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

doi:10.13745/j.esf.sf.2024.6.38

Abstract

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

CLC Number:

P641.12

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.

Figures/Tables 7

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

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

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

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。

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

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

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

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

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