Drying Kinetics of Porous Stones in the Presence of NaCl and \hbox {NaNO}_{3}: Experimental Assessment of the Factors Affecting Liquid and Vapour Transport

Salt decay is one of the most harmful and complex deterioration mechanisms of porous building materials in architectural heritage. Despite several decades of research, it is still insufficiently understood, which hampers the development of effective treatments and prediction models. One key aspect is the influence soluble salts have on the evaporative drying of porous materials. It is often observed, for example, that drying is slower for higher salt concentrations. However, there is still no consensus as to why it happens. In this article, we examine experimentally the drying kinetics of three natural stones impregnated with solutions of sodium chloride or sodium nitrate with different concentrations. The method consisted of the following sequence of determinations: capillary absorption, drying kinetics, vapour pressure and vapour conductivity. It also included a morphological analysis of the efflorescence formed during drying. We have concluded that the slower drying rate was mainly due to the reduced sorptivity that arises at higher salt concentrations. In the cases where compact salt crusts formed on the surface of the stone, there was an additional reduction in the drying rate because these crusts obstructed vapour transport. However, in most cases, efflorescence was porous and had negligible obstructive effects. Efflorescence morphology is conditioned by well-determined causal factors, such as porosity, pore size and mineralogical structure of the stone, or the type of salt and its concentration. Here, it also revealed that it incorporated a component of unpredictability. This suggests that it may be necessary to move beyond purely deterministic approaches to salt decay.     

Impact of Capillary-Driven Liquid Films on Salt Crystallization

Flow-through drying of ionic liquids in porous media can lead to super saturation and hence crystallization of salts. A model for the evolution of solid and liquid concentrations of salt, in porous media, due to evaporation by gas flow is presented. The model takes into account the impact of capillary-driven liquid film flow on the evaporation rates as well as the rate of transport of salt through those films. It is shown that at high capillary wicking numbers and high dimensionless pressure drops, supersaturation of brine takes place in the higher drying rate regions in the porous medium. This leads to solid salt crystallization and accumulation in the higher drying rate region. In the absence of wicking, there is no transport and accumulation of solid salt. Results from experiments of flow-through drying in rock cores are compared with model prediction of salt crystallization and accumulation.     

On Ions Transport during Drying in a Porous Medium

Salt crystallisation at the surface or in a porous medium has been recognised as a major mechanism of deterioration of buildings and historical monuments. Often crystallisation occurs when the concentration of salt dissolved in the water contained in the porous medium reaches the saturation concentration as the result of evaporation. In order to predict the evolution of the ion distribution during drying, we develop a simple volume averaged model combining a semi-analytical model of drying with the numerical computation of the ions transport. The model is used to analyse the influence of the drying rate, size of the porous medium, average pore size and initial ion concentration on the ion distribution during drying and therefore the possible location of crystallisation.     

Multiphase transfer model for intermittent microwave-convective drying of food: Considering shrinkage and pore evolution

Intermittent microwave convective (IMCD) drying is an advanced drying technology that improves both energy efficiency and food quality during drying. Although many experimental studies on IMCD have been conducted, there is no complete multiphase porous media model describing the physics of the process available in the literature. A multiphase porous media model considering liquid water, gases and the solid matrix of food during drying can provide in-depth understanding of IMCD process. Currently there is no IMCD model that have taken shrinkage and pore evolution during drying into consideration. In this study, first a multiphase porous media model with shrinkage (IMCD2) has been developed for IMCD. Then the model has been compared with IMCD model without shrinkage (IMCD1). Simulated temperature, moisture content, density, porosity from IMCD2 are then validated against experimental data. The profile of vapour pressures and evaporation during IMCD are also presented and discussed.     

