Lattice-Boltzmann and finite difference simulations for the permeability of three-dimensional porous media

Numerical micropermeametry is performed on three dimensional porous samples having a linear size of approximately 3 mm and a resolution of 7.5 $\mu$m. One of the samples is a microtomographic image of Fontainebleau sandstone. Two of the samples are stochastic reconstructions with the same porosity, specific surface area, and two-point correlation function as the Fontainebleau sample. The fourth sample is a physical model which mimics the processes of sedimentation, compaction and diagenesis of Fontainebleau sandstone. The permeabilities of these samples are determined by numerically solving at low Reynolds numbers the appropriate Stokes equations in the pore spaces of the samples. The physi…

Spreading dynamics of three-dimensional droplets by the lattice-Boltzmann method

Abstract We have simulated spreading of small droplets on smooth and rough solid surfaces using the three-dimensional lattice-Boltzmann method. We present results for the influence of the initial distance and shape of the drop from the surface on scaling of droplet radius R as a function of time. For relatively flat initial drop shapes our observations are consistent with Tanner's law R ∼ t q , where q =1/10. For increasingly spherical initial shapes, the exponent q increases rapidly being above one half for spherical droplets initially just above the surface. As expected, surface roughness slows down spreading, decreases the final drop radius, and results in irregular droplet shape due to …

A unique microstructure of the fiber networks deposited from foam-fiber suspensions

Abstract Fiber networks can be formed using aqueous foam as the suspending medium. The mean bubble size of the foam affects the resulting pore-size distribution of the fiber network. The foam–fiber interactions cause in particular an increase in the proportion of large micropores of the network, in comparison with the fiber networks that result from traditional water forming at a similar material density. Experiments were carried out for two different types of cellulose fiber, and characterization of the resulting pore structure was based on X-ray microtomography of the resulting fiber networks. The unique pore structure obtained with foam forming was reflected in various macroscopic proper…

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. …

Rheological and Flocculation Analysis of Microfibrillated Cellulose Suspension Using Optical Coherence Tomography

A sub-micron resolution optical coherence tomography device was used together with a pipe rheometer to analyze the rheology and flocculation dynamics of a 0.5% microfibrillated cellulose (MFC) suspension. The bulk behavior of the MFC suspension showed typical shear thinning (power-law) behavior. This was reflected in a monotonously decreasing floc size when the shear stress exceeded the yield stress of the suspension. The quantitative viscous behavior of the MFC suspension changed abruptly at the wall shear stress of 10 Pa, which was reflected in a simultaneous abrupt drop of the floc size. The flocs were strongly elongated with low shear stresses. With the highest shear stresses, the flocs…

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.

Author Correction: Analysis of Industry-Related Flows by Optical Coherence Tomography—A Review

This is a correction to: KONA Powder and Particle Journal No. 37 (2020) 42–63, published January 10, 2020. https://doi.org/10.14356/kona.2020003

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.

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)]

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…

Online measurement of floc size, viscosity, and consistency of cellulose microfibril suspensions with optical coherence tomography

AbstractIn this study, cellulose microfibril (CMF) suspensions were imaged during pipe flow at consistencies of 0.4%, 1.0%, and 1.6% with optical coherence tomography (OCT) to obtain images of the structure and the local velocity of the suspension. The viscosities obtained by combining pressure loss measurement with the OCT velocity data showed typical shear thinning behavior and were in excellent agreement with viscosities obtained with ultrasound velocity profiling. The structural OCT images were used to calculate the radial and the axial floc sizes of the suspension. A fit of power law to the geometrical floc size–shear stress data gave the same power law index for all consistencies, sug…

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…

Iterative momentum relaxation for fast lattice-boltzmann simulations

Lattice-Boltzmann simulations are often used for studying steady-state hydrodynamics. In these simulations, however, the complete time evolution starting from some initial condition is redundantly computed due to the transient nature of the scheme. In this article we present a refinement of body-force driven lattice-Boltzmann simulations that may reduce the simulation time significantly. This new technique is based on an iterative adjustment of the local body-force and is validated on a realistic test case, namely fluid flow in a static mixer reactor.

Fouling dynamics in suspension flows

A particle suspension flowing in a channel in which fouling layers are allowed to form on the channel walls is investigated by numerical simulation. A two-dimensional phase diagram with at least four different behaviors is constructed. The fouling is modeled by attachment during collision with the deposits and by detachment caused by large enough hydrodynamic drag. For fixed total number of particles and small Reynolds numbers, the relevant parameters governing the fouling dynamics are the solid volume fraction of the suspension and the detachment drag force threshold. Below a critical curve in this 2D phase space only transient fouling takes place when the suspension is accelerated from re…

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.

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.

Iterative momentum relaxation for fast lattice-Boltzmann simulations

Abstract Lattice-Boltzmann simulations are often used for studying steady-state hydrodynamics. In these simulations, however, the complete time evolution starting from some initial condition is redundantly computed due to the transient nature of the scheme. In this article we present a refinement of body-force driven lattice-Boltzmann simulations that may reduce the simulation time significantly. This new technique is based on an iterative adjustment of the local body-force. We validate this technique on three test cases, namely fluid flow around a spherical obstacle, flow in random fiber mats and flow in a static mixer reactor.

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…

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…