Multiscale mixing index for granular systems

doi:10.11949/0438-1157.20240194

Abstract

Abstract:

Systematic study of the homogeneity of particle mixtures reveals significant multiscale features in mixing process. In particular, homogenous mixtures at macro-scale may display severe heterogeneity at micro-scale, and vice versa. Meanwhile, different particle sampling methods and mixing indexes may yield significantly varied results for the same mixture at same scales. The results indicate that different mixing indices exhibit inconsistency at different scales. A multiscale mixing index using different methods at appropriate scales and characterizing the homogeneity as a distribution over different scales, rather than a single value at an undefined scale, is hence proposed and considered more precise and comprehensive.

Key words: granular systems, mixing, multiscale, discrete element modeling, Lacey index, relative standard deviation, macromixing, micromixing

摘要：

对颗粒混合物均匀性的系统研究揭示了混合过程中显著的多尺度特征，特别是宏尺度上均匀的混合物在微尺度上可能表现为极度不均匀，反之亦然，同时采用不同的采样方法和混合指数表征同一混合物在同一尺度下的均匀性可能也会有所差异。尝试提出一种多尺度混合指数，即在不同尺度采用不同评价方法，并将混合指数表达为不同尺度上的分布，而不是在未定义尺度上的单一值。该多尺度表征方法可更精确与全面地反映混合物的均匀特性。

关键词: 颗粒体系, 混合, 多尺度, 离散单元法, 莱西指数, 相对标准偏差, 宏尺度混合, 微尺度混合

CLC Number:

TQ 027.1

Jiayu XU, Feiguo CHEN, Ji XU, Wei GE. Multiscale mixing index for granular systems[J]. CIESC Journal, 2024, 75(6): 2214-2221.

徐嘉宇, 陈飞国, 徐骥, 葛蔚. 颗粒体系的多尺度混合指数[J]. 化工学报, 2024, 75(6): 2214-2221.

Figures/Tables 10

Fig.1 Illustration of mixer and mixture generation

Table 1 Parameters for mixture generation

参数	示例Ⅰ	示例Ⅱ	示例Ⅲ	示例Ⅳ
几何尺寸
高度H/mm	60	60	50	60
宽度W/mm	15	15	15	15
深度D/mm	15	15	15	15
进料管直径D_t/mm	2	2	2	2
进料管位置H_进料口/mm	40	40	30	40
颗粒物性
颗粒直径d_p/mm	0.1	0.1	0.1	0.1
颗粒密度ρ/(kg/m³)	2490	2490	2490	2490
杨氏模量E/Pa	6.89×10⁷	6.89×10⁷	6.89×10⁷	6.89×10⁷
泊松比υ	0.22	0.22	0.22	0.22
恢复系数e	0.926	0.926	0.926	0.926
摩擦系数λ_s	0.092	0.092	0.092	0.092
滚动摩擦系数λ_r	0.1	0.1	0.1	0.1
操作参数
质量流率G/(kg/s)	3.92×10^-4	3.92×10^-4	3.92×10^-4	3.92×10^-4
持续时间t/s	2.0	1.0	1.0	1.5
混合物厚度δ/mm	1.6	1.0	1.0	1.3

Fig.2 Particle distribution at different scales (top-view)

Fig.3 Mixing indexes at different scales using different particle partition methods

Fig.4 Ratios of empty subsample (ζ) and standard deviation (σc/σv) at different scales

Fig.5 Particle distribution of mixture with better macromixing

Fig.6 Mixing indexes at different scales for mixture with better macromixing

Fig.7 Particle distribution of mixture with better micromixing

Fig.8 Mixing indexes at different scales for mixture with better micromixing

Fig.9 Multiscale mixing indexes

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