Effect of Rainfall-Induced Soil Seals on the Soil Water Regime: Drying Interval and Subsequent Wetting

The effects of rainfall-induced soil seals on drying processes and on infiltration following drying intervals are simulated for two different soils, a loam and a sandy loam. The simulated drying processes include water content redistribution without evaporation and under a constant evaporation rate of 5 mm day^–1. During evaporation, the water content at the seal surface decreases rapidly. A high water content gradient develops within the seal, which increases along the drying interval. It indicates that, at least during the first hours of drying, the seal layer fulfilled all the evaporation demand and therefore dries faster that an unsealed soil where the evaporation is supplied by a much deeper zone of the soil profile. This phenomenon is more accentuated in the loam than in the sandy loam soil. Considering the subsequent infiltration curves during rainfall following different drying intervals, the ponding time and the post-ponding infiltration rates increase when the antecedent drying period is longer, but no significant effect on the final infiltration is found following drying intervals of few days. Also, the water content at the sealed soil surface before rainfall seems to play a major role on infiltration. Very close infiltration curves were obtained after different drying intervals that ended with similar surface water content.     

Water removal from porous media by gas injection: experiments and simulation

The flow of a saturated gas through a porous medium, partially occupied by a liquid phase, causes evaporation due to gas expansion. This process, referred to as flow-through drying, is important in a wide variety of natural and industrial applications, such as natural gas production, convective drying of paper, catalysts, fuel cells and membranes. X-ray imaging experiments were performed to study the flow-through drying of water-saturated porous media during gas injection. The results show that the liquid saturation profile and the rate of drying are dependent on the viscous pressure drop, the state of saturation of the gas and the capillary characteristics of the porous medium. During the injection of a completely saturated gas, drying occurs only due to gas expansion. Capillary-driven flow from regions of high saturation to regions of low saturation lead to more uniform saturation profiles. During the injection of a dry gas, a drying front develops at the inlet and propagates through the porous medium. The experimental results are compared with numerical results from a continuum model. A good agreement is found for the case of sandstone. The comparison is less satisfactory for the experiments with limestone.     

Drying Rate Measurements in Convection- and Diffusion-Driven Conditions on a Shaly Sandstone Using Nuclear Magnetic Resonance

Carbon Capture and Storage (CCS) is one of the solutions studied to reduce greenhouse gas accumulation in the atmosphere. Depleted oil and gas reservoirs have been studied for potential storage sites but also saline aquifers that have the advantages of much larger pore volume. In this latter case, injection of large volume of anhydrous carbon dioxide will lead to a strong water desaturation of the near wellbore region because of evaporation mechanisms. Even the capillary trapped water can be removed by thermodynamical transfer of water vapor in the CO₂ phase. The extension in time and space of the dry zone will be controlled by the drying rate induced by the gas flow. Consequences of drying may induce alteration of the injectivity by salt precipitation and/or alteration of the rock fabric itself, especially for shaly sandstones in the case of clay drying. The context of CCS has raised new interests in the understanding of drying kinetic where the water vapor is evacuated by gas convection. In this study, we investigated experimentally the drying rate evolution with time on a shaly sandstone sample in two conditions of drying: convective and diffusive. In convective conditions, air is injected at different flow rates through the porous media in conditions of drying representative of a CO₂ injection site at one million ton per year. In diffusive conditions, no flow is imposed and the water vapor escape by diffusion. Drying rates dynamics in both conditions were measured by Nuclear Magnetic Resonance (NMR) and compared. We varied the temperature and the salinity in diffusive-driven drying and the gas flow rate in convective-driven drying. The water distribution in the pore network and the water saturation profiles were monitored continuously using T₂ relaxation and 1D imaging NMR techniques. For the range of temperature and air flow rate used, we show that drying rates in the two drying conditions are similar but not identical. They both present different periods characteristic of the main mechanisms for water mass transfer. Drying rate has a power law dependence on the temperature, as predicted by thermodynamic, and drying rate was found proportional to the flow rate in convective drying. Presence of salt has a complex effect: an increase of the drying rate at early stage of drying followed by a strong decrease for the remaining time of drying.     

