Dynamics of liquid rise in a vertical capillary tube

Masoodi, Reza; Languri, Ehsan Mohseni; Ostadhossein, Alireza

doi:10.1016/j.jcis.2012.09.004

Cited by 71 publications

(54 citation statements)

References 21 publications

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“…We use a more recent reference to Masoodi et al (2013). We note that both Szekely et al (1971) and Masoodi et al (2013) considered a capillary rise rather than infiltration.…”

Section: Pore-scale Modelmentioning

confidence: 99%

“…The Cauchy problem for this equation is solved with the initial conditions F * (0) = 0, dF * /dt * (0) = 0. We recall that the Szekely et al (1971) and Masoodi et al (2013) models take into account inertia of water slugs in the tubes, and therefore, the corresponding nonlinear ODE is of the secondorder and requires two initial conditions. We solve the Cauchy problem in the time interval T * > t * > 0 where T * is the instance at which F * (T * ) = d * .…”

Section: Pore-scale Modelmentioning

confidence: 99%

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Infiltration into Two-Layered Soil: The Green–Ampt and Averyanov Models Revisited

et al. 2015

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Infiltration into a two-layered soil (continuum scale) is studied by the Green-Ampt (GA) model where the rate of infiltration (wetting front propagation) is a non-monotonic and discontinuous function of time. Both a constant ponding depth and a ponding level falling due to evaporation and infiltration are studied theoretically and in column experiments. The triads of saturated conductivity, porosity and front pressure in the two zones, as well as gravity, control vertical infiltration. Another model on the scale of a straight cylindrical capillary uses the Averyanov regime of a film flow, modified to include a front which is a quarter of a torus, rather than a spherical cap in a standard Washburn-Lukas model. The rate of front propagation is controlled by the Newtonian viscosity, tube-film sizes, surface tension, contact angle and gravity. For both scales, Cauchy problems for ODEs with respect to the front position are solved by computer algebra integration. In the field, pedon description and textural analysis of sedimentation-controlled layering are done. Of particular note is the thick cake deposited from a flash flood water pulse, which has very low permeability and can greatly inhibit infiltration. The infiltration rates measured by tension infiltrometers fluctuate, which is attributed to the mosaic and layered special distribution of hydraulic and capillary properties of the accrued sediments. Falling ponding depth laboratory experiments were conducted in four columns with a coarse substratum (sand) subjacent to a layer of thoroughly homogenized repacked dam silt. Imbibition front stopped at the interface between two texturally contrasting B Ali Al-Maktoumi A. Al-Maktoumi et al. strata and the "waiting time" of the capillary barrier breakthrough was measured, as well as further oscillations of the infiltrations rate.

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“…We use a more recent reference to Masoodi et al (2013). We note that both Szekely et al (1971) and Masoodi et al (2013) considered a capillary rise rather than infiltration.…”

Section: Pore-scale Modelmentioning

confidence: 99%

Section: Pore-scale Modelmentioning

confidence: 99%

Infiltration into Two-Layered Soil: The Green–Ampt and Averyanov Models Revisited

et al. 2015

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“…For simplification and clarity of the main process, we do not take into account the influence of the container walls where the narrow tube is immersed. The comprehensive derivation of above governing equation can be found in [10,4,16] and [13]. In our analysis we assume that the initial height is equal to zero and to complete the description of the governing equation we have to choose a proper initial condition for velocity of the flow.…”

Section: Introductionmentioning

confidence: 99%

“…To proceed further with the asymptotic analysis we have to transform (1) into a more convenient form. After reducing the governing equation into a dimensionless form (see [10,13]) and using a simple transformation for both independent variable and height function (for more details see [13]) we are able to write (1) in following form…”

Section: Introductionmentioning

confidence: 99%

Asymptotic behaviour of a solution to a nonlinear equation modelling capillary rise

Płociniczak

Świtała

2020

Physica D: Nonlinear Phenomena

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We are concerned with the asymptotics and perturbation analysis of a singular second-order nonlinear ODE that models capillary rise of a fluid inside a narrow vertical tube. We prove the convergence of the exact solution to a unperturbed solution when a nondimensional parameter decrease to zero. Furthermore, we provide an accurate method of approximating the asymptotic solution for large times. Due to the a fact that the nonlinear component in the main equation does not satisfy the Lipschitz continuity condition the methods used to prove the main theorems are nonstandard, require careful analysis, and can be useful in dealing with similar nonlinear ODEs.

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“…A large number of scholars at home and abroad have paid close attention to the research of solid-liquid contact angle in capillary tube [6][7][8][9][10], because it is an effective method to research the solidliquid wettability. Jurin formula [11][12][13][14] and Rayleigh equation [15,16] are the fundamental formula to characterize the relationship between capillary column height and the contact angle.…”

Section: Introductionmentioning

confidence: 99%

Research on variation of static contact angle in incomplete wetting system and modeling method

Jiang

Guo

Wang³

et al. 2016

Colloids and Surfaces A: Physicochemical and Engineering Aspect

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Dynamics of liquid rise in a vertical capillary tube

Cited by 71 publications

References 21 publications

Infiltration into Two-Layered Soil: The Green–Ampt and Averyanov Models Revisited

Infiltration into Two-Layered Soil: The Green–Ampt and Averyanov Models Revisited

Asymptotic behaviour of a solution to a nonlinear equation modelling capillary rise

Research on variation of static contact angle in incomplete wetting system and modeling method

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