Initial values of the theoretical contact angle (SCA), i.e. the wetting properties of the soil change the temperature coefficient. Density values of air and liquid do influence the sensitivity of the temperature coefficient of SCA.
C HAPTER 1
- General
- Preliminaries
- A historical perspective
- Literature review on moisture transfer under temperature gradient in soilgradient in soil
- Literature review on the relationship of ψ -vs.-η
- Literature review on the relationship of ψ -vs.-T
- Objectives of the thesis
- Organization of the thesis
Each property in this volume is averaged relative to the volume's centroid. Peck (1960) theorized that the temperature derivative of the moisture tension may consist of temperature derivatives of the enclosed air volume, the water moisture, and the surface tension of water.
C HAPTER 2
Introduction
Mathematical modeling
Pc=Pa−Pl, where Pais is the pressure of air in the closed part of the tube [Pa] (temperature dependent), and Pl is the pressure in liquid immediately below the meniscus [Pa] (Lu and Likos, 2004; De Gennes et al. ., 2004). It is assumed that there is no loss of air molecules or no air is dissolved in the liquid from the moment of contact of the capillary tube on the surface of water in the infinite reservoir until the time of reaching Jurin height.
Results and discussion
- Example 1 (Solid: Glass and Liquid: Water)
- Example 2 (Solid: Polytetrafluoroethylene/PTFE and Liquid: n- Hexadecane)
- Discussions
- Open-end capillary tube
Just as before, the capillary pressure is calculated and plotted against temperature (Fig. 2.5) using fθ(T) values in Eq. Similarly, the capillary pressure is high for shorter tubes as the enclosed space for air is low. The effects of vertical length on capillary pressure in closed tubes the researchers investigated the thermal effects of capillary pressure in open-ended tubes.
In the case of open-ended pores, the magnitude of capillary pressure is lower than that of closed-ended pores. Another observation is that the capillary pressure is more sensitive to temperature at the open ends than that of the constriction system. The limitation that can be questioned here is that the current conventional capillary pressure measurement sensors.
Summary
- Questions?
Researchers (Coats and Smith, 1964; Jackson and Klute, 1967; Wirner et al., 2014; Phirani et al., 2018, and others) provided methods to measure the immobile or stagnant or dead-end pore volume, and they always distinguished between two domains – mobile and immobile zone, but only in the form of fully saturated soil. 2.29), the mobile zone consists of fully open pores (saturated as well as unsaturated), and the immobile zone consists of blind pores. If the cul-de-sac pore is only the unsaturated part of the soil, then the expression is ∂ ψ. Therefore, the influence of cul-de-sac is relative to the physical condition of the soil or any other porous medium and depends on the equilibrium contact angle of the liquid over the solid matrix, weighting fraction and physical dimension of cul-de-sac pores in that porous medium.
The effect of temperature on the curvature of the liquid gas meniscus in the open-ended capillary tube also showed a linear decrease in capillary pressure with temperature. However, the magnitude of capillary pressure is much lower compared to the cases of dead-end pores. Furthermore, the chapter provides for the first time a conceptual insight into the significance of dead-end pores on the temperature effects on capillary pressure or on the relationship between capillary pressure and saturation at a given fluid saturation.
C HAPTER 3
- Introduction
- Mathematical modeling
- Results and discussion
- Validation against published results
- Summary
Increasing changes in PC across the meniscus due to temperature change try to start translation of the entire fluid system. Henceforth, the SCA of the meniscus will only change within the temperature range before the meniscus moves up. CAH (CH) can be interpreted as the slope of the graph between SCA and temperature in Teq ie.
Thermal variation of θede depends only on θe(Teq) and radius (R) of the capillary tube and does not depend on L. Initial SCA and radius of the tube have an impact on CAH (from different models, Kuchin and Starov(2016) also conclude that CH is depending on R). The thermal variation of the SCA of the mixture is derived here for different constant temperatures.
C HAPTER 4
Introduction
Equation of meniscus shape
- Modified PME
Phenomenologically, it can be said that the slope of the meniscus is the result of vertical and horizontal forces acting across the meniscus. Fatoorehchi and Abolghasemi gave three new theorems to handle non-linear terms in LTM using well-known Adomian polynomials (one can refer to Adomian, 1994). Decomposition of the non-linearity N(k) = d2k/dr22. first part of the left side of Eq. 4.6)) with the simple algorithm of calculation of Adomian polynomials proposed by Biazar and Shafiof (2007), we have,.
We calculate the Adom polynomials associated with the nonlinearity N(k) = e2k(dk/dr)2 (the second part of the left-hand side of Eq. As can be seen, as the rate r goes from lower to higher in Equation 4.10), the meniscus shape converges to a stable shape. A comparison between the numerical solution with RK4 (achieved by making L = 0 in the PME numerical code) and the analytical solution of mPME is made for the ethanol-air meniscus, and the result is given in Fig.
