纳米粒子在多孔介质中迁移模型的优化

doi:10.11949/0438-1157.20210374

摘要/Abstract

摘要：

当前，纳米粒子在土壤等多孔介质中的传输多采用单集去除率（η）进行定量描述。然而，单集去除率仅考虑单个介质颗粒对纳米粒子的作用，并未考虑介质颗粒之间的孔隙对纳米粒子的拦截效应，如T-E模型。鉴于此，采用持水度（f_r）来定量反映多孔介质的孔隙特征，并对现有的T-E模型进行了修正。实验表明，纳米粒子通过具有相同孔隙度（f）砂柱的穿透率并不相同，且与持水度（f_r）呈反比关系。在此基础上，将截留机制产生的碰撞效率（η_I）调整为与孔隙度（f）和持水度（f_r）同时相关的表达式来实现对原有模型的优化。此外，通过砂柱对纳米二氧化硅（nSiO₂）的传输实验和纳米二氧化钛（nTiO₂）在不同粒径石英砂中的传输实验证明，优化模型适用于不同粒径的多孔介质并可以更准确地预测纳米粒子在多孔介质中的迁移。

关键词: 粒子, 多孔介质, 迁移, 模型, 孔隙

Abstract:

At present, the transport of nanoparticles in porous media such as soil is mostly described by a single-collector removal efficiency (η). However, this efficiency only considers the collecting effect of a single solid matrix, and does not consider the trapping effect of the pore space between the porous media such as T - E model. To address this issue, the water retention capacity (f_r) was employed to reflect the number of small pores and the existing T-E model was modified. Research has shown that the transport of nanoparticles through columns with the same porosity (f) is not the same, but inversely proportional to the water retention capacity, which has been neglected in previous research. On this basis, the collector contact efficiency by the interception mechanism (η_I) is adjusted to be dependent on both porosity (f) and water retention capacity (f_r); thus, the original model was optimized. Furthermore, breakthrough experiments on nanoscale silica particles (nSiO₂) through the sand column and breakthrough experiments on nano titanium dioxide (nTiO₂) through the sand column with different particle sizes proved that the optimized model is applicable to porous media with different particle sizes and is more accurate in predicting the transport of nanoparticles in porous media.

Key words: particle, porous media, particle transport, model, pore

中图分类号:

X 53

彭爱夏,占敬敬,吴明火. 纳米粒子在多孔介质中迁移模型的优化[J]. 化工学报, 2021, 72(10): 5114-5122.

Aixia PENG,Jingjing ZHAN,Minghuo WU. Optimization of nanoparticles transport model in porous media[J]. CIESC Journal, 2021, 72(10): 5114-5122.

图/表 12

图1 纳米粒子悬浮液流入多孔介质示意图

Fig.1 Schematic diagram of nanoparticles flowing into porous media with liquid flow

表1 T-E模型中参数的表达式

Table 1 Expression of parameters in the T-E model

参数	物理意义	表达式
$A s$	孔隙度常数	$A s = 2 (1 - r 5) 2 - 3 r + 3 r 5 - 2 r 6$
$N R$	纵横比	$N R = d p d c$
$N P e$	佩克莱数	$N P e = U d c D$
$N v d W$	范德华数	$N v d W = A K T$
$N A$	引力数	$N A = A 12 π μ a p 2 U$
$N G$	重力数	$N G = 2 a p 2 ρ p - ρ f g 9 μ U$

表1 T-E模型中参数的表达式

Table 1 Expression of parameters in the T-E model

参数	物理意义	表达式
$A s$	孔隙度常数	$A s = 2 (1 - r 5) 2 - 3 r + 3 r 5 - 2 r 6$
$N R$	纵横比	$N R = d p d c$
$N P e$	佩克莱数	$N P e = U d c D$
$N v d W$	范德华数	$N v d W = A K T$
$N A$	引力数	$N A = A 12 π μ a p 2 U$
$N G$	重力数	$N G = 2 a p 2 ρ p - ρ f g 9 μ U$

图2 T-E模型理论曲线

Fig.2 The theoretical curves of T-E model

图3 孔隙度（f）分别为0.435、0.445和0.458时纳米粒子穿透率的实验值

Fig.3 Experimental values of nanoparticle penetration when porosity (f) was 0.435, 0.445 and 0.458

图4 持水度对纳米粒子穿透率的影响

Fig.4 The effect of the water holding capacity on the permeability of nanoparticles

图5 持水度与穿透率的线性关系（孔隙度为0.445）

Fig.5 The linear relationship between the water holding capacity and the effluent concentration (porosity is 0.445)

表2 nTiO2在石英砂中迁移的实验数据（孔隙度为0.445）

Table 2 Experimental data of nTiO2 transported in quartz sand （porosity is 0.445）

