Hydrodynamics in deformable microchannels

Raj, M. Kiran; DasGupta, Sunando; Chakraborty, Suman

doi:10.1007/s10404-017-1908-5

Cited by 45 publications

(71 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Clearly, as t/w → 0 + the solution (14) reduces to that of (thin) plate bending (8), however, it has been pointed out that this convergence process is mathematically subtle and depends strongly on the type of deformation and the value of κ [29]. For reference, from equation (14), it can be shown that…”

Section: The Lubrication Approximation For Flow In a Microchannelmentioning

confidence: 99%

“…For example, the relationship between the pressure drop and the flow rate (a key relationship needed for the design and operation of any fluidic system) in a deformable microchannel remains a topic of vigorous experimental investigation [9,10,11,12,13,14]. However, each new study comes with its own theoretical model, which is sometimes of limited applicability.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Static response of deformable microchannels: a comparative modelling study

Shidhore

Christov

2018

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

Abstract. We present a comparative modelling study of fluid-structure interactions in microchannels. Through a mathematical analysis based on plate theory and the lubrication approximation for low-Reynolds-number flow, we derive models for the flow rate-pressure drop relation for long shallow microchannels with both thin and thick deformable top walls. These relations are tested against full three-dimensional two-way-coupled fluid-structure interaction simulations. Three types of microchannels, representing different elasticity regimes and having been experimentally characterized previously, are chosen as benchmarks for our theory and simulations. Good agreement is found in most cases for the predicted, simulated and measured flow rate-pressure drop relationships. The numerical simulations performed allow us to also carefully examine the deformation profile of the top wall of the microchannel in any cross section, showing good agreement with the theory. Specifically, the prediction that span-wise displacement in a long shallow microchannel decouples from the flow-wise deformation is confirmed, and the predicted scaling of the maximum displacement with the hydrodynamic pressure and the various material and geometric parameters is validated.

show abstract

Section: The Lubrication Approximation For Flow In a Microchannelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Static response of deformable microchannels: a comparative modelling study

Shidhore

Christov

2018

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

show abstract

“…We cannot make all terms agree because (4.7) is based on the cross-sectional displacement profile u(x, z) derived in §3, while Gervais et al (2006) postulated that u/w = αp/E. Raj & Sen (2016) and Raj et al (2017) also observed that α need not be a fitting parameter but, instead, must be related to the various geometric and elasticity constants involved in the problem. A difference between the approaches of Raj & Sen (2016) and Raj et al (2017) and ours is that their derivations are based on correlating the maximum of the cross-sectionally-averaged displacement to the pressure via various approximations/assumptions.…”

Section: Comparison With Previous Modelsmentioning

confidence: 99%

“…constant is α, and it is unknown a priori. Although Gervais et al (2006) only discuss the case of a thick top wall that behaves like an elastic half-space, (4.6) has been used by others (see, e.g., Hardy et al 2009;Cheung et al 2012;Raj et al 2017) for microchannels with much thinner top walls that behave as plates. Consequently, when (4.6) is fit to flow pressure-drop data from microchannels with plate-like top walls, a dependence α ∝ (t/w) 3 is observed (Raj et al 2017).…”

Section: Comparison With Previous Modelsmentioning

confidence: 99%

“…Raj & Sen (2016) and Raj et al (2017) also observed that α need not be a fitting parameter but, instead, must be related to the various geometric and elasticity constants involved in the problem. A difference between the approaches of Raj & Sen (2016) and Raj et al (2017) and ours is that their derivations are based on correlating the maximum of the cross-sectionally-averaged displacement to the pressure via various approximations/assumptions. In particular, Raj & Sen (2016) make the assumption of a parabolic top wall deflection, which does not appear to be well-substantiated by their measurements.…”

Section: Comparison With Previous Modelsmentioning

confidence: 99%

See 1 more Smart Citation

Flow rate–pressure drop relation for deformable shallow microfluidic channels

et al. 2018

View full text Add to dashboard Cite

Laminar flow in devices fabricated from soft materials causes deformation of the passage geometry, which affects the flow rate-pressure drop relation. For a given pressure drop, in channels with narrow rectangular cross-section, the flow rate varies as the cube of the channel height, so deformation can produce significant quantitative effects, including nonlinear dependence on the pressure drop [Gervais, T., El-Ali, J., Günther, A. & Jensen, K. F. 2006 Flow-induced deformation of shallow microfluidic channels. Lab Chip 6, 500-507]. Gervais et al. proposed a successful model of the deformation-induced change in the flow rate by heuristically coupling a Hookean elastic response with the lubrication approximation for Stokes flow. However, their model contains a fitting parameter that must be found for each channel shape by performing an experiment. We present a perturbation approach for the flow rate-pressure drop relation in a shallow deformable microchannel using the theory of isotropic quasi-static plate bending and the Stokes equations under a lubrication approximation (specifically, the ratio of the channel's height to its width and of the channel's height to its length are both assumed small). Our result contains no free parameters and confirms Gervais et al.'s observation that the flow rate is a quartic polynomial of the pressure drop. The derived flow rate-pressure drop relation compares favorably with experimental measurements.

show abstract

Thinning dynamics of the liquid thread at different stages in a rectangular cross junction

Wang

Pang

et al. 2022

AIChE Journal

View full text Add to dashboard Cite

Flow regime maps are plotted and the universal transitional boundary of squeezing regime and dripping regime is gained when both inertial force and viscous force of the dispersed phase are considered. The neck thinning process within the rectangular channel is divided into three stages according to evolutions of the neck width: twodimensional shrinking stage, transitional stage, and collapsing stage. Influences of the flow rates of two phases and the dispersed viscosity on evolutions of the neck width at different stages are explored. Different relations between the neck width and the remaining time are found for the earlier two stages. At the third stage, two physical mechanisms are separated by the dispersed viscosity as the neck width decreases according to w n /W ~τ2/3 under the inertial regime for both water and 40% glycerol, while the neck width reduces linearly as w n ~2(0.0709σ/μ d )t r under the viscous regime for 55% glycerol.

show abstract

Hydrodynamics in deformable microchannels

Cited by 45 publications

References 41 publications

Static response of deformable microchannels: a comparative modelling study

Static response of deformable microchannels: a comparative modelling study

Flow rate–pressure drop relation for deformable shallow microfluidic channels

Thinning dynamics of the liquid thread at different stages in a rectangular cross junction

Contact Info

Product

Resources

About