Wicking Technique for Determination of Pore Size in Ceramic Materials

A technique is described for the measurement of mean pore size in ceramics by wicking. Pore size is derived from the measured rates of capillary rise of several apolar, low-energy liquids of known surface tension through thin slices of porous materials, via the Washburn equation. The use of apolar, low-energy liquids assures that the contact angle θ=0° (and cos θ= 1) so that the mean pore radius, R , is the only unknown in the Washburn equation. Fore-size data are presented for two colloidal gel compositions with engineered pore-size distributions. Pore diameters obtained from wicking are found to be smaller than those afforded by merciury porosimetry by a factor of ∼2.     

Capillary infiltration studies of liquids into 3D-stitched C–C preforms: Part A: Internal pore characterization by solvent infiltration,mercury porosimetry,and permeability studies

Mathematical modeling of silicon infiltration in porous carbon–carbon (C–C) preforms is the key to fabricate liquid silicon infiltration based carbon–silicon carbide (C–SiC) composite components. Existing models for silicon infiltration are based on straight capillaries. For interconnected capillary systems, e.g. as in 3D-stitched C–C preforms these show large deviations when compared with experimental observations. The aim of the present study is to develop a mathematical model suitable for silicon infiltration in 3D-stitched C–C preforms. The work is being presented in two parts: A and B. This part (Part A) describes the experimental details pertaining to the fabrication of the C–C preforms and their pore structure characterization by mercury porosimetry, infiltration of solvents by capillary rise, and by permeability studies. A two-pore capillary infiltration model termed as modified Washburn equation has been proposed. It has been validated by experimental data of solvent infiltration. The same model correlates silicon infiltration observations as well (Part B).     

Liquid metal infiltration of silicon based alloys into porous carbonaceous materials. Part II: Experimental verification of modelling approaches by infiltration of Si-Zr alloy into idealized microchannels

In this work, the mechanisms leading to the pore closure in reactive melt infiltration (RMI) of carbon by pure silicon and a near eutectic Si-8 at-pct Zr alloy at 1500 and 1700 °C under vacuum were studied. Various geometrical configurations of microchannels were fabricated via laser ablation of glassy carbon plates. The micron size capillary channels allowed simplifying the complicated porosity distribution in the infiltration of powder or fibres based porous preform while keeping the physical dimensions in the range of where the physical phenomenon of pore closure takes place. The extent of infiltration was analysed by means of X-ray radiography. For RMI of pure Si, the widely accepted decrease in capillary radius by the formation of a solid state SiC layer by the reaction of liquid Si and C was observed, but did not lead to closure and it is hence not the infiltration limiting step in channels as small as 10 μm. However, in the case of the Si-Zr alloy infiltration, another mechanism of pore closure was observed, namely the precipitation of zirconium silicides at the infiltration front, due to Zr enrichment in the alloy by the continuous consumption of Si for the formation of SiC.     

Sulfur infiltration and allotrope formation in porous cathode hosts for lithium-sulfur batteries

We investigate sulfur infiltration and formation of lower order allotropes in heated porous hosts during fabrication of lithium-sulfur (Li-S) battery cathodes. Sulfur existence in cathode ultramicropores has been an important question for Li-S batteries, as ultramicropores reduce the polysulfides “shuttle effect” but also delay sulfur dissolution and Li⁺ ion diffusion in the trapped solid sulfur. A novel continuum-level model is presented including heat transfer and sulfur infiltration, either from the top of a porous host or from the porous host particle surface, and taking into account the pore size distribution. A novel decay factor in modeling sulfur infiltration incorporates the pore wall repulsion energy and allotrope formation energy (predicted by density functional theory [DFT] simulations). Simulations are performed for a microporous carbon fabric host and an activated carbon powder host with bimodal micropore and macropore size distribution, with Raman and X-ray photoemission spectroscopy (XPS) spectroscopy confirming the predicted existence of linear S₆ and S₄ in ultramicropores.     

