不同直径毛管中水密度变化特性及其对土壤水密度变化的启示

doi:10.13745/j.esf.sf.2024.6.38

地学前缘 ›› 2025, Vol. 32 ›› Issue (1): 440-448.DOI: 10.13745/j.esf.sf.2024.6.38

不同直径毛管中水密度变化特性及其对土壤水密度变化的启示

李超¹^,²(), 程东会¹^,²^,^*(), 马成龙¹, 乔晓英¹^,², 黄梦楠¹, 王一式¹^,², 杨银科¹^,²

1.长安大学水利与环境学院, 陕西西安 710054
2.长安大学旱区地下水文与生态效应教育部重点实验室, 陕西西安 710054

收稿日期:2023-04-07 修回日期:2024-04-16 出版日期:2025-01-25 发布日期:2025-01-15
通信作者: *程东会(1969—),男,教授,博士生导师,主要从事水文地质相关的教学和研究工作。E-mail: chdhbsh@chd.edu.cn
作者简介:李超(1999—),男,硕士研究生,水利工程专业。E-mail: 2021129013@chd.edu.cn
基金资助:
国家自然科学基金项目(41972248);国家自然科学基金项目(42372291);陕西省自然科学基础研究计划项目(2019JM-146);陕西省重点研发计划项目(2021ZDLSF05-03)

Characteristics of water density variation in capillaries of different diameters and its implications for soil water density changes

LI Chao¹^,²(), CHENG Donghui¹^,²^,^*(), MA Chenglong¹, QIAO Xiaoying¹^,², HUANG Mengnan¹, WANG Yishi¹^,², YANG Yinke¹^,²

1. School of Water Resources and Environment, Chang’an University, Xi’an 710054, China
2. Key Laboratory of Groundwater Hydrology and Ecological Effects in Dry Areas of Chang’an University, Ministry of Education, Xi’an 710054, China

Received:2023-04-07 Revised:2024-04-16 Online:2025-01-25 Published:2025-01-15

摘要/Abstract

摘要：

土壤水的密度存在较大的变化范围,但目前还没有一个完整的理论来全面描述这种变化规律。本文利用微米直径的石英管模拟多孔介质的孔隙系统,采用质量-体积法测量了直径在50~530 μm之间的8个不同直径石英管中水的密度。结果表明:当石英管直径小于75 μm时,水的密度大于体相水的密度,最高密度为1.19 g/cm³;而直径为100~250 μm时,水的密度略小于体相水,最低为0.98 g/cm³。水密度随石英管径而变化的规律可以用类似纳兰-琼斯势的经验公式来表达。研究表明:能使水密度增大或减小的水化作用、水-固界面作用、毛细作用或空化机制均不能解释石英管中出现的水密度变化。分析认为,毛管中的复杂的水动力学和流变学,特别是管嘴的剪切增稠及其逆过程可能是不同直径石英管中水密度变化的物理机制。该机制不同于解释土壤水密度变化的传统理论,为土壤水密度变化研究提供了一个崭新的视角。如果把石英管中水密度变化规律与基于多孔介质毛管束概念的土壤含水率模型结合,可以预测不同含水率土壤中水的密度。进一步的研究应该从流变学基本理论出发,建立剪切速率与黏度和黏度与密度之间的定量关系,从理论上构建毛管水和土壤水密度变化模型。

关键词: 微米直径石英管, 高密度水, 低密度水, 剪切增稠, 土壤水密度变化

Abstract:

The density of soil water exhibits significant variation, yet no comprehensive theory currently exists to fully explain this pattern. In this study, quartz tubes with micrometer-scale diameters were used to simulate the pore systems of porous media, and the mass-volume method was employed to measure the density of water in eight quartz tubes with diameters ranging from 50 μm to 530 μm. The results indicate that when the diameter of the quartz tube is less than 75 μm, the density of water exceeds that of bulk water, reaching a maximum of 1.19 g/cm. Conversely, when the diameter ranges between 100 μm and 250 μm, the density of water is slightly lower than that of bulk water, with a minimum of 0.98 g/cm. The variation in water density with quartz tube diameter can be described using an empirical formula similar to the Lennard-Jones potential. The findings suggest that conventional mechanisms such as hydration effects, water-solid interfacial interactions, capillary effects, or cavitation cannot fully account for the observed changes in water density within the quartz tubes. Instead, the analysis indicates that the complex hydrodynamics and rheology within the capillaries: particularly shear thickening at the tube nozzle and its reverse process may be the primary physical mechanism driving the changes in water density across quartz tubes of different diameters. This mechanism represents a departure from traditional theories used to explain variations in soil water density and offers a novel perspective for understanding the phenomenon. It becomes possible to predict the density of water in soils with varying water contents by integrating the observed variation in water density within quartz tubes with soil water content models based on the concept of capillary bundles in porous media. Future research should focus on the fundamental principles of rheology to establish quantitative relationships between shear rate and viscosity, as well as between viscosity and density. Such efforts would enable the theoretical construction of models to describe the density variation of capillary water and soil water.

