A rotating sphere viscometer

Abstract

synopsisThe use of a rotating sphere viscometer for the measurement of parameters in the flow curves of inelastic as well as viscoelastic liquids is examined. An experimental investigation of the primary flow around a sphere rotating in Newtonian and viscoelastic liquids is carried out by using a new "three-dimensional particle technique." Currently available theoretical analyses of rotation of a sphere in viscoelastic liquids are shown to be inadequate to describe the experimental primary velocity distribution data. Theoretical results for the primary distribution derived on the basis of a creeping flow of a power law liquid are found to describe the experimental data well. This distribution is then used to derive torque-angular velocity relationships, which are then confirmed experimentally for both inelastic and viscoelastic liquids. The results of this work justify the use of a rotating sphere viscometer as a useful tool for the measurement of parameters of flow curves of inelastic and visccelastic liquids.

Viscoelastic Liquids in Stirred Vessels – Part I: Power Consumption in Unaerated Vessels

“…In this zone, the results drawn from the literature vary greatly from one author to another. For instance, a small reduction of the power number is observed by Kelkar et al [9] in the laminar region, while Oliver et al [12] observed an enhanced power number for Re < 3 followed by a reduction, leading to a wavy appearance of the power curve over the entire laminar zone. Conversely, some authors, such as Collias and Prud'homme [13], Prud'homme and Shaqfen [14], or Böhme and Stenger [8], report an increase of the power dissipated in a laminar flow in the presence of elasticity.…”

“…Finally, the choice of the shear rate at which dimensionless numbers, such as the Reynolds or the elasticity numbers, are calculated, is another source of variations between results of different articles. As an example, in the Deborah number, the natural time of the fluid can be measured at an arbitrary shear rate or shear stress (Metzner-Otto shear rate in the case of Kelkar et al [9]; _ c = 2 s ±1 in the case of Seyssiecq et al [11], s = 1 Pa in the study of Böhme and Stenger [8]). In contrast, the use of a Weissenberg number requires to calculate the first normal stress difference, at the same shear rate than the one for which the apparent viscosity is evaluated (generally the Metzner-Otto shear rate).…”

“…Different authors have thus used the term of viscosity number for a Deborah number and elasticity number for a ratio V is /Re [8]. Other authors have used the term of Weissenberg number for a Deborah number ( [9,10]). Even when authors have chosen to work with a given dimensionless number, there are several possibilities to express the natural elastic time k, depending on the rheological method chosen to measure it (in particular, oscillatory, relaxation or normal stress difference measurements).…”

“…Some authors have thus proposed dimensionless correlations to account for the effect of the elasticity on the power curve. Most of the time, these equations express Np as a function of Re and a dimensionless group characterizing elasticity, such as a Weissenberg number ( [1,10]), a Deborah number ( [11,31]) or an elasticity number ( [9,32]). However, it should be underlined that most of these correlations have been established for a single flow regime (often the laminar one) and working with constant shear viscosity elastic fluids.…”

Shear-thinning and constant viscosity predictions for rotating sphere flows

“…Using this method, Manero and Mena (1978) acquired values of the second normal stress-difference; such findings lay in good agreement with the values obtained through other methods. In addition, some authors, such as Mashelkar et al (1972), Kelkar et al (1973), Acharya and Maaskant (1978), have used the torque as a function of rotation-speed, to assess the elastic-viscous parameters of some fluids. One of the most common difficulties in the effective use of torque measurements lies in the elimination of wall-effects, which may also affect the development of diverse flow patterns.…”