Influence of Concentration on Sedimentation of a Dense Suspension in a Viscous Fluid

Abstract

Abstract Macroscopic properties of sedimenting suspensions have been studied extensively and can be characterized using the Galileo number ( Ga ), solid-to-fluid density ratio ( $$\pi _p$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>π</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:math> ) and mean solid volume concentration ( $${\bar{\phi }}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mrow> <mml:mi>ϕ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:math> ). However, the particle–particle and particle–fluid interactions that dictate these macroscopic trends have been challenging to study. We examine the effect of concentration on the structure and dynamics of sedimenting suspensions by performing direct numerical simulation based on an Immersed Boundary Method of monodisperse sedimenting suspensions of spherical particles at fixed $$Ga=144$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>G</mml:mi> <mml:mi>a</mml:mi> <mml:mo>=</mml:mo> <mml:mn>144</mml:mn> </mml:mrow> </mml:math> , $$\pi _p=1.5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>π</mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>1.5</mml:mn> </mml:mrow> </mml:math> , and concentrations ranging from $${\bar{\phi }}=0.5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mover> <mml:mrow> <mml:mi>ϕ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mo>=</mml:mo> <mml:mn>0.5</mml:mn> </mml:mrow> </mml:math> to $${\bar{\phi }}=30\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mover> <mml:mrow> <mml:mi>ϕ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mo>=</mml:mo> <mml:mn>30</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> . The corresponding particle terminal Reynolds number for a single settling particle is $$Re_T = 186$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>R</mml:mi> <mml:msub> <mml:mi>e</mml:mi> <mml:mi>T</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>186</mml:mn> </mml:mrow> </mml:math> . Our simulations reproduce the macroscopic trends observed in experiments and are in good agreement with semi-empirical correlations in literature. From our studies, we observe, first, a change in trend in the mean settling velocities, the dispersive time scales and the structural arrangement of particles in the sedimenting suspension at different concentrations, indicating a gradual transition from a dilute regime ( $${\bar{\phi }} \lesssim 2\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mover> <mml:mrow> <mml:mi>ϕ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mo>≲</mml:mo> <mml:mn>2</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> ) to a dense regime ( $${\bar{\phi }} \gtrsim 10\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mover> <mml:mrow> <mml:mi>ϕ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mo>≳</mml:mo> <mml:mn>10</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> ). Second, we observe the vertical propagation of kinematic waves as fluctuations in the local horizontally-averaged concentration of the sedimenting suspension in the dense regime.

Topics & Concepts