-channel viscometer is operated in an oscillatory mode, in which case the floor of the viscometer is oscillated sinusoidally. Simultaneous measurements of the phase angle between the surface motion and the oscillating motion of the bottom dish, and the surface-to-floor amplitude ratio, may permit determination of the viscoelastic properties of the fluid interface, presuming knowledge of an appropriate rheological model [52]. 

In oscillatory shear flow, a sinusoidal strain is imposed on the fluid under test. If the viscoelastic behavior of the fluid is linear, the resulting stress will also vary sinusoidally, but it will be out of phase with the strain, as schematically shown in Figure 5.5. Since the sinusoidal motion can be represented in the complex domain, the following complex quantities may be defined ... 

---