Equilibrium States of Mechanically Loaded Saturated and Unsaturated Polymer Gels

By a gel we mean a system of crosslinked polymer chains mixed together with a low molecular weight liquid. The polymer and liquid components mix in definite proportions as determined primarily by entropic and enthalpic effects. Swollen gels in equilibrium with a surrounding fluid bath in the absence of mechanical load are often described by a generalized Flory-Huggins equation. In this paper we consider the connection between such a treatment and the broader hyperelastic theory that treats the effect of mechanical loading in deforming the gel. A change in the mechanical loading will generally alter the proportion of liquid in the mixture, leading to either fluid loss (swelling reduction) or fluid gain (swelling increase). In such a case the gel reestablishes equilibrium only when the relative motion of the liquid through the polymer has ceased and processes have come to rest. Such processes are inherently dissipative. Our objective is to study how such reestablished equilibria depend upon mechanical load. For quasi-static loadings that give fluid gain, we then consider a situation in which the amount of available fluid is limited. In this case, increasing quasi-static loading may reach a point at which no additional fluid is available for uptake into the gel system. The associated equilibrium then transitions from a state of liquid saturation to a state in which the gel is no longer saturated. We first consider this quasi-static transition in the context of homogeneous deformation where an appropriate hyperelastic analysis shows that the equilibrium mechanical response is inherently stiffer after loss of saturation. We then consider such a transition in the context of inhomogeneous deformation by studying the boundary value problem of an everted tube subject to an axial load. Loss of saturation again leads to an inherently stiffer quasi-static response.     

非饱和介电凝胶的力学性能及力电失稳行为研究

力-电耦合场作用下,介电凝胶的体积、形状会发生相应的变化,在智能传感器与促动器等领域具有广阔的应用前景．浸入溶液中,介电凝胶将吸收溶液而溶胀．当外界溶液的量足够多时,介电凝胶将吸收足量的溶液而达到饱和状态;但如果外界溶液的量较小,没有足够的溶液可被吸收时,介电凝胶将处于非饱和状态．基于介电凝胶大变形与极化理论,对非饱和介电凝胶在等双轴应力与电场耦合作用下的力学行为及力电失稳现象进行研究．结果表明,饱和度越低介电凝胶的刚性越大,材料越硬;预应力技术可以提高介电凝胶的力电稳定性,预应力越大,力电失稳出现时的临界电压值越高．     

Equilibrium morphology of misfit particles in elastically stressed solids under chemo-mechanical equilibrium conditions

This paper studies the effects of chemical, elastic and interfacial energies on the equilibrium morphology of misfit particles due to phase separation in binary alloys under chemo-mechanical equilibrium conditions. A continuum framework that governs the chemo-mechanical equilibrium of the system is first developed using a variational approach by treating the phase interface as a sharp interface endowed with interfacial excess energy. An extended finite element method (XFEM) in conjunction with the level set method is then developed to simulate the behaviors of the coupled chemo-mechanical system. The coupled chemo-mechanics model together with the numerical techniques developed here provides an efficient simulation tool to predict the equilibrium morphologies of precipitates in phase separate alloys.     

Analytical Solutions for Reactive Transport of Multiple Volatile Contaminants in the Vadose Zone

Groundwater contamination usually originates from surface contamination. Contaminants then move downward through the vadose zone and finally reach the groundwater table. To date, however, analytical solutions of multi-species reactive transport are limited to transport only in the saturated zone. The motivation of this work is to utilize analytical solutions, which were previously derived for single-phase transport, to describe the reactive transport of multiple volatile contaminants in the unsaturated zone. A mathematical model is derived for describing transport with phase partitioning of sequentially reactive species in the vadose zone with constant flow velocity. Linear reaction kinetics and linear equilibrium partitioning between vapor, liquid, and solid phases are assumed in this model.     

