| Summary: | <p> The inertial flow of suspensions of neutrally buoyant particles in Newtonian and power law non-Newtonian fluid through bifurcating channels is studied experimentally and by computational methods. First detailed single phase flow behavior in ‘asymmetric T’ and ‘symmetric T’ is studied using finite element method where distinct features arising due to three dimensionality are examined thoroughly.</p><p> For suspension studies, the primary geometry considered is an ‘asymmetric T’: flow in the entering branch divides to either continue straight or to make a right angle turn. All branches are of the same square cross section (<i>D</i><sub>0</sub> = 2.4 mm on a side in the experiments) and have equal lengths from the midpoint of junction subjected to equal pressure at outlets. Thus each downstream branch experience equal Δ<i>P </i>/Δ<i>L</i>. The suspensions are composed of neutrally-buoyant spherical particles in Newtonian liquid, with mean particle diameters of <i> d</i> = 250 μm and 480 μm resulting in <i>d/D</i> ≈ 0.1 and <i>d/D</i> ≈ 0.2. The flow rate ratio (<i>β </i> = <i>Q</i><sub>∥</sub>/<i>Q</i><sub>0</sub> ), defined for the bulk, fluid and solid phases, is used to characterize <i> Q</i><sub>0</sub> the flow behavior as a function of the channel Reynolds number and particle size; here <i>Q</i><sub>∥</sub> and <i> Q</i><sub>0</sub> are volumetric flow rates in straight branch and inlet branch, respectively. The channel Reynolds number <i>Re</i> = <i> ρDU</i>/<i>η</i> was varied over 0 < <i>Re </i> < 900 in experiment; the inlet particle volume fraction varied over 0.05 ≤ <i>&phis;</i><sub>0</sub> ≤ 0.30. Experiments and numerical results show good agreement for single-phase Newtonian fluid, with <i>β</i> increasing with <i>Re</i>, implying more material tending toward the straight branch as the inertia of the flow increases. In suspension flow at small <i>&phis;</i><sub>0</sub>, inertial migration of particles in the inlet branch affects the flow rate ratio for particles (<i>β</i><sub>particle</sub>) and suspension (<i>β</i><sub>suspension</sub>). The flow split for the bulk suspension satisfies <i>β</i> > 0.5 for <i>&phis;</i> ≤ 0.16 and <i>β</i> < 0.5 for <i>&phis;</i> ≥ 0.20; the concentration at which the value of <i>β</i> crosses 0.5 is not precisely determined. This variation of flow split is related to particle migration in the inlet branch, which results in a complex dependence of the mean solid fraction in each of the downstream branches upon the inlet fraction <i>&phis;</i><sub>0</sub> and <i>Re</i>: for <i> &phis;</i><sub>0</sub> < 0.12, the solid fraction in the straight downstream branch initially decreases with <i>Re</i>, before increasing to surpass the inlet fraction at large <i>Re</i> (<i>Re</i> ≈ 500 for <i>&phis;</i><sub>0</sub> = 0.05), while at <i>&phis; </i><sub>0</sub> > 0.12, there is generally an increase in the solid fraction in the side branch which grows with <i>Re</i>; this growth is non-monotonic with <i>&phis;</i><sub>0</sub>.</p><p> Similar analysis for single phase fluid was carried out for non-Newtonian (power law) fluid using different <i>D</i><sub>∥</sub>/<i> D</i><sub>⊥</sub> where <i>D</i><sub>∥</sub> is the width of the straight branch and <i>D</i><sub>⊥</sub> is the width of side branch of the channel for a range of Reynolds numbers, 0 < <i> Re</i> < 800; <i>D</i><sub>∥</sub> = <i>D</i><sub> 0</sub>, with <i>D</i><sub>0</sub> the width of the inlet branch. The single phase non-Newtonian fluid shows good agreement with Newtonian fluid split when described on the basis of <i>Re</i><sub>gen</sub>. The particle-laden experiments are carried out with neutrally buoyant suspension of spherical particles for different inlet solid volume fraction. The role of the size ratio of the side channel to the primary or straight channel, and the relative size of the particle to the channel widths, is examined. </p><p> Furthermore, detailed dynamics of isolated particles and tracer particle in suspension is studied experimentally in ‘asymmetric T’ and ‘symmetric T’ channel for 0 ≤ <i>&phis;</i> ≤ 0.30 and low to moderate <i>Re</i>. The upstream position of the particle before entering the bifurcation plays an important role in determining its motion. For asymmetric T channel, an isolated particle collides on the sharp corner and bounces. These particles are mostly located near wall and show unusual velocity behavior. The bouncing motion of particles gets damped as solid fraction increases. For symmetric T, secondary flow vortices are damped vanished for <i>&phis;</i> > 0.20 in a manner not accounted for by the effective viscosity.</p>
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