Measuring intrinsic thickness of rough membranes: application to nanofibrillated cellulose films

Adequate measurement of thickness of sheet-like materials or membranes is most important for quantifying their properties such as density, barrier properties and mechanical strength. Depending on the surface roughness of the membrane, the thickness measured by standard micrometre devices (apparent thickness) may considerably overestimate the actual geometrical mean thickness (intrinsic thickness) required for such purposes. In this work, we present a method for correcting the measured apparent thickness value of thin membranes for their surface roughness, thereby obtaining an improved estimate of the intrinsic thickness. The surface roughness data required for the correction can be obtained…

X-ray tomographic method for measuring three-dimensional deformation and water content distribution in swelling clays

A non-invasive method for simultaneous measurement of the 3D displacement field and the water content distribution of a wetted solid material is developed. The method is based on comparison of X-ray tomographic images of a material sample in the reference state and in the wetted and deformed state. The deformation and water content analyses were successfully compared with numerical results for a cylindrical rubber test sample under axial compression, and with gravimetric results from axially wetted and sliced cylindrical bentonite samples, respectively. The methods were applied in a 4D study (three spatial dimensions and time) of wetting and deformation of purified swelling bentonite doped …

Equation of state and transverse expansion effects in heavy ion collisions

The effects of the equation of state on the expansion of hadronic matter and on the dilepton production rates in heavy ion collisions are studied. We have used two widely different descriptions of the hadron phase and considered scenarios with and without phase transition. The hadron phase is treated either as a gas of ideal massless pions or, more realistically, as a gas of different kinds of massive hadrons with finite size.

Permeability and effective porosity of porous media

The concept of permeability of porous media is discussed, and a modification of Kozeny’s permeability equation to include the effect of effective porosity is introduced. An analytical expression for the specific surface area of a system constructed of randomly placed identical obstacles with unrestricted overlap is derived, and a lattice-gas cellular automaton method is then used to simulate the dependence on porosity of permeability, tortuosity, and effective porosity for a flow of Newtonian uncompressible fluid in this two-dimensional porous substance. The simulated permeabilities can well be explained by the concept of effective porosity, and the exact form of the specific surface area. …

Comparison of 3D structural characteristics of high and low resolution X-ray microtomographic images of paper

The detailed 3D structure of paper was revealed applying both high and low resolution X-ray microtomography. The qualityof the two techniques with respect to resolution and volume size was compared by measuring various structural andtransport properties of the digital volumes.

A non-destructive X-ray microtomography approach for measuring fibre length in short-fibre composites

An improved method based on X-ray microtomography is developed for estimating fibre length distribution of short-fibre composite materials. In particular, a new method is proposed for correcting th ...

X-ray tomographic method for measuring 3D deformation and liquid content in swelling materials

A non-invasive method for measuring the three-dimensional displacement field and liquid content distribution in a wetting and swelling material using X-ray tomographic imaging is introduced. The method is demonstrated here in monitoring the evolution of 3D deformation and water content distributions in cylindrical samples of swelling clay material wetted in a constant total volume. The measurements were carried out using a high-resolution microtomographic device (SkyScan 1172) and image voxel size 24 µm. The results obtained are repeatable and appear qualitatively correct and plausible. They are useful e.g. in validating models involving transport of water and the resulting deformation of s…

Tortuous flow in porous media

The concept of tortuosity of fluid flow in porous media is discussed. A lattice-gas cellular automaton method is applied to solve the flow of a Newtonian uncompressible fluid in a two-dimensional porous substance constructed by randomly placed rectangles of equal size and with unrestricted overlap. A clear correlation between the average tortuosity of the flow paths and the porosity of the substance has been found. \textcopyright{} 1996 The American Physical Society.

Dry content analysis in wet pressing: Sensitivity to pressing variables

Three dimensional hydrodynamics of ultrarelativistic heavy ion collisions

We have utilized a 2+1 dimensional numerical code based on Flux Corrected Transport method to find a solution for 3+1 dimensional cylindrically symmetric hydrodynamic flow of hadronic matter which is assumed to be formed in extremely high energy heavy ion collisions. The hydrodynamics is supplemented with a decoupling calculation in order to produce measurable particle distributions. This numerical procedure is applied here to Landau type initial conditions which have been fixed using a simple geometrical picture for a central O+Pb collision at 200 GeV/nucleon. The bag equation of state for nonbaryonic matter is used to simulate the deconfinement phase transition to quark gluon plasma. The …

Strain hardening in liquid-particle suspensions

The behavior of a liquid-particle suspension induced to sheared motion was analyzed by numerical simulations. When the velocity (strain) of the suspension began to increase, its viscosity first stayed almost constant, but increased then rapidly to a clearly higher level. This increase in viscosity is shown to be related to formation of clusters of suspended particles. Clusters are shown to increase the viscosity by enhanced momentum transfer though clustered particles. This is the mechanism behind the strain-hardening phenomenon observed in small-strain experiments on liquid-particle suspensions.

