Modeling of capillary-driven flows in axisymmetric geometries

Chassagne, Romain; Dörfler, Fabian; Guyenot, M.; Harting, Jens

doi:10.1016/j.compfluid.2018.08.024

Cited by 20 publications

(7 citation statements)

References 15 publications

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“…In other pore structures, Chassagne et al 54 analytically extended the LW equation to model capillary imbibition of liquids into axisymmetric microchannels with circular cross sections. These researchers employed numerical simulations based on the free surface lattice Boltzmann method to demonstrate the validation of theoretically derived equation in two test geometries (i.e., a sinusoidal capillary and a diverging capillary) (Figure 4).…”

Section: Equationmentioning

confidence: 99%

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Lucas–Washburn Equation-Based Modeling of Capillary-Driven Flow in Porous Systems

et al. 2021

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Fluid flow in porous systems driven by capillary pressure is one of the most ubiquitous phenomena in nature and industry, including petroleum and hydraulic engineering as well as material and life sciences. The classical Lucas–Washburn (LW) equation and its modified forms were developed and have been applied extensively to elucidate the fundamental mechanisms underlying the basic statics and dynamics of the capillary-driven flow in porous systems. The LW equation assumes that fluids are incompressible Newton ones and that capillary channels all have the same radii. This kind of hypothesis is not true for many natural situations, however, where porous systems comprise complicated pore and capillary channel structures at microscales. The LW equation therefore often leads to inaccurate capillary imbibition predictions in such situations. Numerous studies have been conducted in recent years to develop and assess the modifications and extensions of the LW equation in various porous systems. Significant progresses in computational techniques have also been attained to further improve our understanding of imbibition dynamics. A state-of-the-art review is therefore needed to summarize the recent significant models and numerical simulation techniques as well as to discuss key ongoing research topics arising from various new engineering practices. The theoretical basis of the LW equation is first introduced in this review and recent progress in mathematical models is then summarized to demonstrate the modifications and extensions of this equation to various microchannels and porous media. These include capillary tubes with nonuniform and noncircular cross sections, discrete fractures, and capillary tubes that are not straight as well as heterogeneous porous media. Numerical studies on the LW equation are also reviewed, and comments on future works and research directions for LW-based capillary-driven flows in porous systems are listed.

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Section: Equationmentioning

confidence: 99%

“…Capillary imbibition of a liquid into (a) a sinusoidal capillary and (b) a diverging capillary (reproduced with permission).…”

Section: Modifications and Extensions Of The Lw Equationmentioning

confidence: 99%

Lucas–Washburn Equation-Based Modeling of Capillary-Driven Flow in Porous Systems

et al. 2021

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“…The capillary water absorption coefficient A cap is generally calculated to evaluate the liquid water transfer capacity in construction materials 35 . The water absorption test apparatus is shown in detail below in Figure 7.

A_{cap} = \frac{M_{wc} - M_{dr}}{A \sqrt{t}}

…”

Section: Methodsmentioning

confidence: 99%

Characterization of performable geopolymer mortars for use as repair material

Maraş

2021

Structural Concrete

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Heritage masonry constructions constitute an important percentage of the structures in many countries. These structures are highly vulnerable to environmental changes (such as earthquakes), and significant losses in masonry historical constructions occur even in a moderate earthquake. For this reason, damage assessment studies of these structures before earthquakes are of great importance. After an earthquake, historical buildings in Turkey were examined and it was found that many buildings underwent damage. In these structures, damage occurs during the earthquake due to the use of low‐quality materials and a lack of sufficient connections between the layers. In these buildings, damage especially occurs in the parts that undergo restoration. Since low‐strength repair mortars are generally used in the restored sections, wide cracks have occurred in the building elements under the effect of earthquakes. This study aimed to produce alternative materials that could be used as geopolymer binders in restorated buildings. The mechanical, physical, and microstructural characteristics of the geopolymer samples were investigated in detail using laboratory tests. As a result, the strength of geopolymer repair materials with 8 M and 5% calcium hydroxide (Ca[OH]2) was very high when compared with other values. High‐strength compatible alternative geopolymer repair mortars that could be used for restoration were produced. For this reason, mortar is considered a significant application for repairing and strengthening buildings.

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“…Liang et al 28 proposed a phase‐field‐based LB model to study the capillary intrusion of Newtonian flows without considering the influence of gravity. Chassagne et al 29 considered the capillary‐driven flows in axisymmetric geometries by using free‐surface LB model. However, to the best of our knowledge, most of the previous studies only focus on the Newtonian fluids, and relatively little attention has been paid to the capillary rise of non‐Newtonian fluids with including the effects of displaced fluids and gravity.…”

Section: Introductionmentioning

confidence: 99%

“…To solve the problem, in this work an improved phase‐field‐based LB model is developed where the non‐Newtonian effect caused by the variation of viscosity is described by an external force term. Unlike the previous studies, 28‐30,32 in the present LB model, the relaxation time in the collision operator is fixed as a constant, and the change of shear‐rate‐dependent viscosity of two‐phase fluids can be realized through introducing a parameter A . This special treatment can be used to improve the capacity of LB method for non‐Newtonian fluid flows, and also makes the present LB model more stable even when the viscosity is relatively small.…”

Section: Introductionmentioning

confidence: 99%

Lattice Boltzmann modeling of the capillary rise of non‐Newtonian power‐law fluids

Shan

Chai

et al. 2021

Numerical Methods in Fluids

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In this work, a lattice Boltzmann (LB) model is proposed to study the capillary rise phenomena of two‐phase immiscible non‐Newtonian power‐law fluids. The main advantage of the LB model is that it not only allows us to solve the problems of two‐phase flow with a large density difference, but also can overcome the numerical instability caused by the change of relaxation time in the collision operator. In this model, two LB evolution equations are used to solve the conservative Allen–Cahn equation for capturing phase interface and incompressible Navier–Stokes equations for non‐Newtonian power‐law fluid dynamics. Some benchmark examples, including a droplet spreading on a smooth wall and two‐phase power‐law fluid flows between parallel plates, are used to test present LB model, and the results show that the present model is efficient and accurate in the study of two‐phase power‐law fluid flows. Furthermore, we pay attention to the phenomena of capillary rise of non‐Newtonian fluids, and carry out a parametric study on the effects of the gravity, viscosity, contact angle, power‐law index, and displaced fluids. The results show that the factors mentioned above have some significant influences on the rising process of the absorbed fluids.

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Modeling of capillary-driven flows in axisymmetric geometries

Cited by 20 publications

References 15 publications

Lucas–Washburn Equation-Based Modeling of Capillary-Driven Flow in Porous Systems

Lucas–Washburn Equation-Based Modeling of Capillary-Driven Flow in Porous Systems

Characterization of performable geopolymer mortars for use as repair material

Lattice Boltzmann modeling of the capillary rise of non‐Newtonian power‐law fluids

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