Key words: quartz tube with micron-scale diameter, high-density water, low-density water, shear thickening, soil water density changes

中图分类号:

P641.12

李超, 程东会, 马成龙, 乔晓英, 黄梦楠, 王一式, 杨银科. 不同直径毛管中水密度变化特性及其对土壤水密度变化的启示[J]. 地学前缘, 2025, 32(1): 440-448.

LI Chao, CHENG Donghui, MA Chenglong, QIAO Xiaoying, HUANG Mengnan, WANG Yishi, YANG Yinke. Characteristics of water density variation in capillaries of different diameters and its implications for soil water density changes[J]. Earth Science Frontiers, 2025, 32(1): 440-448.

图/表 7

表1 试验蒸馏水和4种电解质溶液的体相密度

Table 1 Bulk density measurements of distilled water and four electrolyte solutions

溶液类型	浓度/(g·L^-1)	体相密度/(g·cm^-3)
蒸馏水		0.992 56
NaCl溶液	1.0	0.994 52
NaCl溶液	5.0	0.996 44
MgSO₄溶液	1.0	0.994 22
MgSO₄溶液	5.0	0.998 44
CaCl₂溶液	1.0	0.995 16
CaCl₂溶液	5.0	0.998 22
AlCl₃溶液	1.0	0.993 84
AlCl₃溶液	5.0	0.996 56

图1 不同直径石英管中密度测量结果 a—水密度,负压进水;b—水密度,正压进水;c—AlCl3溶液,1 g/L; d—AlCl3溶液,5 g/L; e— CaCl2溶液,1 g/L; f—CaCl2溶液,5 g/L; g—MgSO4溶液,1 g/L ;h—MgSO4溶液,5 g/L; i—NaCl溶液,1 g/L; j—NaCl溶液,5 g/L。

Fig.1 Density measurement results in quartz tubes of different diameters

图2 石英管两种进水方式下测量的水密度平均值以及模型计算值

Fig.2 Average water density measurements under two water inlet methods for quartz tube and model calculation values

图3 不同直径石英管中4种电解质溶液测量的溶液密度比较

Fig.3 Comparison of solution densities measured in four electrolyte solutions using quartz tubes of different diameters a—1 g/L;b—5 g/L。

表2 水化离子的离子半径r,水化壳半径Δr,水化壳中水分子数n和水化离子的吉布斯自由能ΔG(据文献[9])

Table 2 Ionic radius (r) of hydrated ions, hydration shell radius (Δr), number of water molecules in the hydration shell (n), and Gibbs free energy (ΔG) of hydrated ions. Adapted from [9].

离子	r/nm	Δr/nm	n	ΔG /(kJ·mol^-1)
Na⁺	0.102	0.116	3.5	-365
Ca²⁺	0.100	0.171	7.2	-1 505
Mg²⁺	0.072	0.227	10	-1 830
Al³⁺	0.053	0.342	20.4	-4 525
Cl^-	0.181	0.043	2.0	-340
$S O 4 2 +$	0.230	0.043	3.1	-1 080

表2 水化离子的离子半径r,水化壳半径Δr,水化壳中水分子数n和水化离子的吉布斯自由能ΔG(据文献[9])

Table 2 Ionic radius (r) of hydrated ions, hydration shell radius (Δr), number of water molecules in the hydration shell (n), and Gibbs free energy (ΔG) of hydrated ions. Adapted from [9].

离子	r/nm	Δr/nm	n	ΔG /(kJ·mol^-1)
Na⁺	0.102	0.116	3.5	-365
Ca²⁺	0.100	0.171	7.2	-1 505
Mg²⁺	0.072	0.227	10	-1 830
Al³⁺	0.053	0.342	20.4	-4 525
Cl^-	0.181	0.043	2.0	-340
$S O 4 2 +$	0.230	0.043	3.1	-1 080

表3 利用毛细力和进口吸力计算的水密度

Table 3 Water density calculated using capillary force and inlet suction

r/μm	p_c/kPa	p_e/kPa	ρ_wc/(g·mL^-1)	ρ_wm/(g·mL^-1)
50	-2.912	-625.3	0.999 621 1	1.221
75	-1.941	-194.5	0.999 819 6	1.000
100	-1.456	-0.823	0.999 909 0	0.982
150	-0.971	-0.675	0.999 909 2	0.978
200	-0.728	-0.784	0.999 909 3	0.969
250	-0.582	-0.635	0.999 909 4	0.974
320	-0.455	-0.397	0.999 909 6	1.002
530	-0.275	-0.356	0.999 909 7	1.000

图4 自由水进进入突然缩小的管口时的流线分布

Fig.4 Streamline distribution of free water entering a suddenly narrowed nozzle

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不同直径毛管中水密度变化特性及其对土壤水密度变化的启示

Characteristics of water density variation in capillaries of different diameters and its implications for soil water density changes

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