Droplet evaporation on porous and non-porous ceramic solids heated from top

 This paper presents the results of an experimental investigation, of the effect of radiation heat, on the evaporation of five droplet sizes of pure water, softly deposited on porous and non-porous ceramic solids, at temperature ranging from 75 to 250 °C. Both solids were instrumented with several surface and in-depth thermocouples, and had the same thermal properties. Results show that, the droplet evaporation time, and the surface recovery time for the porous solid were shorter than that of non-porous solid for the same droplet size under identical conditions. Also, smaller droplets were more efficient for cooling both solids. The results were compared with data for the evaporation of water droplets on similar ceramic solids heated from bottom (Abu-Zaid M; Atreya A (1994) J Heat Transfer 116: 694–701). The comparison shows that, the heat radiation has a significant effect of reducing evaporation time, recovery time, and droplet volume of influence for both solids, at the same initial surface temperature. Received on 6 December 1999 / Published online: 29 November 2001     

Combined resistance bubbling bed model for drying of solids in fluidized beds

Fluidized bed drying kinetics of highly porous material which offers free flow of moisture to surface of the material is modeled utilizing the simplified bubbling bed model. The simplification step utilizes estimation of the overall transfer resistance, by summing all the resistances from the bubble phase to the emulsion phase. The model predictions are compared with the published experimental data covering the operating variables such as the inlet air temperature, the air flow rate, material characteristics and are found to match satisfactorily. The model highlights the importance of bubble size estimation, as it largely dictates the drying kinetics.     

Water Evaporation Versus Condensation in a Hygroscopic Soil

The liquid/vapour phase change of water in soil is involved in many environmental geotechnical processes. In the case of hygroscopic soils, the liquid water is strongly adsorbed on the solid phase and this particular thermodynamic state can highly influence the phase change kinetics. Based on the linear Thermodynamic of Irreversible Processes ideas, the non-equilibrium phase change rate is written as a linear function of the water chemical potential difference between the liquid and vapour state. In this relation, the system is characterized by a phenomenological coefficient that depends on the state variables. Using an original experimental set-up able to analyze the response of a porous medium subjected to non-equilibrium conditions, the phase change coefficient is determined in various configurations. This paper focuses on the influence of the gas phase pressure and underlines that a low gas pressure decreases the phase change kinetics. Then, evaporation and condensation processes are compared showing an asymmetric behaviour. These experimental results are interpreted from a microscopic point of view by relying on recent works dealing with molecular dynamics numerical simulation of the liquid/gas interface.     

Numerical and experimental investigation of convective drying in unsaturated porous media with bound water

The heat and mass transfer in an unsaturated wet cylindrical porous bed packed with quartz particles was investigated theoretically for relatively low convective drying rates. Local thermodynamic equilibrium was assumed in the mathematical model describing the multi-phase flow in the unsaturated porous media using the energy and mass conservation equations to describe the heat and mass transfer during the drying. The drying model included convection and capillary transport of the free water, diffusion of bound water, and convection and diffusion of the gas. The numerical results indicated that the drying process could be divided into three periods, the temperature rise period, the constant drying rate period and the decreasing drying rate period. The numerical results agreed well with the experimental data verifying that the mathematical model can evaluate the drying performance of porous media for low drying rates. The effects of drying conditions such as the ambient temperature, the relative humidity, and the velocity of the drying air, on the drying process were evaluated by numerical solution.     

Internal Heating Effect and Enhancement of Drying of Ceramics by Microwave Heating with Dynamic Control

The effectiveness of internal heating for enhancing the drying of molded ceramics is evaluated by both modeling and experiments. In the theoretical analysis, three dimensional drying-induced strain–stress are modeled, and the numerical solutions show that the internal heating generates lower internal stress than continuous convective heating or intermittent convective heating. Microwave drying is examined experimentally to study the effect of internal heating on the drying behavior of a wet sample of a kaolin slab. The drying behavior is compared among three modes: microwave heating, hot air heating and radiation heating. The transient behavior of temperatures in microwave drying is quite different from conventional drying by external heating. In particular, the temperature of the slab drops once in the progress of drying. This phenomenon cannot be predicted adequately by a simple model of one-dimensional heat conduction and moisture diffusion accompanied with an internal heat generation rate given as a linear function of the moisture content. It should be noted that the temperature behavior takes place due to the combined interactions with internal evaporation of moisture by rise in internal vapor pressure and shift of impedance or interference in the applicator. Microwave heating with a constant power above 100 W results in sample breakage due to the internal vapor pressure. However, if the power is dynamically controlled so as to maintain the temperature less than the boiling point of water, the drying succeeds without any crack generation until completion with a significantly faster drying rate than drying in convective heating or in the oven.     

