Unfrozen water content significantly affects the thermal‐hydro‐mechanical characteristics of frozen soil. Currently, theoretical explanations for the presence of unfrozen water include capillary action, surface effects, adsorption forces, and the electrical double layer. However, the relationships between unfrozen water and these actions are not well explained, except for capillary forces. In addition, although frost heave experiments indicate that the electrical double‐layer solution on a clay particle contains the main portion of unfrozen water, the electrical double‐layer theory which produces a cation solution has not previously been used to calculate unfrozen water content. In this paper, it is assumed that the residual unfrozen water at very low temperatures (below −18°C) is held within the adsorption‐layer solution and that the remaining unfrozen water within the influence of surface effects is the cationic solution in the diffuse layer. Based on these assumptions, a theoretical model of unfrozen water is established with independent variables of temperature, specific surface area, and electrical double‐layer parameters. While the input parameters of the theoretical model are numerous and difficult to obtain, the theoretical model is simplified as a parametric model. Results of the parametric model are strongly consistent with experimental data within a certain temperature range, supporting the hypothetical conditions. The similarity in the underlying mathematical structure of the derived theoretical and parametric models to current semi‐empirical models further suggests that the surface effects of clay are the main causes of unfrozen water in frozen soil.

Complex dielectric constant (CDC) of bound water determines the accuracy of the complex dielectric constant of wet soil. According to electrical double-layer structure and dielectric properties, the bound water on clay particle surface is divided into strongly bound water and weakly bound water. Based on this classification, models for the complex dielectric constants of bound water and soil are established taking into consideration factors such as temperature, moisture, texture, and microwave frequency. The results show that the fundamental reason why the complex dielectric constant of bound water is between that of ice and free water is the adsorption force which forms the electrical double-layer structure on the surface of clay particles. Low-concentration cationic solution could exist in free soil water and was found as the reason for the higher salinity and conductivity of free soil water, as compared to the measured soil solution. Results of soil CDC model are in good agreement with measured data across a wide range of microwave frequencies and soil temperature, moisture, and texture. The absolute root mean square error analysis also shows that the soil CDC model in this paper compared to the other models is more accurate.

The soil complex dielectric permittivity (CDP) is a fundamental physical quantity utilized in microwave remote sensing estimating soil moisture. Although several Four-parameter (soil temperature, moisture, clay content, frequency) semi-empirical dielectric mixing models (SEMs) have been developed, they do not consider the changes in soil CDP caused by the conversion of bound water to free water due to temperature variations. This study proposes an improved SEM (also known as the Dobson-Jin model) based on the Dobson SEM. The improvements include: 1) rectifying the distortion phenomenon in the imaginary part of the Dobson model, and minimizing the error in calculating sand using the Dobson model; 2) reducing the number of input parameters from seven to four; 3) dividing soil water into strongly bound water and soil effective water (the sum of weakly bound water and free water) and successfully simulating the ‘competitive mechanism’ of soil CDP variation with temperature by establishing the weakly bound water to free water conversion functions and the weakly bound water proportion functions. Experimental validation using measured data from 31 types of soils has demonstrated that the Dobson-Jin model is capable of accurately calculating the CDP of sand, loam, and clay within the range of 1.4 to 18 GHz and water content volume of 0 to 0.5 (cm ³ ·cm ^-3 ). In summary, the Dobson-Jin model is expected to improve the accuracy of microwave remote sensing inversion of soil moisture.

The complex permittivity of bound water are uncertain factors in the modeling of soil permittivity. Based on the electrical double-layer theory, this study divides soil bound water into strongly and weakly bound components. These strongly and weakly bound water are assumed to be cation solutions in the adsorption and diffuse layers, respectively. Characteristic functions of the permittivity of weakly bound water were proposed to describe the variation in the complex permittivity of weakly bound water with changes in moisture, and a soil semi-empirical dielectric model (SEM) was established based on these characteristic functions. Through further fitting, this SEM only requires the soil temperature, moisture, clay content, and microwave frequency to obtain the soil complex permittivity. Measured data from 20 soils and four SEMs were used for model validation. The results show that this SEM can accurately calculate the complex permittivity of sand, silt, clay, and soils with low organic matter and low salinity in the range of 0 to 0.5 volume moisture content at 1.4–18 GHz. The characteristic functions link the electrical properties of clay with the complex permittivity of bound water. The two constituent formulas of the characteristic functions (the cation concentration and electric field strength) are almost independent of soil texture. Soil texture affects the soil complex permittivity by changing the contents of strongly and weakly bound water. This phenomenon suggests that the dielectric algorithm of bound water is minimally affected by soil texture. The dielectric algorithms of bound water utilized in existing SEMs are reasonable.

Unfrozen water affects the thermal-hydro-mechanical characteristics, microbial activity and freeze-thaw processes in frozen soils. This study found that part of the unfrozen water is formed by the coupling of adsorption and capillary action in soils with mid to low clay content, which is called bound-capillary water and located in nanopores between clay and sand (silt) particles. The nature of the bound-capillary water affects soil freezing characteristics, which varies with the initial water content. The influence of coupling effects arises from the adsorption effects on the clay surface and the capillary action between the clay-sand particles. The adsorption effects (or surface effects) establish an electrical double-layer structure for bound-capillary water. The capillary action (surface tension) forms bound-capillary water in a shape of meniscuses, which significantly increases its content. Here, we established four theoretical models and a parametric model of unfrozen water based on the coupling effects. The basic mathematical expressions of four theoretical models are almost identical to those of 10 existing unfrozen water semi-empirical models, demonstrating that the semi-empirical models are representative of empirical formulas describing the freezing characteristics of the bound-capillary water. A comparison of model results with the measured unfrozen water content of 9 soils verifies that the parametric model is suitable for soils with low to medium clay content.

The heat sink has played an important role in the thermal design of high power LED lamps. In this study, a pin-fin heat sink is designed for the 3-chips high power LED down-light. Thermal performance of pin-fin heat sink is researched by changing the fin height, fin number and lamp’s irradiation angle. Simulation results gotten by CFD software show that the pin-fin heat sink has better thermal performance with fin height of 40mm and fin number of 75. The LED down-light with a pin-fin heat sink has a better cooling effect in multi-angle irradiation. The results provide a reference for future design of pin-fin heat-sink.