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Fluid dynamics and passive scalar transport driven by non-uniform tumbling of a prolate spheroid in simple shear flow
Published online by Cambridge University Press: 14 October 2025
Abstract
Using high-fidelity numerical simulations based on a lattice Boltzmann framework, the advection-enhanced transport of a passive scalar from a prolate spheroid in simple shear flow has been thoroughly investigated across various parameters, including the spheroid’s aspect ratio, particle-to-fluid density ratio, Reynolds number (defined as 
${\textit{Re}}=\textit{GR}^{2}/\nu$, where 
$G$ is the flow shear rate, 
$R$ is the radius of a sphere of the same volume as the spheroid and 
$\nu$ is the kinematic viscosity of the fluid) and Schmidt number (defined as 
$\textit{Sc}=\nu /D$, where 
$D$ is the diffusivity of passive scalar transport). The Reynolds number is constrained to the range of 0 ≤ Re ≤ 1, where the prolate spheroid tumbles around its minor axis, aligned with the vorticity axis, in an equilibrium state. Several key findings have emerged: (i) particle inertia significantly influences the uniformity of the spheroid’s tumbling, affecting flow patterns around the spheroid and, consequently, the modes of scalar transport; (ii) both uniform and non-uniform tumbling generate a scalar line in the fluid with elevated scalar concentration, which sweeps through the wake region and merges with clusters of previously formed scalar lines; (iii) fluid passing over the spheroid carries the passive scalar downstream along these scalar lines; (iv) variations in the uniformity of spheroid tumbling result in distinct flow patterns and scalar transport modes, leading to different transport rates; (v) within the studied parameter ranges, increased particle inertia enhances the scalar transport rate; (vi) when particle inertia is minimal, the dimensionless scalar transport rate for different aspect ratios converges to a common dependence on the Péclet number. These phenomena are analysed in detail.
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Wang et al. supplementary movie 1
Evolution of typical streaklines of microtracers released at various locations around a prolate spheroid with $rc/R=3$ and ε=0.4 at $Re=1$ , along with the evolution of scalar concentration on the central x-z plane for $Sc = 100$ .
File
6 MB
Wang et al. supplementary movie 2
Evolution of streaklines of microtracers released on the central x-z plane, upstream of a prolate spheroid with $rc/R=3$ and ε=0.4 at $Re=1$ , along with the evolution of scalar concentration on the same plane for $Sc = 100$ .
File
3.1 MB
Wang et al. supplementary movie 3
Evolution of typical streaklines of microtracers released at various locations around a prolate spheroid with $rc/R=3$ and ε=40 at $Re=1$ , along with the evolution of scalar concentration on the central x-z plane for $Sc = 100$ .
File
8.5 MB
Wang et al. supplementary movie 4
Evolution of streaklines of microtracers released on the central x-z plane, upstream of a prolate spheroid with $rc/R=3$ and ε=40 at $Re=1$ , along with the evolution of scalar concentration on the same plane for $Sc = 100$ .
File
4.3 MB