持水度f_r	穿透率C/C₀	孔隙常数F	去除率η	碰撞效率η₀'	拦截机制的碰撞效率η_I'
0.1275	0.8333	0.2865	0.00111	0.04086 (=η₀)	0.00486 (=η_I)
0.1313	0.8496	0.2951	0.00987	0.03652	0.00052
0.1376	0.8370	0.3092	0.00108	0.03987	0.00387
0.1421	0.8287	0.3193	0.00114	0.04208	0.00608
0.1598	0.8259	0.3591	0.00116	0.04284	0.00684
0.1663	0.8125	0.3737	0.00126	0.04650	0.01050
0.1721	0.8185	0.3867	0.00121	0.04487	0.00887
0.1820	0.8133	0.4090	0.00125	0.04628	0.01028
0.1894	0.8143	0.4256	0.00124	0.04601	0.01001
0.1953	0.8052	0.4389	0.00131	0.04852	0.01251
0.1971	0.8094	0.4429	0.00128	0.04737	0.01137
0.2116	0.7961	0.4755	0.00138	0.05107	0.01507
0.2237	0.7883	0.5027	0.00144	0.05330	0.01730
0.2296	0.7935	0.5160	0.00140	0.05181	0.01581
0.2318	0.7811	0.5209	0.00150	0.05534	0.01934
0.2351	0.7762	0.5283	0.00153	0.05676	0.02076
0.2453	0.7631	0.5512	0.00164	0.06057	0.02457
0.2487	0.7708	0.5589	0.00158	0.05830	0.02230

图6 ηI'与F的对应关系及拟合曲线

Fig.6 Correspondence and fitting curve of the pore space-dependent parameter (F) and ηI'

表3 优化前后T-E模型计算值（nSiO2）

Table 3 Values calculated by the T-E model before and after optimization （nSiO2）

$η D$	$η G$	$η$	优化前			优化后
$η D$	$η G$	$η$	$η I$	$η 0$	$α$	$η I'$	$η 0'$	$α'$
0.025	2.3×10^-6	0.000409	1.1×10^-6	0.025	0.01637	0.01523	0.04023	0.01017
0.025	2.3×10^-6	0.000356	1.1×10^-6	0.025	0.01425	0.00989	0.03489	0.01021
0.025	2.3×10^-6	0.000349	1.1×10^-6	0.025	0.01397	0.00925	0.03426	0.01020
0.025	2.3×10^-6	0.000326	1.1×10^-6	0.025	0.01303	0.00705	0.03206	0.01017
0.025	2.3×10^-6	0.000316	1.1×10^-6	0.025	0.01262	0.00593	0.03094	0.01020
0.025	2.3×10^-6	0.000303	1.1×10^-6	0.025	0.01210	0.00466	0.02967	0.01020

表3 优化前后T-E模型计算值（nSiO2）

Table 3 Values calculated by the T-E model before and after optimization （nSiO2）

$η D$	$η G$	$η$	优化前			优化后
$η D$	$η G$	$η$	$η I$	$η 0$	$α$	$η I'$	$η 0'$	$α'$
0.025	2.3×10^-6	0.000409	1.1×10^-6	0.025	0.01637	0.01523	0.04023	0.01017
0.025	2.3×10^-6	0.000356	1.1×10^-6	0.025	0.01425	0.00989	0.03489	0.01021
0.025	2.3×10^-6	0.000349	1.1×10^-6	0.025	0.01397	0.00925	0.03426	0.01020
0.025	2.3×10^-6	0.000326	1.1×10^-6	0.025	0.01303	0.00705	0.03206	0.01017
0.025	2.3×10^-6	0.000316	1.1×10^-6	0.025	0.01262	0.00593	0.03094	0.01020
0.025	2.3×10^-6	0.000303	1.1×10^-6	0.025	0.01210	0.00466	0.02967	0.01020

图7 基于优化前后T-E模型计算的nSiO2附着效率（α）

Fig.7 The attachment efficiency （α） of nSiO2 calculated by the T-E model before and after optimization

表4 优化前后T-E模型计算值（nTiO2）

Table 4 Values calculated by the T-E model before and after optimization（nTiO2）

$η D$	$η G$	$η$	优化前			优化后
$η D$	$η G$	$η$	$η I$	$η 0$	$α$	$η I'$	$η 0'$	$α'$
0.058	2.0×10^-6	0.001362	2.5×10^-6	0.058	0.02337	0.15141	0.20968	0.00649
0.058	2.0×10^-6	0.001227	2.5×10^-6	0.058	0.02105	0.13077	0.18903	0.00649
0.058	2.0×10^-6	0.001041	2.5×10^-6	0.058	0.01785	0.10399	0.16225	0.00641
0.058	2.0×10^-6	0.001017	2.5×10^-6	0.058	0.01745	0.09987	0.15813	0.00643
0.058	2.0×10^-6	0.000860	2.5×10^-6	0.058	0.01476	0.07661	0.13488	0.00638

表4 优化前后T-E模型计算值（nTiO2）

Table 4 Values calculated by the T-E model before and after optimization（nTiO2）

$η D$	$η G$	$η$	优化前			优化后
$η D$	$η G$	$η$	$η I$	$η 0$	$α$	$η I'$	$η 0'$	$α'$
0.058	2.0×10^-6	0.001362	2.5×10^-6	0.058	0.02337	0.15141	0.20968	0.00649
0.058	2.0×10^-6	0.001227	2.5×10^-6	0.058	0.02105	0.13077	0.18903	0.00649
0.058	2.0×10^-6	0.001041	2.5×10^-6	0.058	0.01785	0.10399	0.16225	0.00641
0.058	2.0×10^-6	0.001017	2.5×10^-6	0.058	0.01745	0.09987	0.15813	0.00643
0.058	2.0×10^-6	0.000860	2.5×10^-6	0.058	0.01476	0.07661	0.13488	0.00638

图8 基于优化前后T-E模型计算的附着效率（α）

Fig.8 The attachment efficiency (α) calculated by the T-E model before and after optimization

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