A new model to determine contact angles on swelling polymer particles by the column wicking method

The contact angle determination on swelling polymer particles by the Washburn equation using column wicking measurements may be problematic because swelling occurs during the wicking process. The objective of this research was to develop a new model to more accurately determine contact angles for polymer particles that undergo solvent swelling during the column wicking process. Two phenomena were observed related to the swelling effect during the wicking process: (1) a temperature rise was detected during the wicking process when the swelling polymer particles interacted with polar liquids, and (2) a smaller average capillary radius (r) was obtained when using methanol (polar liquid) compared to using hexane (non-polar liquid). The particle swelling will induce both particle geometry changes and energy loss which will influence the capillary rise rate. The model developed in this study considered the average pore radius change and the energy loss due to the polymer swelling effect. Contact angle comparisons were conducted on wood with formamide, ethylene glycol, and water as test liquids, determined by both the new model and the Washburn equation. It was shown that the contact angles determined by the new model were about 4-37° lower than those determined by the Washburn equation for water, formamide, and ethylene glycol. Todetermine whether the polymer particles are swelling, two low surface tension liquids, one polar (methanol) and the other non-polar (hexane), can be used to determine the average pore radius (r values) using the Washburn equation. If the same r values are obtained for the two liquids, no swelling occurs, and the Washburn equation can be used for the contact angle calculation. Otherwise, the model established in this study should be used for contact angle determination.     

Capillary Pressure Estimation Using Statistical Pore Size Functions

Capillary pressure curves, which have been employed for a long period of time by researchers interested in pore size distribution, are commonly obtained from experimental measurements. The dynamic capillary pressure that influences the flow is affected by many factors including the pore size characteristics and pore scale dynamics. Hence, it is important to investigate the variation of the estimated pore size distribution with capillary number. In this study, a glass type micromodel is considered as the porous media sample. A parametric probability density function is proposed to express the pore size distribution of the porous model, which is also measured using an image analysis technique. The capillary pressure saturation mathematical model is developed by integrating the pore size distribution function. Model parameters with a physical significance are estimated by fitting the model to the measured capillary pressure data at different capillary numbers. The results of capillary pressure obtained are well matched to the measured values. The results show that the trends of the extracted pore size distribution curves have similar trends, but they are not exactly the same. Therefore, the dynamic capillary pressure data alone are not sufficient for estimation of the pore size distribution. As a related development, the prediction of the capillary pressure curves based on measured pore size distributions is also presented. The proposed probability distribution function has the flexibility of representing a wide variety of pore size distributions.     

ONE- AND TWO-PHASE FLOW IN NETWORK MODELS OF POROUS MEDIA

We discuss the low Reynolds number flow of one or two immiscible Newtonian fluids in network models of microscopically random porous media. For the case of a single fluid, we reduce the flow problem to an analog random electrical resistor problem and use an 'effective medium theory' to express the permeability of such networks in terms of the pore space geometry. For the flow of two fluids we use the Washburn approximation to incorporate capillary pressure differences, and show that this problem may also be formulated as a random electrical network. In this case, the capillary menisci correspond to moving batteries, and we follow the motion of the fluid-fluid interface (the ensemble of analog batteries) by a time-step procedure. We study the time evolution of the interface and the dynamics of blobs of one fluid contained in the other, as a function of the network geometry.'     

Evaluation of the pore size distribution in mercury porosimetry using computer simulations of porous media

The pore size distribution calculated using the Washburn equation was evaluated. The pore-sphere network was selected as a model for porous media since this model could qualitatively describe hysteresis and retention phenomena. 3-Dimensional lattices of square configuration were considered with normal, skewed and bimodal pore size distributions. The calculated pore size distribution was accurate up to the average size pores, but significantly different for larger pores. The fraction of average size pores was always exaggerated. Pore connectivity had larger influence on the pore size distribution than the lattice structures.     