Hydrodynamical forces acting on particles in a two-dimensional flow near a solid wall

The hydrodynamical forces acting on a single particle and on a random rigid array of particles suspended in a two-dimensional shear flow of Newtonian fluid near a rigid wall were studied numerically in the flow regime where the relevant Reynolds numbers are of the order of unity. The simulations were done with conventional finite volume method for single-particle cases and with lattice-Boltzmann method for many-particle cases. A set of comparison cases was solved with both methods in order to check the accuracy of the lattice-Boltzmann method. For the single-particle case analytic formulae for the longitudinal drag force and for the transverse lift force were found. A modification to Darcy'…

Publisher’s Note: Strain hardening in liquid-particle suspensions [Phys. Rev. E72, 061402 (2005)]

Hydro-mechanical modelling of MX-80 bentonite: one dimensional study

As a first step towards modelling the coupled Thermo-Hydro-Mechanical-Chemical (THMC) behaviour of bentonite, the Barcelona Basic Model (BBM) has been implemented into Numerrin finite element code. This model has been fully coupled with the single phase flow equation for unsaturated soils which models liquid water transport. Suction obtained from solving the flow equation is used as an input for the BBM model and the volumetric deformations from the mechanical analysis are used to update the pore water pressure field. As an alternative, BBM is used alongside the Kröhn’s model which assumes that bentonite re-saturation is mainly driven by water vapour diffusion. The paper simulates one dimen…

Characterization of micro-fibrillated cellulose fiber suspension flow using multi scale velocity profile measurements

Rheological properties and boundary layer flow behavior of Micro Fibrillated Cellulose (MFC) suspended in water was studied using a novel velocity profiling rheometric technique. The method is based on measuring stationary velocity profiles of fluid flow in a straight tube simultaneously by Doppler Optical Coherence Tomography (DOCT) and by Ultrasound Velocity Profiling (UVP). The high resolution DOCT provides velocity profiles near the transparent tube wall, while UVP yields corresponding information in the interior parts of the flow. The data from the two instruments is combined into a comprehensive velocity profile including both the thin boundary layer near the wall and the interior par…

Time-resolved X-ray microtomographic measurement of water transport in wood-fibre reinforced composite material

Natural fibre composites are prone to absorb moisture from the environment which may lead to dimensional changes, mold growth, degradation of mechanical properties or other adverse effects. In this work we develop a method for direct non-intrusive measurement of local moisture content inside a material sample. The method is based on X-ray microtomography, digital image correlation and image analysis. As a first application of the method we study axial transport of water in a cylindrical polylactic acid/birch pulp composite material sample with one end exposed to water. Based on the results, the method seems to give plausible estimates of water content profiles inside the cylindrical sample.…

Settling of dilute and semidilute fiber suspensions at finite Re

The motion of tracer fibers settling in a suspension made optically transparent using an index-of refraction matching technique is studied as a function of concentration, aspect ratio, fluid viscosity, and fiber length distribution. At Re ∼ O (1), two different regimes of sedimentation are clearly identified. For small volume fractions we find that fibers settle with their long-axis preferentially in the horizontal state. With increasing volume fraction, fibers settle preferentially with their long-axis aligned in the direction of gravity. These findings are strikingly different than for those conducted with Re → 0 and qualitatively support the numerical simulations reported by Kuusela et a…

Hydrodynamical Description of 200 A GeV/c S+Au Collisions: Hadron and Electromagnetic Spectra

We study relativistic S+Au collisions at 200 A GeV/c using a hydrodynamical approach. We test various equations of state (EOSs), which are used to describe the strongly interacting matter at densities attainable in the CERN-SPS heavy ion experiments. For each EOS, suitable initial conditions can be determined to reproduce the experimental hadron spectra; this emphasizes the ambiguity between the initial conditions and the EOS in such an approach. Simultaneously, we calculate the resulting thermal photon and dielectron spectra, and compare with experiments. If one allows the excitation of resonance states with increasing temperature, the electro-magnetic signals from scenarios with and witho…

