Sessile droplet spread into porous substrates—Determination of capillary pressure using a continuum approach

Navaz, Homayun K.; Markicevic, B.; Zand, Ali; Sikorski, Yuri; Chan, Ewen; Sanders, Matthew S.; D'Onofrio, Terrence G.

doi:10.1016/j.jcis.2008.04.078

Cited by 34 publications

(42 citation statements)

References 21 publications

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“…As suggested from Eq. (3) and models of Denesuk et al [7] and Navaz et al [12] the group (t in r/l) collapses the infiltration time on the same value irrespective of l and r. The numerical results for (t in r/l) as a function of ðV 0 =r 3 0 Þ and four distinct pairs (l, r) investigated are shown in Fig. 4 for / = 0.5 and r 0 = 2 mm.…”

Section: Resultsmentioning

confidence: 77%

“…(1) that the porosity (/) does not influence (t in ) as it is included in the areal density of the capillaries (integrated in the model development). For porous media with both parallel and perpendicular flow in which the capillaries are cross-linked to some extent, Navaz et al [12] have shown that the porosity influences the infiltration time, where the solution is given as a family of infiltration time curves as a function of the dynamic contact angle with porosity as a parameter.…”

Section: Problem Formulationmentioning

confidence: 99%

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Infiltration time and imprint shape of a sessile droplet imbibing porous medium

Markicevic

Sikorski

et al. 2009

Journal of Colloid and Interface Science

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Section: Resultsmentioning

confidence: 77%

Section: Problem Formulationmentioning

confidence: 99%

Infiltration time and imprint shape of a sessile droplet imbibing porous medium

Markicevic

Sikorski

et al. 2009

Journal of Colloid and Interface Science

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“…In either approach there are several fitting constants that need to be determined experimentally. Using continuum multiphase flow formulation, Navaz et al (2008) have solved the droplet infiltration problem for times much longer than it takes sessile volume to infiltrate porous medium. The procedure how to determine the capillary pressure is also proposed.…”

Section: Introductionmentioning

confidence: 99%

Primary and Secondary Infiltration of Wetting Liquid Sessile Droplet into Porous Medium

Markicevic

Navaz

2010

Transp Porous Med

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The infiltration of a wetting droplet into the porous medium is a two-step process referred to as primary and secondary infiltration. In the primary infiltration there is a free liquid present at the porous medium surface, and when no fluid is left on the surface, the secondary infiltration is initiated. In both situations the driving force is the capillary pressure that is influenced by the local medium heterogeneities. A capillary network model based on the micro-force balance is developed with the same formulation applied to both infiltrations. The only difference between the two is that the net liquid flow into the porous medium in the secondary infiltration is equal to zero. The primary infiltration starts as a single-phase (fully saturated) flow and may proceed as a multiphase flow. The multiphase flow emerges as the interface (flow front) becomes irregular in shape. The immobile clusters of the originally present phase can be locally formed due to entrapment. Throughout the infiltration, it was found that portions of the liquid phase can be detached from the main body of the liquid phase forming some isolated liquid ganglia that increase in number and decrease in size. The termination of the secondary infiltration occurs once the ganglia become immobile due to their reduction in size. From the transient solution, the changes in the liquid saturation and capillary pressure during the droplet infiltration are determined. The solution developed in this study is used to investigate the droplet infiltration dynamics. However, the solution can be used to study the flow in fuel cell, nano-arrays, composites, and printing.Keywords Multiphase flow in porous media · Primary and secondary infiltration of wetting droplet · Capillary network model with micro-force balance · Phase content (saturation) and capillary pressure Electronic supplementary material The online version of this article (Power law parameters in Eq. 16 A System matrix for pressure solution (m 3 /(Pa × s)) bForce vector for pressure solution (m 3 /s) cCoordination number g Throat conductance (m 3 /(Pa × s)) K Permeability of isotropic medium, (m 2 ) K Permeability tensor (K for isotropic medium) (m 2 ) l x , l y , l z Porous medium dimensions in x, y, and z direction (m) n x , n y , n z Number of pores in x, y, and z directions pPressure (Pa) q Flow rate into one pore (m 3 /s) Q Flow rate across macroscopic boundary (m 3 /s) r Radius (m) l Length (m) s Liquid saturation S Surface area (m 2 ) t Time (s) u Throat velocity (m/s) u Macroscopic velocity vector (m/s) V 0 Initial sessile droplet volume (m 3 ) V free Sessile droplet volume (m 3 ) V 0 − V free Liquid volume within porous medium (m 3 ) V p Pore volume (m 3 ) V por Porous medium wetted volume (m 3 )Greek symbols φ Porosity μ Viscosity (Pa × s) σ Surface tension (Pa × m) σ t Standard deviation of log-normal throat radii distribution θ Liquid/solid phase contact angle in porous medium ( • ) θ d Sessile droplet dynamic contact angle at the porous medium surface ( • )

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“…Equations (3) and (4) were transformed into the computational domain ½n ¼ nðx; y; zÞ; g ¼ gðx; y; zÞ; f ¼ fðx; y; zÞ and marched in time to obtain the saturation function via the explicit fourth-order RungeKutta. 21 At the boundary between the droplet and the porous substrate, the liquid saturation is unity (s l ¼ 1), and the capillary pressure is enhanced by the local hydrostatic pressure (based on local height, h * of the sessile droplet). Mass is being transported into the porous medium according to ðq l v/Þ=J, where J is the Jacobian for the transformation and v is the contra-variant vertical velocity given by u ¼ g x u þ g y v þ g z w with u, v, w being the three components of the velocity and g x ; g y ; g z being the metrics for the transformation.…”

mentioning

confidence: 99%

“…This model has been extensively validated by previous studies. [20][21][22] We simulated a 40 ll de-ionized water droplet positioned on the outer-layer and on the inner-layer. The evaporation module was activated to monitor the vapor concentration as well as liquid saturation.…”

mentioning

confidence: 99%

Asymmetric wicking and reduced evaporation time of droplets penetrating a thin double-layered porous material

Gat

Vahdani

Navaz

et al. 2013

Applied Physics Letters

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We study numerically and experimentally the penetration and evaporation dynamics of droplets wicking into a thin double-layered porous material with order-of-magnitude difference in the physical properties between the layers. We show that such double-layered porous materials can be used to create highly asymmetrical wicking properties, preventing liquid droplets wicking from one surface to the other, while allowing wicking in the reverse direction. In addition, these double-layered porous materials are shown to reduce the evaporation time of droplets penetrating into the porous material, compared with a single-layered porous material of equal thickness and physical properties similar to either of the layers.

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Sessile droplet spread into porous substrates—Determination of capillary pressure using a continuum approach

Cited by 34 publications

References 21 publications

Infiltration time and imprint shape of a sessile droplet imbibing porous medium

Infiltration time and imprint shape of a sessile droplet imbibing porous medium

Primary and Secondary Infiltration of Wetting Liquid Sessile Droplet into Porous Medium

Asymmetric wicking and reduced evaporation time of droplets penetrating a thin double-layered porous material

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