Slip flow in a microchannel driven by rhythmic wall contractions

Chatterjee, Krishnashis; Staples, Anne

doi:10.1007/s00707-018-2210-7

Cited by 10 publications

(5 citation statements)

References 32 publications

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“…For example, the material composing the tube may not be only elastic but also porous (i.e., poroelastic ) [95]. It may also be worthwhile to consider microflows of gases in elastic tubes, which necessitates accounting for compressibility of the fluid [96, 97] and, possibly, wall slip [98, 99]. Another potential avenue for future research stems from the fact that many soft biological tissues are hyperelastic .…”

Section: Discussionmentioning

confidence: 99%

Revisiting steady viscous flow of a generalized Newtonian fluid through a slender elastic tube using shell theory

Anand

Christov

2020

Z Angew Math Mech

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A flow vessel with an elastic wall can deform significantly due to viscous fluid flow within it, even at vanishing Reynolds number (no fluid inertia). Deformation leads to an enhancement of throughput due to the change in cross‐sectional area. The latter gives rise to a non‐constant pressure gradient in the flow‐wise direction and, hence, to a nonlinear flow rate–pressure drop relation (unlike the Hagen–Poiseuille law for a rigid tube). Many biofluids are non‐Newtonian, and are well approximated by generalized Newtonian (say, power‐law) rheological models. Consequently, we analyze the problem of steady low Reynolds number flow of a generalized Newtonian fluid through a slender elastic tube by coupling fluid lubrication theory to a structural problem posed in terms of Donnell shell theory. A perturbative approach (in the slenderness parameter) yields analytical solutions for both the flow and the deformation. Using matched asymptotics, we obtain a uniformly valid solution for the tube's radial displacement, which features both a boundary layer and a corner layer caused by localized bending near the clamped ends. In doing so, we obtain a “generalized Hagen–Poiseuille law” for soft microtubes. We benchmark the mathematical predictions against three‐dimensional two‐way coupled direct numerical simulations (DNS) of flow and deformation performed using the commercial computational engineering platform by ANSYS. The simulations show good agreement and establish the range of validity of the theory. Finally, we discuss the implications of the theory on the problem of the flow‐induced deformation of a blood vessel, which is featured in some textbooks.

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Section: Discussionmentioning

confidence: 99%

Revisiting steady viscous flow of a generalized Newtonian fluid through a slender elastic tube using shell theory

Anand

Christov

2020

Z Angew Math Mech

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“…From the first term on the right-hand side of Eq. ( 23), we deduce that to retain the transient response of the pressure changes in the balanced continuity equation (22), the time scale of compressibility must be T compressibility ∼ αT f = α /V z . Likewise, from the second term on the right-hand side of Eq.…”

Section: Unsteady Volumetric Flow Rate and Time Scalesmentioning

confidence: 96%

Transient compressible flow in a compliant viscoelastic tube

Anand,

Christov

2020

Preprint

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Motivated by problems arising in the pneumatic actuation of controllers (for MEMS, labs-on-a-chip or biomimetic soft robots) and the study of microrheology of both gases and soft solids, we analyze the transient fluid-structure interactions (FSIs) in a viscoelastic tube conveying compressible flow at low Reynolds number. We express the density of the fluid as a linear function of the pressure, and we use the lubrication approximation to further simplify the fluid dynamics problem. On the other hand, the structural mechanics is governed by a modified Donnell shell theory accounting for Kelvin-Voigttype linear viscoelastic mechanical response. The fluid and structural mechanics problems are coupled through the tube's radial deformation and the hydrodynamic pressure. For small compressibility numbers and weak coupling, the equations are solved analytically via a perturbation expansion. Three illustrative problems are analyzed. First, we obtain exact implicit solutions for the pressure under steady conditions, taking into account flow rarefaction. Second , we solve the transient problem of impulsive pressurization of the tube's inlet. Third, we analyze the transient response to an oscillatory inlet pressure. We show that an oscillatory inlet pressure leads to acoustic streaming in the tube, attributed to the nonlinear pressure gradient induced by the interplay of FSI and compressibility. Furthermore, we demonstrate an enhancement in the volumetric flow rate due to the coupling. The hydrodynamics pressure oscillations are shown to exhibit a low-pass frequency response (when averaging over the period of oscillations), while the frequency response of the tube itself is similar to that of a band-pass filter.

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“…In addition to using a single pressurized actuation chamber, we incorporated both the directional and discrete collapse phenomena that have been observed [23][24][25][26]29] and modeled [30][31][32][33] In one device (S11, as shown in Figure 2(a)), we held the actuation frequency and duty cycle constant and varied the actuation pressure, and found that the flow rate could be controlled continuously with actuation pressure (Figure 3(c)).…”

Section: Single-channel Devicesmentioning

confidence: 99%

“…Devices S1 and S3-11 reproduce the discrete collapse phenomenon by incorporating two discrete collapse locations. Devices S1 and S6-11 incorporate a u-shaped actuation channel in order to produce a time lag between collapses, following the theoretical models in [30][31][32][33]. These observed features were combined randomly in the devices in order to span the design space.…”

Section: Single-channel Devicesmentioning

confidence: 99%

“…To do this, we extended current three-layer polydimethylsiloxane (PDMS) technology by connecting the overlying actuation channels in the top layer to a single, global actuation chamber, so that they are all actuated simultaneously by the same source, at an actuation frequency f and a differential pressure across the elastomeric membrane, Δp (as shown in figure 2(b)). In addition to using a single pressurized actuation chamber, we incorporated both the directional and discrete collapse phenomena that have been observed [23][24][25][26]29] and modeled [30][31][32][33] ) exhibited a time lag between the occurrence of the first and second collapses in a contraction cycle, following the theoretical models in [30][31][32][33]. This time lag was accomplished by incorporating u-shaped actuation channels in these devices so that the pressurized gas (air or nitrogen) in the actuation channel would reach one collapse site slightly before the other, owing to the finite time required for the pressure wave to propagate through the gas.…”

Section: Single-channel Devicesmentioning

confidence: 99%

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Frequency-specific, valveless flow control in insect-mimetic microfluidic devices

Chatterjee¹,

Graybill²,

Socha³

et al. 2021

Bioinspir. Biomim.

Self Cite

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Inexpensive, portable lab-on-a-chip devices would revolutionize fields like environmental monitoring and global health, but current microfluidic chips are tethered to extensive off-chip hardware. Insects, however, are self-contained and expertly manipulate fluids at the microscale using largely unexplored methods. We fabricated a series of microfluidic devices that mimic key features of insect respiratory kinematics observed by synchrotron-radiation imaging, including the collapse of portions of multiple respiratory tracts in response to a single fluctuating pressure signal. In one single-channel device, the flow rate and direction could be controlled by the actuation frequency alone, without the use of internal valves. Additionally, we fabricated multichannel chips whose individual channels responded selectively (on with a variable, frequency-dependent flow rate, or off) to a single, global actuation frequency. Our results demonstrate that insect-mimetic designs have the potential to drastically reduce the actuation overhead for microfluidic chips, and that insect respiratory systems may share features with impedance-mismatch pumps.

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Slip flow in a microchannel driven by rhythmic wall contractions

Cited by 10 publications

References 32 publications

Revisiting steady viscous flow of a generalized Newtonian fluid through a slender elastic tube using shell theory

Revisiting steady viscous flow of a generalized Newtonian fluid through a slender elastic tube using shell theory

Transient compressible flow in a compliant viscoelastic tube

Frequency-specific, valveless flow control in insect-mimetic microfluidic devices

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