Liquid superheat during nonequilibrium boiling

Heat and mass transfer processes in a pure liquid subject to intense heating is investigated. The temperature escalation rate in a heated pure liquid is controlled by two competing processes; the external power deposition and the rate of nuclei formation and growth in the liquid, which acts as a heat sink. A heat balance equation is developed and solved numerically to yield the liquid temperature curve and the evaporation rate up to the maximum attainable superheat point. The effect of heating rate on the liquid temperature curve is quantified.     

Analysis of Crack Patterns in Drying Corn Starch by in-situ Radiography and X-ray Computer Tomography

The formation of crack patterns in drying starch-water slurries is studied by means of in-situ radiography (measuring of the crack front velocity) and X-ray microtomography as an example of crack patterns driven by inhomogeneous shrinkage. The tomograms show the 3D crack networks forming columns with polygonal cross-sections. After crack initiation, the average crack spacing increases with growing depth, even if the crack front velocity is constant. A constant velocity is obtained by maintaining a constant evaporation rate using a feedback control. When the crack front has propagated at a constant evaporation rate over a distance of some millimeters, the average crack spacing approaches a stable value which depends on crack front velocity according to a power law. This relationship is compared to corresponding results of other authors and model predictions. The increase of crack spacing before stable values are achieved, is interpreted as a result of successive crack front instabilities.     

Sweep numerical method and mass transport analysis in atmospheric freeze drying of protein particles

This work covers heat pump drying of protein with high quality and low cost. It consists of atmospheric freeze drying to keep product quality followed by evaporation to reduce time. A sweep numerical method was applied to predict the mass transport from the porous particle to gas. The maximum deviation between predictions and mass transfer data was below 4% indicating that the method well describes mass transport during protein drying.     

Some nonlinear problems of groundwater flow through a porous medium

Self-similar solutions of the equation of groundwater gravity flow through a porous medium are given. The water flows from a basin into an underground permeable reservoir bounded from below by an impervious bed. A periodic problem of flow through a porous medium in which the water level in the basin periodically oscillates is considered. It is shown that in this case the water table elevation effect, i.e., water pumping into the aquifer, develops at a sufficient distance from the littoral zone. The invariant-group solutions of the problem of flow through a porous medium are investigated with allowance for evaporation from the groundwater surface.     

Relative permeability relations: A key factor for a drying model

In the modelling of heat, mass and momentum transfer phenomena which occur in a capillary porous medium during drying, the liquid and gas flows are usually described by the generalised Darcy laws. Nevertheless, the question of how to determine experimentally the relative permeability relations remains unanswered for most materials that consist of water and humid air, and as a result, arbitrary functions are used in the drying codes. In this paper, the emphasis is on deducing from both numerical and experimental studies a method for estimating pertinent relations for these key parameters. In the first part, the sensitivity of liquid velocity and, consequently, of drying kinetics in the variation of the relative permeabilities is investigated numerically by testing various forms. It is concluded that in order to predict a realistic liquid velocity behaviour, relative permeabilities can be linked to a measurable quantity: the capillary pressure. An estimation technique, based on simulations coupled with experimental measurements of capillary pressure, together with moisture content kinetics obtained for low or middle temperature convective drying, is deduced. In the second part, the proposed methodology is applied to pine wood. It is shown that the obtained relations provide closer representation of physical reality than those commonly used.     