ONE- AND TWO-PHASE FLOW IN NETWORK MODELS OF POROUS MEDIA

We discuss the low Reynolds number flow of one or two immiscible Newtonian fluids in network models of microscopically random porous media. For the case of a single fluid, we reduce the flow problem to an analog random electrical resistor problem and use an 'effective medium theory' to express the permeability of such networks in terms of the pore space geometry. For the flow of two fluids we use the Washburn approximation to incorporate capillary pressure differences, and show that this problem may also be formulated as a random electrical network. In this case, the capillary menisci correspond to moving batteries, and we follow the motion of the fluid-fluid interface (the ensemble of analog batteries) by a time-step procedure. We study the time evolution of the interface and the dynamics of blobs of one fluid contained in the other, as a function of the network geometry.’     

A NUMERICAL AND EXPERIMENTAL STUDY OF MICROWAVE DRYING USING A RECTANGULAR WAVE GUIDE

The drying of a capillary porous packed bed of glass beads by microwave energy using a rectangular wave-guide was investigated numerically and experimentally. The effects of moisture content, particle size and microwave power level on the drying kinetics were examined. Most importantly, this work focuses on the prediction of the distribution of the electromagnetic field as well as the temperature and moisture distribution within the capillary porous medium. The model, which combines the electromagnetic, temperature, and moisture fields, predicted results which were in good agreement with the experimental data.     

A NUMERICAL AND EXPERIMENTAL STUDY OF MICROWAVE DRYING USING A RECTANGULAR WAVE GUIDE

The drying of a capillary porous packed bed of glass beads by microwave energy using a rectangular wave-guide was investigated numerically and experimentally. The effects of moisture content, particle size and microwave power level on the drying kinetics were examined. Most importantly, this work focuses on the prediction of the distribution of the electromagnetic field as well as the temperature and moisture distribution within the capillary porous medium. The model, which combines the electromagnetic, temperature, and moisture fields, predicted results which were in good agreement with the experimental data.     

Darcy's law‐based model for wicking in paper‐like swelling porous media

The wicking of liquid into a paper‐like swelling porous medium made from cellulose and superabsorbent fibers was modeled using Darcy's law. The work is built on a previous study in which the Washburn equation, modified to account for swelling, was used to predict wicking in a composite of cellulose and superabsorbent fibers. In a new wicking model proposed here, Darcy's law for flow in porous media is coupled with the mass conservation equation containing an added sink or source term to account for matrix swelling and liquid absorption. The wicking‐rate predicted by the new model compares well with the previous experimental data, as well as the modified Washburn equation predictions. The effectiveness of various permeability models used with the new wicking model is also investigated. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

The Freezing Point of Water in Porous Glass

Lowering of the freezing point of water in porous glass was studied by a DTA technique. The samples contained a spectrum of average pore sizes. The freezing-point lowerings measured from melting and freezing curves correlated, as predicted by simple capillary theory, with the average pore size of the sample. This result is discussed in terms of capillary-condensation theory and theories of frost damage in porous materials.     

Wicking into porous polymer-derived ceramic monoliths fabricated by freeze-casting

Silicon oxycarbide monoliths of different pore size distribution were fabricated by freeze-casting. The samples revealed a lamellar pore structure with an axial anisotropy. To evaluate the capillary transport abilities we performed wicking experiments. The sample weight measurement method was applied during the imbibition. The samples show deviations in permeability from 10% to 49% at different sample orientations that quantifies the impact of the anisotropy in the axial direction. The deviations were larger for the samples with smaller pore size. For these samples we also observed larger differences in the wicking behaviour. The samples with bigger pore size demonstrated higher permeability and faster wicking. Imbibition results at both sample orientations showed a good agreement with a prediction via the Lucas–Washburn equation with gravity effects. We demonstrate hereby, that our approach of macroscopic modelling predicts wicking behaviour in anisotropic structures reasonably well, providing a simple tool for further porous material investigations.     