The 3D structure of fabric and its relationship to liquid and vapor transport

Polymeric carrier fabrics are commonly used in many industrial processes including manufacture of paper and board. Apart from acting as a carrier for the compressible porous material during the manufacturing process, the synthetic woven fabrics comprising mainly of poly ethylene terypthalate (PET) yarns, impart valuable product attributes, i.e. softness, bulk, absorbency, etc. in consumer products. The three-dimensional structure of the fabrics plays a critical role in deciding the manufacturing and energy efficiency as well as product end-use properties. X-ray micro computed tomography (X-CT) provides a non-intrusive technique to visualize and analyze the three-dimensional structure of por…

Permeability of three-dimensional random fiber webs

We report the results of essentially ab initio simulations of creeping flow through large threedimensional random fiber webs that closely resemble fibrous sheets such as paper and nonwoven fabrics. The computational scheme used in this Letter is that of the lattice-Boltzmann method and contains no free parameters concerning the properties of the porous medium or the dynamics of the flow. The computed permeability of the web is found to be in good agreement with experimental data, and confirms that permeability depends exponentially on porosity over a large range of porosity. [S0031-9007(97)05087-4]

Simulation of liquid penetration in paper

Capillary penetration of a wetting liquid in a microtomographic image of paper board, whose linear dimension was close to the average length of wood fibers, was simulated by the lattice-Boltzmann method. In spite of the size of the system not being large with respect to the size of structural inhomogeneities in the sample, for unidirectional penetration the simulated behavior was described well by that of the Lucas-Washburn equation, while for radial penetration a radial capillary equation described the behavior. In both cases the average penetration depth of the liquid front as a function of time followed a power law over many orders of magnitude. Capillary penetration of small droplets of…

Intrusion of nonwetting liquid in paper

The saturation curve of a sample of paper board was measured with mercury-intrusion porosimetry, and the three-dimensional structure of its pore space was determined by x-ray tomographic imaging. Ab initio numerical simulation of intrusion on the tomographic reconstruction, based on the lattice-Boltzmann method, was in excellent agreement with the measured saturation curve. A numerical invasion-percolation simulation in the same tomographic reconstruction showed good agreement with the lattice-Boltzmann simulation. The access function of the sample, determined from the saturation curve and the pore-throat distribution determined from the tomographic reconstruction, indicated that the ink-bo…

A method for measuring wetting and swelling of bentonite using X-ray imaging

A non-invasive method based on X-ray imaging for measuring deformation and water transport in wetting and swelling bentonite samples is introduced. Sequential X-ray images taken of the samples were used to calculate the attenuation coefficient and deformation. These results, together with careful calibration, allowed finding the dry density and water content distributions and their temporal evolution in the wetting and swelling samples. A specific correction technique, based on regularly taking reference X-ray images of aluminum plates of varying thickness, was developed and used to take into account X-ray beam instabilities and thus to improve the accuracy of density analysis. Large deform…

Evaluation of a lattice-Boltzmann method for mercury intrusion porosimetry simulations

We have simulated intrusion of a non-wetting liquid into pores of varying shape and size. Simulations were based on the lattice-Boltzmann method and the Shan–Chen multiphase model. The liquid–solid contact angle for pores with circular cross-section was found to be equal to that for pores with square cross-section, and constant even for small pore sizes if the discretised shape of the circular cross-section was taken into account. For comparison, contact angle was also determined for a liquid column descending in a capillary tube, and the results were found to be consistent. Application of the method to mercury intrusion porosimetry is discussed.

Non-destructive automatic determination of aspect ratio and cross-sectional properties of fibres

A novel method for computerised estimation of the aspect ratio distribution and various cross-sectional geometrical properties of fibres in short-fibre reinforced composites is proposed. The method, based on X-ray micro-computed tomography, is non-destructive and does not require user intervention. Based on results on specially fabricated model material, the accuracy and precision of the method seems adequate. The method is applied in analysing a manufacturing process of wood fibre reinforced thermoplastic composite. The results indicate a significant decrease of the aspect ratio of fibres during the processing steps. Finally, the feasibility of the method is assessed by estimating paramete…

Simulations of non-spherical particles suspended in a shear flow

The lattice-Boltzmann method was used to investigate the effects of the shape and concentration of the particles on the rheological properties of non-Brownian suspensions for non-zero Reynolds numbers. Several case studies were analyzed and the methods used were found to give accurate predictions for these systems. The viscosity of suspensions of both spherical and non-spherical particles was determined as functions of shear rate and concentration of particles. It was shown that, for high shear rates, shear thickening appears. This phenomenon is particularly pronounced for particles of irregular shape.

