Effects of Polarization on Particle-Laden Flows

Simulations of particle-laden flow with dielectric particles are carried out with varying levels of electrical charging and particle polarization. Simulation results reveal three distinct flow regions. For low particle charge and polarizability, flow is nearly symmetric and nonmeandering. For strong charging and polarization, particles form a continuous and tightly clustered sheet close to one of the walls. Between these extremes, particles form localized particle-rich regions, around which the gas executes a meandering flow. These results indicate that polarization can lead to qualitative changes in the characteristics of particle-laden flows subject to tribocharging.

Figure 1

(a) Mean particle contact coordination number $⟨Z⟩$ (number of particles contacting a given particle), as a function of the dimensionless ratio of Coulombic and gravitational forces ($e/g$) and polarizability (${\alpha }_p$). The black dashed line shows contour where average particle contact number $⟨Z⟩=0.8$. (b) Driving gas pressure difference normalized by the suspension weight [$\overline{\rho }g=(⟨{\varphi }_s⟩{\rho }_p+⟨1-{\varphi }_s⟩{\rho }_g)g$]. White line, see caption of Fig. 2. Contour plots have been smoothed and interpolated from the actual simulation values, which can be found from the Supplemental Material [31].

Figure 2

Flow behavior of nearly symmetric, meandering, and sheeted regions as a function of the dimensionless ratio of Coulombic and gravitational forces ($e/g$) and polarizability (${\alpha }_p$). (a) Color coding represents the domain-averaged slip velocity (${\tilde{u}}_{\mathrm{slip}}={\tilde{u}}_{g,z}-{\tilde{u}}_{p,z}$) normalized by the particle terminal velocity $u_t=0.432\mathrm{m}/\mathrm{s}$. Here, ${\tilde{u}}_{g,z}$ denotes the Favre-averaged gas velocity, and ${\tilde{u}}_{p,z}$ denotes the average velocity of all the particles in the domain. (b) Domain-averaged variance of the Eulerian particle volume fraction field (for Eulerian grid size $3d_p$). The black dashed line shows contour where the average particle contact number $⟨Z⟩=0.8$ [refer to 1], and the white dashed line identifies both the fastest slip between particles and fluid and the highest variability in particle concentrations. Contour plots have been smoothed and interpolated from the actual simulation values, which can be found from the Supplemental Material [31].

Figure 3

(a) Snapshot taken after 7.5 s of simulation time from $e/g=7$ and ${\alpha }_p=0$ (no polarization). Background color shows vertical fluid velocity, and particles show the local volume fraction. Yellow (green) particles have local volume fraction above (below) the average volume fraction ($⟨{\varphi }_p⟩=0.1$) and on an average tend to move downward (upward). Only every 20th particle is shown and they are magnified to 2.5 times their actual size for ease of visualization. White arrows identify the particle flow directions. Some particles appear outside the channel due to image perspective. (b) The same plot as in panel (a), but for ${\alpha }_p=3$ (largest amount of polarization). (c) Time-averaged vertical particle velocity profile for nonsheeted flow configurations. (d) Vertical particle velocity profile for the sheeted flow configuration. Solid red and purple lines show the profile for panel (a) and (b) flows, respectively. Velocity profiles are normalized by particle terminal velocity: $u_t=0.432\mathrm{m}/\mathrm{s}$. The flow patterns illustrated in the snapshots shown in panels (a) and (b) persist in time (see Supplemental Material [31]).