Temperature effects on capillary pressure
- Steps to calculate capillary pressure in a porous media (soil)
Numerical value of mean curvature can be found by summing the above series iMup to some finite terms (let's say number of terms). Percentages of soil separation can be known from particle size distribution (PSD) (using sieve analysis, etc.) or soil texture triangle (STT) from the Soil Conservation Service (1975). Our choice of cylindrical pore space justifies that volumetric porosity or porosity will be the same as areal porosity (as in Eq. 1.3.8 of Bear, 1972).
Equivalence of porosity and liquid content of the soil with the total volume of cylinder and liquid inside the cylinder generates a constant length value (L), for all arrangements:. where η is liquid content, wt is the statistical weight per equation. 4.21) fourth arrangement, φt = (Av)t/4t is the volumetric porosity of the cell in the fourth arrangement, (Av)t and 4t are respectively the area of voids and the total area of the tested arrangement (see expression in (4.27) ), max. Capillary pressure in triangular prism cell of the th arrangement(Pc)t (or more precisely the cylindrical pore of radius(Rp)t and length L inside the prism cell) can be evaluated through Eq. Here we calculate Mt from Eq. 4.31a) by taking up to the 22 degree power of the coefficients c2ito keep the results on a safer side (since we have used different pore sizes) and ∆rof Eq.
Results and discussion
- Effect of temperature on capillary pressure
- Effect of temperature on ACA
- Effect of liquid and air Content
- Comparison of PME and mPME results
Whenever capillary pressure-vs-temperature results at a constant moisture content are not directly given, we have fitted the van Genuchten model (van Genuchten, 1978) to available published data of dynamic capillary pressures-vs-liquid content in various constant temperatures. to interpolate and derive the information of saturated liquid content (η, i.e. maximum η) and residual saturation (ηr, i.e. following the above steps shown in Table 4.3, we have found the capillary pressure at constant temperatures. As the liquid content becomes less and less, the air-column will be more and more above the capillary liquid.
Thus, the air effect can be understood by analyzing PME and mPME capillary pressure results at different liquid contents, while keeping other parameters constant. Our results apply to static conditions and this means that we calculate the capillary pressure at a certain liquid content and temperature while the entire system is in static equilibrium. The above results of Pc, θa, air and liquid content due to T already confirm the effectiveness of PME overmPME results with respect to experimental observations.
Summary
The difference between PME and mPME in the calculation of Pc is visible as one traces the results from one soil texture to texture. These results show that PME results include the whole effect of pore radius, contact angle and surface tension of liquid, while PME results lack the information of contact angle. Here we consider the meniscus from a mechanical point of view rather than a chemical or physio-chemical point of view although chemical forces are involved at a microscopic level.
Phenomenologically, the inclination of the meniscus at each point can be written as the resultant of two forces - vertical and horizontal, i.e. The molecular component of the separation pressure arises from van der Waals bonds between condensed bodies (Lebeau and Konrad, 2010). The inclusion of this thin plane component. film in the vertical component of the force as an opposing force to gravity produces the following equation:.
C HAPTER 5
Overview
- Plausible answers
- Practical perspective
We have studied trapped air in terms of trapped pores, not as Peck's (1960) account of trapped air bubbles in liquid. Although Grant and Bachmann (2002) mentioned entrapped air effects as a possible mechanism, in their conclusions they rejected this as a contributing factor to the disparity between experimental and model developed values of the temperature coefficient of Pc .Gao and Shao (2015) after modeling and experiments noted the effects of entrapped air as a possible influencing factor. The question of the impact or importance of trapped air can be answered if it is taken into the pores of the trapped air and how many of such pores there are in an average volume or weighting factor of these pores as mentioned in Chapter-2 (Eq.
This gives the temperature gradient (∇T) in the thermal component of unsaturated soil-water flux, i.e. In the following section, we show with an example the effects of temperature on unsaturated flow. Assuming a linear relationship between temperature and soil depth in the downward z-direction with ground level as the reference axis asT =Taz+Tb, where Ta is the temperature gradient and Tb is the temperature at the soil surface.
Conclusions
If you want to use h(Pc)Y-Li= h2σcos(θ)R Y-Li instead, we recommend using a correction factor to include the missing meniscus information, ie.
Future directions
Non-steady-state fluid flow and diffusion in porous media containing unequal pore volume. A simple model for describing hydraulic conductivity in unsaturated porous media for the calculation of film and capillary flow. A simple model for describing hydraulic conductivity in unsaturated porous media for the calculation of film and capillary flow. Water Resources Research, 44:W11417.
Adsorption and Capillary Condensation in Porous Media: Fluid Retention and Interfacial Configurations in Angular Pores. A mathematically continuous model for describing the hydraulic properties of unsaturated porous media over the entire range of matric suctions. Geometric interpretation of long tails of first transit time distributions in porous media with stagnant particles.
