Laser Doppler velocimetry measurements of particle velocity fluctuations in a concentrated suspension

Abstract

Recent statistical constitutive models of suspensions of neutrally buoyant, non-Brownian, noncolloidal, solid spheres in Newtonian fluids suggest that the particles nijgrate in response to gradients in "suspension temperature," defined as the average kinetic energy contained in the particle velocity fluctuations. These models have not yet been compared systematically with experimental data.In addition, the "temperature" models assume isotropic particle velocity fluctuations, since the "suspension temperature" is given as a scalar, in analogy to molecular systems. However, highly anisotropic particle velocity fluctuations have been observed in settling suspensions, which suggests that a "suspension temperature" tensor would be more realistic.We used laser Doppler velocimetry (LDV) to make a set of experimental observations of particle velocity fluctuations arising from inter-particle collisions in a concentrated non-colloidal suspension under nearly homogeneous shear flow in a narrow-gap concentric cylinder Couette device. We compared the relative sizes of the fluctuating velocity components and observed the variation of each component with particle volume fraction, shear rate, and radial position. In addition, we assessed the implications of these observations for suspension temperature models.The data indicate that the suspension temperature is anisotropic. The flow direction component is overwhelmingly the largest at every concentration and shear rate, followed by the neutral and then the gradient components. Meanwhile, each fluctuating velocity component demonstrates a distinct variation with the shear rate and with the particle volume fraction, but only slight variation with radial position, over the region of the flow accessible to measurement.Comparison between model predictions and measured shear rate and particle volume fraction profiles shows that several models capture the measured profiles qualitatively but not quantitatively, with better agreement for moderately concentrated suspensions than for highly concentrated suspensions. Also, comparison between predicted scalar suspension temperature profiles and the sum of the measured velocity fluctuation components demonstrates that most of the models underpredict the sum of the temperature components by a large factor. Finally, comparison among the models shows that the models are quite sensitive to the choice of transport coefficients that are functions of the particle volume fraction.

Microstructure and velocity fluctuations in sheared suspensions

“…Specifically, the component of the temperature in the direction of flow was found to decrease with concentration, that in the direction of the gradient stayed constant, while that in the vorticity direction initially increased in magnitude with increasing concentrations and then decreased for concentrations larger than 40%. Finally, and most surprisingly, Shapley et al (2002) found that, whereas the fluctuations in the direction of the flow increased linearly with shear rate (as expected for any flow in the Stokes regime), the STD in the vorticity direction increased non-linearly, while that in the gradient direction slightly decreased with shear rate.…”

“…Even an apparently very simple case, that of determining the dependence on the shear rate of the velocity fluctuations in simple shear flows, remains a matter of some controversy (Shapley et al 2002). What is clear is that, although the suspension might be homogeneous at macroscopic scales, the continuous rearrangements in the suspension microstructure and the corresponding hydrodynamic interactions between particles lead to fluctu-ations in the particle velocities about their mean values, in both the transverse and the flow directions.…”

“…In addition, Lyon & Leal (1998) estimated the contribution from the mean particle rotation to be one order of magnitude lower than the velocity fluctuations resulting from interparticle interactions, and based upon this argument neglected its effect. Shapley et al (2002) explicitly computed the contribution of the average rotation of the spheres to the measured velocity fluctuations, but also concluded that its magnitude was negligible compared to the fluctuations resulting from collisions between particles. However, the spurious contributions to the measured velocity fluctuations originating from the mean angular velocity in the vorticity direction are independent of concentration in the dilute limit, and moreover, we have shown earlier that, again in the dilute limit, the angular velocity fluctuations are proportional to the volume fraction.…”

“…Lyon & Leal (1998) measured the timeaveraged local STD in the direction of the flow, for concentrated suspensions flowing in a two-dimensional rectangular channel, and also found a linear dependence on the volumetric flow rate. Shapley et al (2002) presented the first detailed measurements of the velocity fluctuations in both the transverse and the flow directions, as well as of the dependence of the suspension temperature on the volume fraction and shear rate, for suspensions undergoing simple shear flow in a Couette device. Their results stress the difficulties encountered in such measurements and the discrepancy among different experimental results.…”

“…Unfortunately, and in contrast to the well-studied sedimentation problem, velocity fluctuations in sheared suspensions have received little attention thus far. In recent experiments, Averbakh et al (1997); Shauly et al (1997); Lyon & Leal (1998) and Shapley et al (2002) used laser-Doppler velocimetry (LDV) to measure the velocity fluctuations in concentrated suspensions of monodisperse spheres. Averbakh et al (1997) and Shauly et al (1997) measured such velocity fluctuations in rectangular ducts and found that the STD's, both along and transverse to the flow, depend linearly on the shear rate (or on the maximum velocity inside the rectangular channel), as expected in the Stokes limit †.…”