Nonlinear vibrations of a vapor film in the presence of intense heat fluxes

Waves propagating along the interface between a thin vapor film and a liquid layer in the presence of a heat flux are investigated. The boundary conditions on the vapor-liquid phase surface take into account the temperature dependence of the pressure and the possibilities of formation of the metastable state of the superheated liquid and mass flow. Variations in the saturation pressure as functions of the temperature and mass flux lead to generation of weakly damped periodic waves of low amplitude whose velocity can be much higher than the velocity of the gravity waves. The waves ensure stability of the vapor film beneath the liquid layer in the gravity field. The finite-amplitude waves on the surface of the vapor film differ from the Stokes surface waves on the free surface of isothermal fluid. Instability regimes related with superheating of the liquid ant its explosive boiling when the amplitude of an initially small wave increases to infinity in a finite time can develop in a certain working-parameter regime.     

Mechanics of inhomogeneous large deformation of photo-thermal sensitive hydrogels

A polymer network can imbibe copious amounts of solvent and swell, the resulting state is known as a gel. Depending on its constituents, a gel is able to deform under the influence of various external stimuli, such as temperature, pH-value and light. In this work, we investigate the photo-thermal mechanics of deformation of temperature sensitive hydrogels impregnated with light-absorbing nano-particles. The field theory of photo-thermal sensitive gels is developed by incorporating effects of photochemical heating into the thermodynamic theory of neutral and temperature sensitive hydrogels. This is achieved by considering the equilibrium thermodynamics of a swelling gel through a variational approach. The phase transition phenomenon of these gels, and the factors affecting their deformations, are studied. To facilitate the simulation of large inhomogeneous deformations subjected to geometrical constraints, a finite element model is developed using a user-defined subroutine in ABAQUS, and by modeling the gel as a hyperelastic material. This numerical approach is validated through case studies involving gels undergoing phase coexistence and buckling when exposed to irradiation of varying intensities, and as a microvalve in microfluidic application.     

Coupled Solvent and Heat Transport of a Mixture of Swelling Porous Particles and Fluids: Single Time-Scale Problem

A three-spatial scale, single time-scale model for both moisture and heat transport is developed for an unsaturated swelling porous media from first principles within a mixture theoretic framework. On the smallest (micro) scale, the system consists of macromolecules (clay particles, polymers, etc.) and a solvating liquid (vicinal fluid), each of which are viewed as individual phases or nonoverlapping continua occupying distinct regions of space and satisfying the classical field equations. These equations are homogenized forming overlaying continua on the intermediate (meso) scale via hybrid mixture theory (HMT). On the mesoscale the homogenized swelling particles consisting of the homogenized vicinal fluid and colloid are then mixed with two bulk phase fluids: the bulk solvent and its vapor. At this scale, there exists three nonoverlapping continua occupying distinct regions of space. On the largest (macro) scale the saturated homogenized particles, bulk liquid and vapor solvent, are again homogenized forming four overlaying continua: doubly homogenized vicinal fluid, doubly homogenized macromolecules, and singly homogenized bulk liquid and vapor phases. Two constitutive theories are developed, one at the mesoscale and the other at the macroscale. Both are developed via the Coleman and Noll method of exploiting the entropy inequality coupled with linearization about equilibrium. The macroscale constitutive theory does not rely upon the mesoscale theory as is common in other upscaling methods. The energy equation on either the mesoscale or macroscale generalizes de Vries classical theory of heat and moisture transport. The momentum balance allows for flow of fluid via volume fraction gradients, pressure gradients, external force fields, and temperature gradients.     

A mixture theory analysis for the surface-wave propagation in an unsaturated porous medium

The mixture theory is employed to the analysis of surface-wave propagation in a porous medium saturated by two compressible and viscous fluids (liquid and gas). A linear isothermal dynamic model is implemented which takes into account the interaction between the pore fluids and the solid phase of the porous material through viscous dissipation. In such unsaturated cases, the dispersion equations of Rayleigh and Love waves are derived respectively. Two situations for the Love waves are discussed in detail: (a) an elastic layer lying over an unsaturated porous half-space and (b) an unsaturated porous layer lying over an elastic half-space. The wave analysis indicates that, to the three compressional waves discovered in the unsaturated porous medium, there also correspond three Rayleigh wave modes (R1, R2, and R3 waves) propagating along its free surface. The numerical results demonstrate a significant dependence of wave velocities and attenuation coefficients of the Rayleigh and Love waves on the saturation degree, excitation frequency and intrinsic permeability. The cut-off frequency of the high order mode of Love waves is also found to be dependent on the saturation degree.     

