Particle spacing and stability of initially staggered deformable particle trains migrating in a channel

Abstract We investigated the inertial migration of deformable particles in a two-dimensional channel flow. This study analyzes the effects of the channel Reynolds number ( Re ), channel blockage ratio ( k ), particle number ( N p ) and reduced bending modulus ( E b ) on the formation of staggered particle trains. The results show that the stable normalized distance <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>d</mml:mi> <mml:mrow> <mml:msub> <mml:mi>p</mml:mi> <mml:mrow> <mml:mi>e</mml:mi> <mml:mi>q</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> </mml:math> between two staggered particles is influenced by Re , k and E b , where H is the channel width. As k increases or E b decreases, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>d</mml:mi> <mml:mrow> <mml:msub> <mml:mi>p</mml:mi> <mml:mrow> <mml:mi>e</mml:mi> <mml:mi>q</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> </mml:math> decreases. The value of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>d</mml:mi> <mml:mrow> <mml:msub> <mml:mi>p</mml:mi> <mml:mrow> <mml:mi>e</mml:mi> <mml:mi>q</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> </mml:math> initially increases and then decreases with the increase of Re ; when E b is large and k is small, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>d</mml:mi> <mml:mrow> <mml:msub> <mml:mi>p</mml:mi> <mml:mrow> <mml:mi>e</mml:mi> <mml:mi>q</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> </mml:math> continuously increases with increasing Re . With the increase of N p , the closely arranged staggered particle trains evolve into five distinct migration Regimes. We explain the conditions for the formation of each Regime and explore the mechanisms of their interconversion. The findings of this study contribute to a better understanding of the self-organization process of deformable particles in channel flow.