790 research outputs found
Computing stationary free-surface shapes in microfluidics
A finite-element algorithm for computing free-surface flows driven by
arbitrary body forces is presented. The algorithm is primarily designed for the
microfluidic parameter range where (i) the Reynolds number is small and (ii)
force-driven pressure and flow fields compete with the surface tension for the
shape of a stationary free surface. The free surface shape is represented by
the boundaries of finite elements that move according to the stress applied by
the adjacent fluid. Additionally, the surface tends to minimize its free energy
and by that adapts its curvature to balance the normal stress at the surface.
The numerical approach consists of the iteration of two alternating steps: The
solution of a fluidic problem in a prescribed domain with slip boundary
conditions at the free surface and a consecutive update of the domain driven by
the previously determined pressure and velocity fields. ...Comment: Revised versio
Pearling instability of nanoscale fluid flow confined to a chemical channel
We investigate the flow of a nano-scale incompressible ridge of
low-volatility liquid along a "chemical channel": a long, straight, and
completely wetting stripe embedded in a planar substrate, and sandwiched
between two extended less wetting solid regions. Molecular dynamics
simulations, a simple long-wavelength approximation, and a full stability
analysis based on the Stokes equations are used, and give qualitatively
consistent results. While thin liquid ridges are stable both statically and
during flow, a (linear) pearling instability develops if the thickness of the
ridge exceeds half of the width of the channel. In the flowing case periodic
bulges propagate along the channel and subsequently merge due to nonlinear
effects. However, the ridge does not break up even when the flow is unstable,
and the qualitative behavior is unchanged even when the fluid can spill over
onto a partially wetting exterior solid region.Comment: 17 pages, 12 figures, submitted to Physics of Fluids, fixed equation
numbering after Eq. (17
Boundary elements method for microfluidic two-phase flows in shallow channels
In the following work we apply the boundary element method to two-phase flows
in shallow microchannels, where one phase is dispersed and does not wet the
channel walls. These kinds of flows are often encountered in microfluidic
Lab-on-a-Chip devices and characterized by low Reynolds and low capillary
numbers.
Assuming that these channels are homogeneous in height and have a large
aspect ratio, we use depth-averaged equations to describe these two-phase flows
using the Brinkman equation, which constitutes a refinement of Darcy's law.
These partial differential equations are discretized and solved numerically
using the boundary element method, where a stabilization scheme is applied to
the surface tension terms, allowing for a less restrictive time step at low
capillary numbers. The convergence of the numerical algorithm is checked
against a static analytical solution and on a dynamic test case. Finally the
algorithm is applied to the non-linear development of the Saffman-Taylor
instability and compared to experimental studies of droplet deformation in
expanding flows.Comment: accepted for publication, Computers and Fluids 201
A comparison of slip, disjoining pressure, and interface formation models for contact line motion through asymptotic analysis of thin two-dimensional droplet spreading
The motion of a contact line is examined, and comparisons drawn, for a
variety of models proposed in the literature. Pressure and stress behaviours at
the contact line are examined in the prototype system of quasistatic spreading
of a thin two-dimensional droplet on a planar substrate. The models analysed
include three disjoining pressure models based on van der Waals interactions, a
model introduced for polar fluids, and a liquid-gas diffuse-interface model;
Navier-slip and two non-linear slip models are investigated, with three
microscopic contact angle boundary conditions imposed (two of these contact
angle conditions having a contact line velocity dependence); and the interface
formation model is also considered. In certain parameter regimes it is shown
that all of the models predict the same quasistatic droplet spreading
behaviour.Comment: 29 pages, 3 figures, J. Eng. Math. 201
Elastocapillary Levelling of Thin Viscous Films on Soft Substrates
A thin liquid film with non-zero curvature at its free surface spontaneously
flows to reach a flat configuration, a process driven by Laplace pressure
gradients and resisted by the liquid's viscosity. Inspired by recent progresses
on the dynamics of liquid droplets on soft substrates, we here study the
relaxation of a viscous film supported by an elastic foundation. Experiments
involve thin polymer films on elastomeric substrates, where the dynamics of the
liquid-air interface is monitored using atomic force microscopy. A theoretical
model that describes the coupled evolution of the solid-liquid and the
liquid-air interfaces is also provided. In this soft-levelling configuration,
Laplace pressure gradients not only drive the flow, but they also induce
elastic deformations on the substrate that affect the flow and the shape of the
liquid-air interface itself. This process represents an original example of
elastocapillarity that is not mediated by the presence of a contact line. We
discuss the impact of the elastic contribution on the levelling dynamics and
show the departure from the classical self-similarities and power laws observed
for capillary levelling on rigid substrates
Topology and Shape optimization for CFD-Computational Fluid Dynamics
On this work a CFD optimization problem is treated from two different points of view -- In one hand, topology optimization using a homogenization method based on the Brinkmann penalization is presented, implemented using the finite elements method and optimized with a mesh adaptation step -- Secondly, a shape optimization method based on Hadamard boundary variation using differentiation with respect to the domain is developed, imple- mented and tested -- Finally, a coupling of both methods taking advantage of their own attributes is proposed and tested -- The expected results are obtaine
A distributed resistance inverse method for flow obstacle identification from internal velocity measurements
We present a penalization parameter method for obstacle identification in an incompressible fluid flow for a modified version of the Oseen equations. The proposed method consist in adding a high resistance potential to the system such that some subset of its boundary support represents the obstacle. This allows to work in a fixed domain and highly simplify the solution of the inverse problem via some suitable cost functional. Existence of minimizers and first and second order optimality conditions are derived through the differentiability of the solutions of the Oseen equation with respect to the potential. Finally, several numerical experiments using Navier-Stokes flow illustrate the applicability of the method, for the localization of a bi-dimensional cardiac valve from MRI and ultrasound flow type imaging data
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