Dimensionless scaling methods for capillary rise

Fries, Nicolas; Dreyer, Michael

doi:10.1016/j.jcis.2009.06.036

Cited by 76 publications

(53 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The suggested dimensionless governing equation has just one parameter and is similar to an equation reported by some authors (i.e. [10,12,24]). The dimensionless equation was solved numerically and results compared well with the experimental data.…”

Section: Introductionsupporting

confidence: 66%

See 1 more Smart Citation

Dynamics of liquid rise in a vertical capillary tube

Masoodi

Languri

Ostadhossein

2013

Journal of Colloid and Interface Science

View full text Add to dashboard Cite

Section: Introductionsupporting

confidence: 66%

“…Note that H and s are identical to h and t reported by Fries [10] and Fries and Dreyer [24]. The parameter defined by Eq.…”

Section: Dimensionless Parametersmentioning

confidence: 62%

Dynamics of liquid rise in a vertical capillary tube

Masoodi

Languri

Ostadhossein

2013

Journal of Colloid and Interface Science

View full text Add to dashboard Cite

“…(29) corresponds to the Fries and Dreyer (2009) case 3 where the basic parameter is gravity and the scaling parameters are inertia and viscosity. Our definitions of X and T are not identical to their scaled variables in the case of a tube, but our controlling parameter G is simply related to their  by G=2 1/2 /.…”

Section: Bousanquet Solution For a Horizontal Capillarymentioning

confidence: 99%

Wetting considerations in capillary rise and imbibition in closed square tubes and open rectangular cross-section channels

Ouali

McHale

Javed

et al. 2013

Microfluid Nanofluid

149

View full text Add to dashboard Cite

The spontaneous capillary-driven filling of microchannels is important for a wide range of applications. These channels are often rectangular in cross-section, can be closed or open, and horizontal or vertically orientated. In this work, we develop the theory for capillary imbibition and rise in channels of rectangular cross-section, taking into account rigidified and non-rigidified boundary conditions for the liquid-air interfaces and the effects of surface topography assuming Wenzel or Cassie-Baxter states. We provide simple interpolation formulae for the viscous friction associated with flow through rectangular cross-section channels as a function of aspect ratio. We derive a dimensionless cross-over time, T c , below which the exact numerical solution can be approximated by the Bousanquet solution and above which by the visco-gravitational solution. For capillary rise heights significantly below the equilibrium height, this cross-over time is T c  (3X e /2) 2/3 and has an associated dimensionless crossover rise height X c  (3X e /2) 1/3 , where X e =1/G is the dimensionless equilibrium rise height and G is a dimensionless form of the acceleration due to gravity. We also show from wetting considerations that for rectangular channels, fingers of a wetting liquid can be expected to imbibe in advance of the main meniscus along the corners of the channel walls. We test the theory via capillary rise experiments using polydimethylsiloxane oils of viscosity 96.0, 48.0, 19.2 and 4.8 mPa s within a range of closed square tubes and open rectangular cross-section channels with SU-8 walls. We show that the capillary rise heights can be fitted using the exact numerical solution and that these are similar to fits using the analytical visco-gravitational solution. The viscous friction contribution was found to be slightly higher than predicted by theory assuming a non-rigidified liquid-air boundary, but far below that for a rigidified boundary, which was recently reported for imbibition into horizontally mounted open microchannels. In these experiments we also observed fingers of liquid spreading along the internal edges of the channels in advance of the main body of liquid consistent with wetting expectations. We briefly discuss the implications of these observations for the design of microfluidic systems.

show abstract

“…(1) The ambient temperature was recorded and the value was stable for a given experiment and varied in the range [23][24][25][26] o C between experiments. The variation in viscosity from the temperature variation was confirmed using rheology measurements to be less than 5% of the values at 25° C.…”

Section: Experimental Methodsmentioning

confidence: 99%

Capillary Penetration into Inclined Circular Glass Tubes

et al. 2016

View full text Add to dashboard Cite

The spontaneous penetration of a wetting liquid into a vertical tube against the force of gravity and the imbibition of the same liquid into a horizontal tube (or channel) are both driven by capillary forces and described by the same fundamental equations. However, there have been few experimental studies of the transition from one orientation to the other. We report systematic measurements of capillary penetration of polydimethylsiloxane oils of viscosities 9.6, 19.2 and 48.0 mPas into glass capillary tubes. We first report the effect of tube radii R between 140 µm and 675 µm on the dynamics of spontaneous imbibition We show that the data can be fitted using the exact numerical solution to the governing equations and that these are similar to fits using the analytical visco-gravitational approximation. However, larger diameter tubes show a rate of penetration slower than expected using an equilibrium contact angle and the known value of liquid viscosity. To account for the slowness, an increase in viscosity by a factor (η/ρ) scaling is needed. We show full agreement with theory requires the ratio R/κ

show abstract

Dimensionless scaling methods for capillary rise

Cited by 76 publications

References 20 publications

Dynamics of liquid rise in a vertical capillary tube

Dynamics of liquid rise in a vertical capillary tube

Wetting considerations in capillary rise and imbibition in closed square tubes and open rectangular cross-section channels

Capillary Penetration into Inclined Circular Glass Tubes

Contact Info

Product

Resources

About