skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Average stress in a dilute suspension of rigid spheroids in a second-order fluid in a linear flow
The microhydrodynamics of particle suspensions in polymeric fluids has a wide range of applications in industry and biology. To discern the dynamics of particles in such systems, it is important to analyze the stress response of the suspension to applied flow fields. While such investigations have been theoretically done for suspensions of rigid spheres in weakly viscoelastic fluids, the effect of nonsphericity of particles on the stress remains relatively unexplored. The interplay between the response of the polymeric fluid and the particle orientation yields rich physics. The viscoelastic torques make the particle inhabit a preferred orientation in a given flow, resulting in time-dependent stresses. In this paper, we determine the average extra stress in a dilute suspension of rigid, non-Brownian spheroids in a second-order fluid subject to shear and extensional flows. We perform this task by examining the flow around a single spheroid in the limit of small Weissenberg number (Wi≪1) and perform an ensemble average of the stress tensor over all particle configurations. There are two contributions to the extra stress: one from the force dipole on the particles (stresslet) and another from the fluctuations in the velocity in the bulk fluid (fluid-induced particle stress), the latter of which does not arise in a zero Reynolds number Newtonian fluid. We present results for the 𝑂⁡(𝜙⁢Wi) corrections to the long-time effective shear viscosity, normal stress coefficients, and extensional viscosities in the suspension in shear, uniaxial extensional, and planar extensional flows, where 𝜙 is the particle volume fraction. To elucidate the effect of particle shape on the effective viscosity, we repeat this analysis for different aspect ratios (𝐴𝑅) for prolate (needlelike) and oblate (disklike) spheroids.  more » « less
Award ID(s):
2341154
PAR ID:
10647837
Author(s) / Creator(s):
; ;
Publisher / Repository:
American Physical Society
Date Published:
Journal Name:
Physical Review Fluids
Volume:
10
Issue:
5
ISSN:
2469-990X
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. This dataset is for the following study: Anomalous crystalline ordering of particles in a viscoelastic fluid under high shear by Sijie Sun, Nan Xue, Stefano Aime, Hyoungsoo Kim, Jizhou Tang, Gareth H. McKinley, Howard A. Stone, and David A. Weitz. In this research, the authors investigate the high-shear-rate behavior of particle suspensions in viscoelastic fluids using a fully immersed parallel plate geometry. They discover an unexpected particle separation within the suspension, leading to the formation of a crystalline layer in the center of the cell. This solid layer disrupts the flow instability and introduces a new single-frequency component to the torque fluctuations, reflecting a dominant velocity pattern in the flow. The findings reveal the complex interplay between particles and the suspending viscoelastic fluid under extreme shear conditions. The SI videos, raw data and code of postprocessing are included 
    more » « less
  2. This paper evaluates the behavior of a single rigid ellipsoidal particle suspended in homogeneous viscous flow with a power-law generalized Newtonian fluid rheology using a custom-built finite element analysis (FEA) simulation. The combined effects of the shear-thinning fluid rheology, the particle aspect ratio, the initial particle orientation, and the shear-extensional rate factor in various homogeneous flow regimes on the particles dynamics and surface pressure evolution are investigated. The shear-thinning fluid behavior was found to modify the particle’s trajectory and alter the particle’s kinematic response. Moreover, the pressure distribution over the particle’s surface is significantly reduced by the shear-thinning fluid rheology. The FEA model is validated by comparing results of the Newtonian case with results obtained from the well-known Jeffery’s analytical model. Furthermore, Jeffery’s model is extended to define the particle’s trajectory in a special class of homogeneous Newtonian flows with combined extension and shear rate components typically found in axisymmetric nozzle flow contractions. The findings provide an improved understanding of key transport phenomenon related to physical processes involving fluid–structure interaction such as that which occurs within the flow field developed during material extrusion–deposition additive manufacturing of fiber reinforced polymeric composites. These results provide insight into important microstructural formations within the print beads. 