Evaporation From Confined Porous Media Due to Controlled IR Heating From Above

We report an experimental study of evaporation due to controlled infrared (IR) heating from above from an initially saturated confined porous medium consisting of nearly ‘mono-disperse’ particles which has been rarely used earlier. We have used three diagnostic tools simultaneously, evaporation rate measurements using a precision weighing balance, surface temperature measurements using IR imaging, and fluorescein dye mixed with water to visualize the drying front and the evaporation sites. IR images show that the first stage, so-called constant rate period (CRP), was maintained due to films of water reaching the top surface from the saturated region below. Gradually reducing evaporation rate in stage 1 is shown to be related to ‘shrinking evaporating patches’ on the top surface, clearly revealed as lower-temperature regions in the IR images. End of CRP coincides with disappearance of the low-temperature patches. We give end of CRP in terms of the average depth (L_cap) of the liquid level from the top surface at that time. L_cap and duration of CRP are strong functions of the porous medium bead size, transition to stage 2 happening earlier for coarser spheres. The obtained L_cap values deviated from the predictions of Lehmann et al. (Phys Rev E 77(5):056309, 2008) which we show is due to a small range of pore sizes in the current experiments. For both water and highly volatile n-pentane, we show that L_cap normalized by a length scale derived from gravity-surface tension force balance goes like Bo^0.20, for Bo varying from 2.0E ? 04 to 1.0E ? 01; Bo is the Bond number. Fluorescein dye imaging shows a different view of the evaporation stages. During CRP, highly concentrated deposits of the fluorescein dye particles, orange in colour, are seen in the top few bead layers. These orange deposits represent the sites on the beads surfaces where the evaporation has taken place. Even with external heating, evaporation from such a porous medium is limited to a finite depth from the evaporating end, similar to the observation by Lehmann et al. (2008) for isothermal evaporation in Hele-Shaw cell.     

Staggered Finite Volume Modeling of Transport Phenomena in Porous Materials with Convective Boundary Conditions

The aim of this article is to present a one-dimensional finite volume modeling of mass transport phenomena in partially saturated open porous media. The finite volume model is based on a staggered solution strategy which permits to solve the equations sequentially. This appropriate partitioning reduces thus the size of the system to be solved at each time step. Therefore, two iterative algorithms are proposed to solve the discretized problem. Moreover, an original treatment of the convective boundary condition, based on a suitable linearization to derive the algebraic form of this condition, is also presented. The computational model is then specifically used for studying the drying process of a cementitious material. For this purpose, the two proposed algorithms are compared in terms of computational efficiency. Thereafter, the convective boundary condition is analyzed with regard to the drying kinetics. Finally, a one-dimensional drying experimental test is simulated.     

交变电场作用下单液滴蒸发的分子动力学模拟

利用分子动力学方法研究了正弦形式的交变电场对三维悬浮水滴在超临界氮气环境下蒸发特性的影响, 主要考虑了电场幅值和频率对液滴蒸发寿命和液滴瞬时蒸发速率的影响. 其中水滴由8000个水分子组成, 环境气体由27000个氮气分子组成. 首先利用分子动力学方法模拟计算了不同状态下水的物性参数以及亚临界条件下匀强电场对液滴蒸发特性的影响, 从而验证了分子模型和蒸发模型的正确性. 接着模拟了在不同幅值和频率的交变电场作用下水滴在氮气环境下的蒸发过程, 结果表明, 相比于无电场或匀强电场, 交变电场能够更显著地促进水滴的蒸发. 在频率一定时, 随着电场幅值的增大, 液滴的蒸发速率不断升高, 蒸发寿命不断下降, 且液滴的瞬时蒸发速率、液滴温度、水分子的排列结构等参数都会产生频率为所加电场二倍的振荡特性, 且电场幅值越大, 振荡幅值也越大. 而在电场幅值一定时, 随着频率的增大, 液滴蒸发寿命和速率并不是单调变化的, 而是在频率$f=5$GHz时, 分别达到一个极大值和极小值, 文中从液滴能量和分子排列结构两个方面解释了产生了这一现象的原因.