储层含水条件下致密砂岩/页岩无机质纳米孔隙气相渗透率模型

页岩及致密砂岩储层富含纳米级孔隙,且储层条件下页岩孔隙(尤其无机质孔隙)及致密砂岩孔隙普遍含水,因此含水条件下纳米孔隙气体的流动能力的评价对这两类气藏的产能分析及生产预测具有重要意义.本文首先基于纳米孔隙内液态水及汽态水热力学平衡理论,量化了储层孔隙含水饱和度分布特征;进一步在纳米孔隙单相气体传质理论的基础上,考虑了孔隙含水饱和度对气体流动的影响;最终建立了含水饱和度与气相渗透率的关系曲线. 基于本文岩心孔隙分布特征,计算结果表明:储层含水饱和度对气体流动能力的影响不容忽视,在储层含水饱和度20%的情况下,气相流动能力与干燥情况相比将降低约10%;在含水饱和度40% 的情况下,气相流动能力将降低约20%.      

Thermodynamic Correction for Salts in Variably Saturated Porous Media

Using thermodynamic principles, the general relationship describing the equilibrium vapor content in the gas phase above a saline liquid and across a curved liquid–gas interface is developed. Since high salt concentration affects the intensive and extensive liquid properties, it is also necessary to account for these effects in liquid water content/liquid water pressure relationship curves so that experimentally derived curves for pure water may be useful for elevated salt concentrations. The appropriate thermodynamic relationships are derived to describe the salt effects on liquid and vapor properties. The resulting equations are valid for salt concentrations between zero and saturation, and for any temperatures that nominally occur in nearsurface geologic materials.     

Molecular gas dynamics applied to phase change processes at a vapor–liquid interface: shock-tube experiment and MGD computation for methanol

This paper deals with a molecular gas-dynamics method applied to the accurate determination of the condensation coefficient of methanol vapor. The method consisted of an experiment using a shock tube and computations using a molecular gas-dynamics equation. The experiments were performed in such situations where the shift from a vapor–liquid equilibrium state to a nonequilibrium one is realized by a shock wave in a scale of molecular mean free time of vapor molecules. The temporal evolution in thickness of a liquid film formed on the shock-tube endwall behind a reflected shock wave is measured by an optical interferometer. By comparing the measured liquid-film thickness with numerical solutions for a polyatomic version of the Gaussian–BGK model of the Boltzmann equation, the condensation coefficient of methanol vapor is accurately determined in vapor–liquid nonequilibrium states. As a result, it is clear that the condensation coefficient is just unity very near to an equilibrium state, but is smaller far from the equilibrium state.     

基于介观结构的饱和与非饱和多孔介质有效应力

基于描述含液颗粒材料介观结构的Voronoi 胞元模型和离散颗粒集合体与多孔连续体间的介-宏观均匀化过程, 定义饱和与非饱和多孔介质有效应力. 导出了计及孔隙液压引起之颗粒体积变形的饱和多孔介质广义有效应力. 用以定义广义有效应力的Biot 系数不仅依赖于颗粒材料的多孔连续体固体骨架及单个固体颗粒的体积模量(材料参数),同时与固体骨架当前平均广义有效应力及单个固体颗粒的体积应变(状态量) 有关. 提出了描述非饱和多孔介质中非混和固体颗粒、孔隙液体和气体等三相相互作用的具介观结构的Voronoi 胞元模型.具体考虑在低饱和度下双联(binary bond) 模式的摆动(pendular) 液桥系统介观结构. 导出了基于介观水力-力学模型的非饱和多孔介质的各向异性有效应力张量与有效压力张量. 考虑非饱和多孔介质Voronoi 胞元模型介观结构的各向同性情况,得到了与非饱和多孔连续体理论中唯象地假定的标量有效压力相同的有效压力形式.但本文定义的与确定非饱和多孔介质有效应力和有效压力相关联的Bishop 参数由基于三相介观水力-力学模型, 作为饱和度、孔隙度和介观结构参数的函数导出,而非唯象假定.      

