3,340 research outputs found
Flow rate--pressure drop relation for deformable shallow microfluidic channels
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., G\"unther, A. \& Jensen, K.\ F.}\ 2006
Flow-induced deformation of shallow microfluidic channels.\ \textit{Lab Chip}
\textbf{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.Comment: 20 pages, 6 figures; v2 minor revisions, accepted for publication in
the Journal of Fluid Mechanic
Fluid-structure interaction in blood flow capturing non-zero longitudinal structure displacement
We present a new model and a novel loosely coupled partitioned numerical
scheme modeling fluid-structure interaction (FSI) in blood flow allowing
non-zero longitudinal displacement. Arterial walls are modeled by a {linearly
viscoelastic, cylindrical Koiter shell model capturing both radial and
longitudinal displacement}. Fluid flow is modeled by the Navier-Stokes
equations for an incompressible, viscous fluid. The two are fully coupled via
kinematic and dynamic coupling conditions. Our numerical scheme is based on a
new modified Lie operator splitting that decouples the fluid and structure
sub-problems in a way that leads to a loosely coupled scheme which is
{unconditionally} stable. This was achieved by a clever use of the kinematic
coupling condition at the fluid and structure sub-problems, leading to an
implicit coupling between the fluid and structure velocities. The proposed
scheme is a modification of the recently introduced "kinematically coupled
scheme" for which the newly proposed modified Lie splitting significantly
increases the accuracy. The performance and accuracy of the scheme were studied
on a couple of instructive examples including a comparison with a monolithic
scheme. It was shown that the accuracy of our scheme was comparable to that of
the monolithic scheme, while our scheme retains all the main advantages of
partitioned schemes, such as modularity, simple implementation, and low
computational costs
The effect of a concentration-dependent viscosity on\ud particle transport in a channel flow with porous walls
We analyse the transport of a dilute suspension of particles through a channel with porous walls accounting for the concentration dependence of the viscosity. Two cases of leakage flow of fluid through the porous channel walls are studied: (i) constant flux, and (ii) dependent on the pressure drop across the wall. The effect of mixing the suspension first compared with point injection is examined by considering inlet concentration distributions of different widths. We find that a pessimal distribution width exists that maximizes the required hydrodynamic pressure for a constant fluid influx. We also show that the presence of an osmotic pressure may lead to fluid being sucked into the channel. We consider how the application of an external hydrodynamic pressure affects this observation and discuss the significance of our results for water filtration
Asymptotic approach to the generalized Brinkman’s equation with pressure dependent viscosity and drag coefficient
In this paper we investigate the fluid flow through a thin (or long) channel filled with a fluid saturated porous medium. We are motivated by some important applications of the porous medium flow in which the viscosity of fluids can change significantly with pressure. In view of that, we consider the generalized Brinkman’s equation which takes into account the exponential dependence of the viscosity and the drag coefficient on the pressure. We propose an approach using the concept of the transformed pressure combined with the asymptotic analysis with respect to the thickness of the channel. As a result, we derive the asymptotic solution in the explicit form and compare it with the solution of the standard Brinkman’s model with constant viscosity. To our knowledge, such analysis cannot be found in the existing literature and, thus, we believe that the provided result could improve the known engineering practice.Croatian Science FoundationFundação de Amparo à Pesquisa do Estado de São PauloConselho Nacional de Desenvolvimento Científico e TecnológicoMinisterio de Economía y CompetitividadJunta de Andalucí
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