Hydrostatic and structural pressure in compressed paper webs and press felts

Implementation Aspects of 3D Lattice-BGK: Boundaries, Accuracy, and a New Fast Relaxation Method

In many realistic fluid-dynamical simulations the specification of the boundary conditions, the error sources, and the number of time steps to reach a steady state are important practical considerations. In this paper we study these issues in the case of the lattice-BGK model. The objective is to present a comprehensive overview of some pitfalls and shortcomings of the lattice-BGK method and to introduce some new ideas useful in practical simulations. We begin with an evaluation of the widely used bounce-back boundary condition in staircase geometries by simulating flow in an inclined tube. It is shown that the bounce-back scheme is first-order accurate in space when the location of the non…

Simulations of single-fluid flow in porous media

Several results of lattice-gas and lattice-Boltzmann simulations of single-fluid flow in 2D and 3D porous media are discussed. Simulation results for the tortuosity, effective porosity and permeability of a 2D random porous medium are reported. A modified Kozeny–Carman law is suggested, which includes the concept of effective porosity. This law is found to fit well the simulated 2D permeabilities. The results for fluid flow through large 3D random fibre webs are also presented. The simulated permeabilities of these webs are found to be in good agreement with experimental data. The simulations also confirm that, for this kind of materials, permeability depends exponentially on porosity over…

Transport properties of heterogeneous materials. Combining computerised X-ray micro-tomography and direct numerical simulations

Feasibility of a method for finding flow permeability of porous materials, based on combining computerised X-ray micro-tomography and numerical simulations, is assessed. The permeability is found by solving fluid flow through the complex 3D pore structures obtained by tomography for actual material samples. We estimate overall accuracy of the method and compare numerical and experimental results. Factors contributing to uncertainty of the method include numerical error arising from the finite resolution of tomographic images and the rather small sample size available with the present tomographic techniques. The total uncertainty of computed values of permeability is, however, not essentiall…

A method for measuring Darcian flow permeability of thin compressed fibre mats

Three-Dimensional Microstructural Properties of Nanofibrillated Cellulose Films

Abstract: Nanofibrillated cellulose (NFC) films have potential as oxygen barriers for, e.g., food packaging applications, but their use is limited by their hygroscopic characteristics. The three-dimensional microstructure of NFC films made of Pinus radiata (Radiata Pine) kraft pulp fibres has been assessed in this study, considering the structural development as a function of relative humidity (RH). The surface roughness, micro-porosity, thickness and their correlations were analyzed using X-ray microtomography (X–μCT) and computerized image analysis. The results are compared to those from scanning electron microscopy and laser profilometry. Based on a series of films having varying amounts…

Clustering and viscosity in a shear flow of a particulate suspension

A shear flow of particulate suspension is analyzed for the qualitative effect of particle clustering on viscosity using a simple kinetic clustering model and direct numerical simulations. The clusters formed in a Couette flow can be divided into rotating chainlike clusters and layers of particles at the channel walls. The size distribution of the rotating clusters is scale invariant in the small-cluster regime and decreases rapidly above a characteristic length scale that diverges at a jamming transition. The behavior of the suspension can qualitatively be divided into three regimes. For particle Reynolds number Re(p) less than or approximately equal 0.1, viscosity is controlled by the char…

Structural characterisation of wood pulp fibres and their nanofibrillated materials for biodegradable composite applications

Introduction: The utilization of wood pulp fibres in composite materials has gained major interest during the last years. One of the major motivations has been the potential of wood pulp fibres and their nanofibrillated derivatives for increasing the mechanical properties of some materials. However, in order to exploit the full potential of wood pulp fibres and cellulose nanofibrils as reinforcement in hydrophilic and hydrophobic matrices, several characteristics of fibres and their interactions with a given matrix need to be understood. With the increasing capabilities of novel microscopy techniques and computerized image analysis, structural analysis is moving forward from visual and subj…