Sorption hysteresis on microrough surfaces

Numerical experiments on the adsorption of water vapor based on vapor silver substrates with different microroughness were performed using a modified Langmuir adsorption model. The calculations revealed a number of phenomena making it possible to clarify the interpretation of many experimental data on sorption. It is established that significant initial microroughness of a silver substrate causes a sharp increase in the number of molecules of an equilibrium adsorbate and provides a stable liquid film of the adsorbate under conditions close to saturation conditions. It is shown that stability of the film state is due to the fact that its further growth or evaporation are only possible because of nucleation processes under significant supersaturation or overheating. The results obtained can be used to improve technologies based on adsorption processes.     

考虑耦合质量影响的饱和多孔介质动力响应分析的显式有限元法

根据Biot饱和多孔介质动力方程,采用解耦技术,提出了考虑耦合质量Pd影响的饱和多孔介质中动力响应分析的显式有限元法。文中建立并推导了显式有限元的公式,编制了相应的计算程序并进行了实例计算。计算结果与解析解进行了对比,两者符合很好,表明本文方法是处理饱和多孔介质动力问题的一种有效方法。文中还分析了耦合质量ρa对固相和液相动位移的影响。     

Dynamics of Viscous Entrapped Saturated Zones in Partially Wetted Porous Media

As a typical multiphase fluid flow process, drainage in porous media is of fundamental interest both in nature and in industrial applications. During drainage processes in unsaturated soils and porous media in general, saturated regions, or clusters, in which a liquid phase fully occupies the pore space between solid grains, affect the relative permeability and effective stress of the system. Here, we experimentally study drainage processes in unsaturated granular media as a model porous system. The distribution of saturated clusters is analysed by optical imaging under different drainage conditions, with pore-scale information from Voronoi and Delaunay tessellation used to characterise the topology of saturated cluster distributions. By employing statistical analyses, we describe the observed spatial and temporal evolution of multiphase flow and fluid entrapment in granular media. Results indicate that the distributions of both the crystallised cell size and pore size are positively correlated to the spatial and temporal distribution of saturated cluster sizes. The saturated cluster size is found to follow a lognormal distribution, in which the generalised Bond number (\( Bo^{*} \)) correlates negatively to the scale parameter (μ) and positively to the shape parameter (σ). With further consideration of the total surface energy obtained based on liquid–air interfaces, we were able to include additional grain-scale information in the constitutive modelling of unsaturated soils using both the degree of saturation and generalised Bond number. These findings can be used to connect pore-scale behaviour with overall hydro-mechanical characteristics in granular systems.     

地下水位上升下黄土斜坡稳定性分析

黄土高原一些地区,由于塬上引水灌溉使得地下水位不断抬升,造成黄土滑坡频繁发生。地下水位变化严重影响着黄土斜坡的稳定性。基于饱和-非饱和渗流理论和延伸的摩尔-库伦破坏准则,结合室内饱和和非饱和试验结果,针对泾阳南塬一典型黄土斜坡,考虑地下水位上升情况下,对其进行了瞬态饱和-非饱和渗流分析;然后将计算得到的瞬态孔隙水压力分布用于斜坡的极限平衡分析。结果表明:地下水位上升对暂态渗流场和斜坡稳定性有明显影响;考虑非饱和渗流和吸力强度的边坡稳定分析方法更加符合实际情况。     

