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<p>Non-spherical grains exhibit complex orientation behaviors under boundary excitation, with significant implications for various industrial applications. While previous studies have focused primarily on spherical grains, the orientation dynamics of non-spherical grains remain less understood, particularly regarding the influence of boundary excitation. This paper presents a theoretical framework coupling a tensorial granular temperature motivated by the directional nature of boundary forcing with an orientation evolution equation that preserves the unit-trace constraint and drives randomization towards the isotropic state. Discrete Element Method (DEM) simulation of frictionless spherocylinders (aspect ratios AR<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(=2\)</EquationSource> </InlineEquation> and AR<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(=4\)</EquationSource> </InlineEquation>) confined in a cubic container with sinusoidally oscillating opposing walls are used to calibrate the model on AR<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(=4\)</EquationSource> </InlineEquation> data and cross-validate it on AR<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(=2\)</EquationSource> </InlineEquation> without parameter adjustment. The framework captures three key phenomena: (1) the inverse relationship between excitation frequency and steady-state alignment, (2) enhanced alignment at higher aspect ratios, and (3) transient reorientation dynamics upon excitation switching. The granular temperature is found to scale as <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\Theta _{ss} \propto f^{1.04}\)</EquationSource> </InlineEquation> rather than the theoretically predicted <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(f^2\)</EquationSource> </InlineEquation>, attributed to the <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\Theta ^{1/2}\)</EquationSource> </InlineEquation> dependence of the dissipation rate and reported as a model limitation. The spatial temperature profile decays exponentially from the boundaries (<InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\lambda = 3.95\)</EquationSource> </InlineEquation> mm, wall-to-center ratio <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\approx 28\times \)</EquationSource> </InlineEquation>), confirming the boundary-value nature of the problem and quantifying the conditions under which a spatially-averaged approximation remains valid.</p> Graphical Abstract <p></p>

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Orientation dynamics of non-spherical grains under boundary excitation: theory and DEM validation

  • 期刊论文

  • 发表日期：

    2026年7月8日

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  • Saeed Naamnh

摘要

Non-spherical grains exhibit complex orientation behaviors under boundary excitation, with significant implications for various industrial applications. While previous studies have focused primarily on spherical grains, the orientation dynamics of non-spherical grains remain less understood, particularly regarding the influence of boundary excitation. This paper presents a theoretical framework coupling a tensorial granular temperature motivated by the directional nature of boundary forcing with an orientation evolution equation that preserves the unit-trace constraint and drives randomization towards the isotropic state. Discrete Element Method (DEM) simulation of frictionless spherocylinders (aspect ratios AR \(=2\) and AR \(=4\) ) confined in a cubic container with sinusoidally oscillating opposing walls are used to calibrate the model on AR \(=4\) data and cross-validate it on AR \(=2\) without parameter adjustment. The framework captures three key phenomena: (1) the inverse relationship between excitation frequency and steady-state alignment, (2) enhanced alignment at higher aspect ratios, and (3) transient reorientation dynamics upon excitation switching. The granular temperature is found to scale as \(\Theta _{ss} \propto f^{1.04}\) rather than the theoretically predicted \(f^2\) , attributed to the \(\Theta ^{1/2}\) dependence of the dissipation rate and reported as a model limitation. The spatial temperature profile decays exponentially from the boundaries ( \(\lambda = 3.95\) mm, wall-to-center ratio \(\approx 28\times \) ), confirming the boundary-value nature of the problem and quantifying the conditions under which a spatially-averaged approximation remains valid.

Graphical Abstract