Interface motion of capillary-driven flow in rectangular microchannel

Ichikawa, Naoki; Hosokawa, Kazuo; Maeda, Ryutaro

doi:10.1016/j.jcis.2004.07.017

Cited by 173 publications

(142 citation statements)

References 24 publications

(40 reference statements)

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“…The hydraulic diameter D h = 2dw t /(d + w t ) is used as the characteristic length scale L s for evaluating t v . Ichikawa, Hosokawa & Maeda (2004) examined the interface motion driven by capillary action in the case of three-dimensional channels with a rectangular cross-section. Using the analytical solution of Brody, Yager & Austin (1996) for the velocity profile in a rectangular channel of aspect ratio = d/w t and balancing the relevant forces, they estimated the dimensionless relation for the interface position as a function of time l * 2 = cos θ eq (t * − 1 + e −t * ).…”

Section: Spontaneous Imbibitionmentioning

confidence: 99%

Pore-filling events in single junction micro-models with corresponding lattice Boltzmann simulations

et al. 2017

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The aim of this work is to better understand fluid displacement mechanisms at the pore scale in relation to capillary-filling rules. Using specifically designed micro-models we investigate the role of pore body shape on fluid displacement during drainage and imbibition via quasi-static and spontaneous experiments at ambient conditions. The experimental results are directly compared to lattice Boltzmann (LB) simulations. The critical pore-filling pressures for the quasi-static experiments agree well with those predicted by the Young-Laplace equation and follow the expected filling events. However, the spontaneous imbibition experimental results differ from those predicted by the Young-Laplace equation; instead of entering the narrowest available downstream throat the wetting phase enters an adjacent throat first. Thus, pore geometry plays a vital role as it becomes the main deciding factor in the displacement pathways. Current pore network models used to predict displacement at the field scale may need to be revised as they currently use the filling rules proposed by Lenormand et al. (J. Fluid Mech., vol. 135, 1983, pp. 337-353). Energy balance arguments are particularly insightful in understanding the aspects affecting capillary-filling rules. Moreover, simulation results on spontaneous imbibition, in excellent agreement with theoretical predictions, reveal that the capillary number itself is not sufficient to characterise the two phase flow. The Ohnesorge number, which gives the relative importance of viscous forces over inertial and capillary forces, is required to fully describe the fluid flow, along with the viscosity ratio.

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Section: Spontaneous Imbibitionmentioning

confidence: 99%

Pore-filling events in single junction micro-models with corresponding lattice Boltzmann simulations

et al. 2017

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“…For the closed rectangular channel geometry Brody et al (1996) give the general approach and solution for the flow (see also Ichikawa et al, 2004). The non-zero component of the equations relates the flow velocity, u(y,z), in the x-direction to the pressure gradient,…”

Section: Viscous Terms and Interpolation Formulaementioning

confidence: 99%

“…Strage et al, 2003), rectangular (e.g. Ichikawa et al, 2004;Jong et al, 2007;Zhu and Petkovic-Duran, 2010) and grooved/triangular (Yost and Holm, 1995;Romero and Yost, 2006;Baret et al, 2007). Moreover, the same approach has been taken for channels defined by hydrophilic paths on a hydrophobic substrate (Darhuber et al, 2001) and by the space between two parallel plates (Rosendahl et al, 2004) under the assumption of flow with low Reynolds number and liquid imbibing in a tube/slablike manner.…”

Section: Introductionmentioning

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

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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.

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“…Gas-liquid and liquid-liquid flows with a fluid-fluid interface moving on solid surfaces are widely encountered in various science and engineering fields (1) . Computational fluid dynamics (CFD) simulations facilitate the understanding and prediction of such two-phase flows for flexible and accurate fluid motion and position control; the result can be used to optimally design microfluidic devices, machineries, and fabrication processes (2)- (4) .…”

Section: Introductionmentioning

confidence: 99%

Phase-Field Model-Based Simulation of Motions of a Two-Phase Fluid on Solid Surface

Tsuji

Matsumoto

2013

JCST

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A preliminary numerical simulation of the microscopic two-phase fluid motion on a solid surface was conducted using an interface-tracking method based on the phase-field model (PFM). Two variations of the lattice Boltzmann method (LBM) based on fictitious particle kinematics are proposed for solving diffuse-interface advection equations which were revised to improve volume-of-fluid conservation in the PFM simulations. The major findings are as follows: (1) the interface-tracking method accurately predicted the capillary force effect on dynamic two-phase fluid systems with a high density ratio between parallel plates; (2) the initial shape and volume of the two-phase fluid were retained adequately in linear translation with the use of the LBMs. These results proved that the PFM-based method and the LBM-based advection schemes can be used for simulating two-phase fluid motions in various macro-and microfluidics problems for devices, machineries and higher-throughput microdevice fabrication processes.

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Interface motion of capillary-driven flow in rectangular microchannel

Cited by 173 publications

References 24 publications

Pore-filling events in single junction micro-models with corresponding lattice Boltzmann simulations

Pore-filling events in single junction micro-models with corresponding lattice Boltzmann simulations

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

Phase-Field Model-Based Simulation of Motions of a Two-Phase Fluid on Solid Surface

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