Migration of particles undergoing pressure-driven flow in a circular conduit

This study focuses on the demixing of neutrally buoyant suspensions of spheres during slow, pressure driven flows in circular conduits. Distributions of the solid fraction of particles, φ, and the suspension velocity, ν, are measured at different lengths from a static in-line mixer. Experiments were conducted over a range of volume average solids fractions, $φbulk (0.10⩽φ⩽0.50),$ and at two different ratios of the particle radius, $a,$ to the radius of the circular conduit, $R$ (⁠$a/R=0.0256$ and $a/R=0.0625$⁠). At $φbulk⩾0.20,$ the particles rapidly migrate to the low-shear-rate region in the center of the conduit. This migration results in a blunting of the ν profile, relative to the parabolic profile observed in homogeneous Newtonian fluids. For the flow geometry with the smaller ratio of $a/R,$ the φ profile builds to a sharp maximum or cusp in the center. Particle structures are observed in the experiments with the higher $a/R.$ The entrance lengths for the development of the φ and ν fields, $Lφ$ and $Lν,$ respectively, are strong functions of $a/R$ and $φbulk.$ $Lφ$ and $Lν$ rapidly decrease as φ and $a/R$ increase. Over the range of our data, the ν profiles are observed to develop more rapidly than the φ profiles. The experimental results are compared with fully developed flow predictions from the shear-induced migration (SIM) model and the suspension balance (SB) model. At the smaller $a/R,$ the SIM model more accurately predicts the experimental results. At larger $a/R,$ some qualitative features of the experimental results are better predicted by the SB model, however, neither model provides good quantitative predictions, especially at low $φbulk.$