    more » « less
  3. Understanding the orientation dynamics of anisotropic colloidal particles is important for suspension rheology and particle self-assembly. However, even for the simplest case of dilute suspensions in shear flow, the orientation dynamics of non-spherical Brownian particles are poorly understood. Here we analytically calculate the time-dependent orientation distributions for non-spherical axisymmetric particles confined to rotate in the flow–gradient plane, in the limit of small but non-zero Brownian diffusivity. For continuous shear, despite the complicated dynamics arising from the particle rotations, we find a coordinate change that maps the orientation dynamics to a diffusion equation with a remarkably simple ratio of the enhanced rotary diffusivity to the zero shear diffusion: $$D_{eff}^{r}/D_{0}^{r}=(3/8)(p-1/p)^{2}+1$$ , where $$p$$ is the particle aspect ratio. For oscillatory shear, the enhanced diffusion becomes orientation dependent and drastically alters the long-time orientation distributions. We describe a general method for solving the time-dependent oscillatory shear distributions and finding the effective diffusion constant. As an illustration, we use this method to solve for the diffusion and distributions in the case of triangle-wave oscillatory shear and find that they depend strongly on the strain amplitude and particle aspect ratio. These results provide new insight into the time-dependent rheology of suspensions of anisotropic particles. For continuous shear, we find two distinct diffusive time scales in the rheology that scale separately with aspect ratio $$p$$ , as $$1/D_{0}^{r}p^{4}$$ and as $$1/D_{0}^{r}p^{2}$$ for $$p\gg 1$$ . For oscillatory shear flows, the intrinsic viscosity oscillates with the strain amplitude. Finally, we show the relevance of our results to real suspensions in which particles can rotate freely. Collectively, the interplay between shear-induced rotations and diffusion has rich structure and strong effects: for a particle with aspect ratio 10, the oscillatory shear intrinsic viscosity varies by a factor of $${\approx}2$$ and the rotational diffusion by a factor of $${\approx}40$$ . 
    more » « less
  4. We present a numerical study of non-colloidal spherical and rigid particles suspended in Newtonian, shear thinning and shear thickening fluids employing an immersed boundary method. We consider a linear Couette configuration to explore a wide range of solid volume fractions ( $$0.1\leqslant \unicode[STIX]{x1D6F7}\leqslant 0.4$$ ) and particle Reynolds numbers ( $$0.1\leqslant Re_{p}\leqslant 10$$ ). We report the distribution of solid and fluid phase velocity and solid volume fraction and show that close to the boundaries inertial effects result in a significant slip velocity between the solid and fluid phase. The local solid volume fraction profiles indicate particle layering close to the walls, which increases with the nominal $$\unicode[STIX]{x1D6F7}$$ . This feature is associated with the confinement effects. We calculate the probability density function of local strain rates and compare the latter’s mean value with the values estimated from the homogenisation theory of Chateau et al. ( J. Rheol. , vol. 52, 2008, pp. 489–506), indicating a reasonable agreement in the Stokesian regime. Both the mean value and standard deviation of the local strain rates increase primarily with the solid volume fraction and secondarily with the $$Re_{p}$$ . The wide spectrum of the local shear rate and its dependency on $$\unicode[STIX]{x1D6F7}$$ and $$Re_{p}$$ point to the deficiencies of the mean value of the local shear rates in estimating the rheology of these non-colloidal complex suspensions. Finally, we show that in the presence of inertia, the effective viscosity of these non-colloidal suspensions deviates from that of Stokesian suspensions. We discuss how inertia affects the microstructure and provide a scaling argument to give a closure for the suspension shear stress for both Newtonian and power-law suspending fluids. The stress closure is valid for moderate particle Reynolds numbers, $$O(Re_{p})\sim 10$$ . 
    more » « less
  5. Mud is a suspension of fine-grained particles (sand, silt, and clay) in water. The interaction of clay minerals in mud gives rise to complex rheological behaviors, such as yield stress, thixotropy, and viscoelasticity. Here, we experimentally examine the flow behaviors of kaolinite clay suspensions, a model mud, using steady shear rheometry. The flow curves exhibit both yield stress and rheological hysteresis behaviors for various kaolinite volume fractions ([Formula: see text]). Further understanding of these behaviors requires fitting to existing constitutive models, which is challenging due to numerous fitting parameters. To this end, we employ a Bayesian inference method, Markov chain Monte Carlo, to fit the experimental flow curves to a microstructural viscoelastic model. The method allows us to estimate the rheological properties of the clay suspensions, such as viscosity, yield stress, and relaxation time scales. The comparison of the inherent relaxation time scales suggests that kaolinite clay suspensions are strongly viscoelastic and weakly thixotropic at relatively low [Formula: see text], while being almost inelastic and purely thixotropic at high [Formula: see text]. Overall, our results provide a framework for predictive model fitting to elucidate the rheological behaviors of natural materials and other structured fluids. 
    more » « less