Mixture theory and unsaturated flow in swelling soils

The current state of knowledge on various aspects of mixture theory applied to unsaturated/saturated swelling soils is discussed. Two and three phase problems are studied. On the smallest scale (micro) the individual platelets and adsorbed (vicinal) water exist as separate phases. On the intermediate scale (meso) the platelets and vicinal water are homogenized to form a saturated particle where vicinal water and solid are overlaying continua. On the macroscale, bulk water, water vapor, and the mesoscale particles are homogenized resulting in three overlaying continua for solid, bulk water, vicinal water, and water vapor. Stress tensor formulations and Darcy’s laws are presented at the mesoscale and macroscales. A theoretical formulation for surface crusting is presented at the mesoscale. General viscoelastic mesoscale and macroscale models are discussed and related to classical approaches.     

非饱和土-隧道系统动力响应计算的波函数法

针对非饱和地基土中埋置隧道的三维动力响应计算问题, 提出了波函数法.采用无限长的Flügge薄壁圆柱壳模拟圆形隧道衬砌,采用流、固、气组成的三相介质模拟非饱和地基土体.分别采用分离变量法以及Helmholtz矢量分解定理求解薄壁圆柱壳的振动控制方程与非饱和土的波动方程.根据隧-土交界面与地表面处的应力、位移以及孔隙流体压力等边界条件,利用平面波与柱面波的转换性质,实现了隧道内作用单位简谐载荷时隧道衬砌与土体系统动力响应的耦合求解.通过与既有单相弹性介质2.5维有限元-边界元法、两相饱和多孔介质2.5维有限元-边界元法以及三相非饱和介质Pip in Pip半解析法的计算结果进行对比, 验证了本文计算方法的可靠性. 最后,基于该方法, 通过算例分析了不同饱和度下非饱和土-隧道系统的动力响应特征.结果表明, 饱和度对土体动位移与超孔隙水压力的幅值响应有较大影响.该方法的非饱和地基土参数退化后,也可用来计算和分析饱和地基土或单相弹性地基土与隧道系统的动力响应.      

Formulation of a finite deformation model for the dynamic response of open cell biphasic media

The paper illustrates a biphasic formulation which addresses the dynamic response of fluid saturated porous biphasic media at finite deformations with no restriction on the compressibility of the fluid and of the solid skeleton. The proposed model exploits four state fields of purely kinematic nature: the displacements of the solid phase, the velocity of the fluid, the density of the fluid and an additional macroscopic scalar field, termed effective Jacobian, associated with the effective volumetric deformation of the solid phase.The governing equations are characterized by the property of being all expressed in the reference configuration of the solid phase and by the property of employing only work-conjugate variables, thus avoiding the use of a total Cauchy stress tensor.In particular, the set of governing equations includes a momentum balance equation associated with the effective Jacobian field. This equation, differently from the closure-equations proposed by other authors which express a saturation constraint or a porosity balance, is derived as a stationarity condition on account of a least-action variational principle.     

Analysis of coupled thermo-hydro-mechanical behavior of unsaturated soils based on theory of mixtures I

This paper analyzes a coupled thermo-hydro-mechanical behavior of unsaturated soils based on the theory of mixtures. Unsaturated soil is considered as a mixture composed of soil skeleton, liquid water, vapor, dry air, and dissolved air. In addition to the mass and momentum conservation equations of each component and the energy conservation equation of the mixture, the system is closed using other 37 constitutive （or restriction） equations. As the change in water chemical potential is identical to the change in vapor chemical potential, a thermodynamic restriction relationship for the phase transition between pore water and pore vapor is formulated, in which the impact of the change in gas pressure on the phase transition is taken into account. Six final govern- ing equations are given in incremental form in terms of six primary variables, i.e., three displacement components of soil skeleton, water pressure, gas pressure, and temperature. The processes involved in the coupled model include thermal expansions of soil skeleton and soil particle, Soret effect, phase transition between water and vapor, air dissolution in pore water, and deformation of soil skeleton.