Spherical Particles In Newtonian Fluid Research Articles

Forced convective heat transfer from spheres to Newtonian fluids in steady axisymmetric flow regime with velocity slip at fluid–solid interface

The heat transfer phenomenon of spherical particles in Newtonian fluids with velocity slip and uniform thermal boundary condition at the fluid–solid interface has been numerically investigated using a computational fluid dynamics (CFD) based in-house solver. At the interface linear slip velocity boundary condition has been adopted. The dimensionless continuity, momentum and energy equations along with the appropriate non-dimensional boundary conditions are solved by a segregated approach. This numerical procedure is a finite difference method based CFD solver implemented on a staggered grid arrangement in spherical coordinates. The convective and diffusive terms are discretized using the quadratic upstream interpolation for convective kinematics and a second order central differencing scheme respectively. Prior to obtaining new results, the present numerical solver is extensively validated by comparing the present values of the average Nusselt numbers with the existing literature values for either extreme values of the slip conditions, i.e., for fully slip and no-slip conditions. Further new results are obtained over the range of conditions as the Reynolds number, Re = 0.1–200; the Prandtl number, Pr = 1–100; and dimensionless slip parameter, λ = 0.01–100. The effects of these parameters on the isotherm contours and the local and average Nusselt numbers are thoroughly discussed and finally on the basis of present numerical results (196 data points), an empirical correlation is proposed for the average Nusselt numbers of single spheres with velocity slip at the interface as function of Re, Pe, and λ.

Simulating the interactions of two freely settling spherical particles in Newtonian fluid using lattice-Boltzmann method

The interactions of two freely settling spherical particles in a three dimensional channel are investigated employing the lattice-Boltzmann method with discrete external boundary force (LBM-EBF). By changing the initial separation distance and relative angle between the two particles, a comprehensive analysis about the impact of various parameters on the dynamics of the particle motion and particle–particle interactions is made. The terminal Reynolds numbers based on the diameter of particle and the terminal vertical velocity is about O(100). Three different regimes are identified in the two particles settling system: repulsion, attraction and transition regime. Each regime depends on the initial separation distance and the relative angle of the two particles. The general trend is that the smaller the initial angle, the more likely interaction between them is repulsion. On the contrary, the larger the initial angle, the more likely interaction is attraction. Further, the translation and the rotation of the particles as well as the long-body particle pair behavior and some flow patterns are systematically investigated.

Microstructure and rheology of finite inertia neutrally buoyant suspensions

AbstractThe microstructure and rheological properties of suspensions of neutrally buoyant hard spherical particles in Newtonian fluid under finite inertia conditions are studied using the lattice-Boltzmann method (LBM), which is based on a discrete Boltzmann model for the fluid and Newtonian dynamics for the particles. The suspensions are subjected to simple-shear flow and the properties are studied as a function of Reynolds number and volume fraction, $\phi $. The inertia is characterized by the particle-scale shear flow Reynolds number $\mathit{Re}= {(\rho \dot{\gamma }a^{2})/\mu }$, where $a$ is the particle radius, $\dot{\gamma }$ is the shear rate and $\rho $ and $\mu $ are the density and viscosity of the fluid, respectively. The influences of inertia and of the volume fraction are investigated for $0.005\leqslant \mathit{Re}\leqslant 5$ and$0.1\leqslant \phi \leqslant 0.35$. The flow-induced microstructure is studied using the pair distribution function $g(\boldsymbol {r})$. Different stress mechanisms, including those due to surface tractions (stresslet), acceleration and the Reynolds stress due to velocity fluctuations are computed and their influence on the first and second normal stress differences, the particle pressure and the viscosity of the suspensions are detailed. The probability density functions (PDFs) of linear and angular accelerations are also presented.

Cell models for suspension viscosity

Abstract Cell models for the viscosity μ of a suspension of spherical particles in Newtonian fluid of viscosity μ 0 are discussed. Various boundary conditions on the outer boundary of the spherical cell lead to different results: the viscosity predicted for a zero velocity perturbation boundary condition is higher than those predicted with zero tangential stress perturbation. However, in all cases Einstein's prediction μ / μ 0 = 1 + 2.5 φ + ⋯ holds in the limit of small solid volume fraction φ ⪡ 1 .

The application of dynamic clustering data to the sedimentation rates of concentrated suspensions

A modified Stokes equation is proposed for the settling of concentrated suspensions of spherical particles in Newtonian fluids. The proposed hindered settling model was derived semi-analytically incorporating data obtained on dynamic particle clustering in concentrated suspensions by Graham and Bird. The approach differs from previous models which either neglected the influence of one particle on another or treated these interactions in an empirical manner with minimal physical or mechanistic basis for their design. The phenomenon of dynamic clustering which has recently been observed experimentally and shown to occur in flowing suspensions and sedimentation provides the basis for this study. Cluster size distributions are estimated based on suspension properties and a summation of Stokes terms provides a settling velocity prediction of concentrated systems. The validity of the model is supported by comparing calculated sedimentation rates with measured values for a number of data sets obtained from a variety of different authors.