Visualizing multiphase flow and trapped fluid configurations in a model three‐dimensional porous medium

We report an approach to fully visualize the flow of two immiscible fluids through a model three‐dimensional (3‐D) porous medium at pore‐scale resolution. Using confocal microscopy, we directly image the drainage of the medium by the nonwetting oil and subsequent imbibition by the wetting fluid. During imbibition, the wetting fluid pinches off threads of oil in the narrow crevices of the medium, forming disconnected oil ganglia. Some of these ganglia remain trapped within the medium. By resolving the full 3‐D structure of the trapped ganglia, we show that the typical ganglion size, as well as the total amount of residual oil, decreases as the capillary number Ca increases; this behavior reflects the competition between the viscous pressure in the wetting fluid and the capillary pressure required to force oil through the pores of the medium. This work thus shows how pore‐scale fluid dynamics influence the trapped fluid configurations in multiphase flow through 3‐D porous media. © 2013 American Institute of Chemical Engineers AIChE J, 59:1022‐1029, 2013     

Modeling of Chemical Vapor Infiltration Rate Considering a Pore Size Distribution

To analyze chemical vapor infiltration (CVI) rates, a simulation model (PC model) was proposed, which is capable of considering difficulties of densification in the internal regions of porous bodies and the pore closure phenomena. In the model, a fictitious tapered pore is constructed based on the pore size distribution of the preform body, and variation of the pore shape during the process is calculated. For simulation study, fictitious tapered pores were constructed using different pore size distribution functions of Gaussian, δ-function, and flat distribution, and their shapes and characteristics were compared. In the case of the Gaussian flat distribution (large dispersion), the fraction of fine pores was large and these pores became closed near their mouths. Reconversion of temporal fictitious pore shape into the pore distribution function was attempted and the PC model was successfully applied to monitor variations in the pore size distributions during the CVI process.     

APPLICATION OF THE PRECONDITIONED CONJUGATE GRADIENTS METHOD IN THE SIMULATION OF RELATIVE PERMEABILITY PROPERTIES OF POROUS MEDIA

A model that is after the determination of the relative permeability characteristics of porous media is presented. It is part of a general model that deals with the simulation of capillary phenomena and immiscible fluid flow behaviour in porous media. The relative permeability characteristics in a water wet porous medium are simulated with the use of three-dimensional (3-D) network models of pore structure with pore body and pore throat size distributions. The major assumption involved is that a cubic network of pore bodies connected by pore throats with pore body and pore throat size distribution respectively, is a realistic representation of the pore structure of a porous medium. The physical laws that apply in real media are simulated in the network analysis, and the computed results are compared with experimental findings. A new algorithm was developed that leads to the solution of a large set of linear equations, with a sparse and positive definite coefficient matrix. Results obtained with the application of the Preconditioned Conjugate Gradients method and numerical aspects of the simulation are presented and discussed. Comparison of this method with other available numerical methods is also made. It is concluded that the Preconditioned Conjugate Gradients method is advantageous for large networks with regards to time of solution, convergence, and accuracy. The validity of the algorithm is tested against other methods in the literature.     

Micro Structural Investigations and Mechanical Properties of Macro Porous Ceramic Materials from Capillary Suspensions

Recently, we have introduced a novel, material‐independent processing method for producing macro porous ceramics with capillary suspensions as a stable precursor. A capillary suspension is a three‐phase system where a small amount of an immiscible secondary liquid is added to a suspension resulting in the formation of a sample spanning particle network. This technology provides open porosities well above 50% and pore sizes ranging from 0.5–100 μm. Here we focus on microstructure formation in the capillary suspensions and its impact on mechanical strength of the corresponding sintered parts. Based on the rheological data and SEM‐images, three regimes (I, II, III) are identified with distinctly different flow properties of the wet suspension and characteristic structural features of the sintered ceramic parts depending on the amount of added secondary liquid phase. The average pore size increases and the pore size distribution changes from monomodal (I) to bimodal (II) and broad multimodal (III) with increasing amount of secondary liquid phase. A clear correlation between the yield stress of the wet suspension and the porosity and pore size is observed for regime (I) and (II). Compressive and flexural strength as well as the Young's modulus monotonically decrease with increasing amount of the secondary liquid phase. Absolute values are mainly determined by the porosity and are well predicted by the Gibson & Ashby model for samples corresponding to regime (I) and (II). The broad pore size distribution in regime (III) results in a significantly lower mechanical strength.