Migration of buoyant particles in low-Reynolds-number pressure-driven flows

Abstract

Neutrally buoyant particles in low-Reynolds-number pressure-driven suspension flows migrate from regions of high to low shear, and this migration is a strong function of the local concentration. When the particle density differs from that of the suspending fluid, buoyancy forces also affect particle migration. It is the ratio between the buoyancy and viscous forces, as quantified by a dimensionless buoyancy number, which determines the phase distribution of the suspension once the flow is fully developed. Although several experiments have verified shear-induced particle migration in neutrally buoyant suspensions, data for particle migration when buoyancy effects are important are scarce. Electrical impedance tomography (EIT) is used here to non-invasively measure particle concentration across a pipe arising from the low-Reynolds-number flow of heavy conducting particles and light non-conducting particles in a viscous suspending fluid. A range of buoyancy numbers was investigated by varying the flow rate. In all of the experiments, a significant fraction of the particle phase was observed to migrate towards the top or bottom of the pipe, depending on the relative density of the particles. The amount of migration away from the centre of the pipe increased with increasing magnitude of the buoyancy number. Furthermore, observations of the phase distribution at several positions downstream of the inlet indicate that these suspension flows become fully developed earlier than that observed for neutrally buoyant particles. A scaling analysis for the prediction of the fully developed length is presented, which predicts shorter lengths for higher buoyancy numbers and is consistent with experimental observations. The experimental data were compared to an isotropic suspension balance model, and it was found that the particle phase distributions predicted by this model agree fairly well with the experimental observations.

The dam-break problem for concentrated suspensions of neutrally buoyant particles

“…a scaling that is close to the relation obtained by Nott & Brady (1994) and Norman, Nayak & Bonnecaze (2005) except for the weighting coefficient (Nott & Brady (1994) established thatt ss ≈ H 3 * /(a 2ū ) in its dimensional form). We solved the evolution equation (2.17) numerically by assuming a no-flux condition at the boundaries ( j = 0 at y = 0 and y = h) and a uniform profile as the initial condition (φ =φ at t = 0).…”

Normal stress-driven migration and axial development in pressure-driven flow of concentrated suspensions

“…This is a result of the form of the radial migration flux, which in cylindrical coordinates has form j ⊥, r ∼ (∇ · P ) r = ∂Σ P,rr /∂r + N 2 /r, and the relevance to the prediction of particle concentration evolution along the flow axis is illustrated by comparing the marching method approximations of the particle conservation equations, (16) and (17) for the channel and pipe, respectively. While normal stress differences are known to have a role in curvilinear flows, here the relevance is seen in pipe flow.…”

“…doi:10.1016/j.jnnfm.2005. 11.009 perimental data on the axial development in a neutrally buoyant suspension; Norman et al [16] have recently published a study describing axial variation of the flow of particles both more and less dense than the suspending fluid, with comparison to their own calculations using a model similar to that described here. Little prior attention has been given to modeling the development of the φ profile and the associated changes to the velocity field and axial pressure variation.…”

The suspension balance model revisited

“…However, the normal stress differences of the particle phase are not the same as that of the suspension. The numerous studies [19][20][21][22][23][24][25][26][27] that have used and extended the SBM have retained the error of equating ͗ h ͘ p with ⌺ h͑p͒ . The outline of this paper is as follows.…”