551 research outputs found
Deformation and break-up of viscoelastic droplets Using Lattice Boltzmann Models
We investigate the break-up of Newtonian/viscoelastic droplets in a
viscoelastic/Newtonian matrix under the hydrodynamic conditions of a confined
shear flow. Our numerical approach is based on a combination of
Lattice-Boltzmann models (LBM) and Finite Difference (FD) schemes. LBM are used
to model two immiscible fluids with variable viscosity ratio (i.e. the ratio of
the droplet to matrix viscosity); FD schemes are used to model viscoelasticity,
and the kinetics of the polymers is introduced using constitutive equations for
viscoelastic fluids with finitely extensible non-linear elastic dumbbells with
Peterlin's closure (FENE-P). We study both strongly and weakly confined cases
to highlight the role of matrix and droplet viscoelasticity in changing the
droplet dynamics after the startup of a shear flow. Simulations provide easy
access to quantities such as droplet deformation and orientation and will be
used to quantitatively predict the critical Capillary number at which the
droplet breaks, the latter being strongly correlated to the formation of
multiple neckings at break-up. This study complements our previous
investigation on the role of droplet viscoelasticity (A. Gupta \& M.
Sbragaglia, {\it Phys. Rev. E} {\bf 90}, 023305 (2014)), and is here further
extended to the case of matrix viscoelasticity.Comment: 8 pages, 5 figures, IUTAM Symposium on Multiphase flows with phase
change: challenges and opportunities, Hyderabad, India 201
Analytical calculation of slip flow in lattice Boltzmann models with kinetic boundary conditions
We present a mathematical formulation of kinetic boundary conditions for
Lattice Boltzmann schemes in terms of reflection, slip, and accommodation
coefficients. It is analytically and numerically shown that, in the presence of
a non-zero slip coefficient, the Lattice Boltzmann flow develops a physical
slip flow component at the wall. Moreover, it is shown that the slip
coefficient can be tuned in such a way to recover quantitative agreement with
analytical and experimental results up to second order in the Knudsen number.Comment: 27 pages, 4 figure
Linear shear flow past a hemispherical droplet adhering to a solid surface
This paper investigates the properties of a three dimensional shear flow
overpassing a hemispherical droplet resting on a plane wall. The exact solution
is computed as a function of the viscosity ratio between the droplet and the
surrounding fluid and generalizes the solution for the hemispherical no-slip
bump given in an earlier paper by Price (1985). Several expressions including
the torque and the force acting on the drop will be considered as well as the
importance of the deformations on the surface for small Capillary numbers.Comment: 10 figures, Accepted for publication in Journal of Engineering
Mathematic
A Lattice Boltzmann study of the effects of viscoelasticity on droplet formation in microfluidic cross-junctions
Based on mesoscale lattice Boltzmann (LB) numerical simulations, we
investigate the effects of viscoelasticity on the break-up of liquid threads in
microfluidic cross-junctions, where droplets are formed by focusing a liquid
thread of a dispersed (d) phase into another co-flowing continuous (c)
immiscible phase. Working at small Capillary numbers, we investigate the
effects of non-Newtonian phases in the transition from droplet formation at the
cross-junction (DCJ) to droplet formation downstream of the cross-junction (DC)
(Liu Zhang, , 082101 (2011)). We will
analyze cases with (DV), where viscoelastic
properties are confined in the dispersed phase, as well as cases with (MV), where viscoelastic properties are confined in
the continuous phase. Moderate flow-rate ratios of the
two phases are considered in the present study. Overall, we find that the
effects are more pronounced in the case with MV, where viscoelasticity is found
to influence the break-up point of the threads, which moves closer to the
cross-junction and stabilizes. This is attributed to an increase of the polymer
feedback stress forming in the corner flows, where the side channels of the
device meet the main channel. Quantitative predictions on the break-up point of
the threads are provided as a function of the Deborah number, i.e. the
dimensionless number measuring the importance of viscoelasticity with respect
to Capillary forces.Comment: 15 pages, 14 figures. This Work applies the Numerical Methodology
described in arXiv:1406.2686 to the Problem of Droplet Generation in
Microfluidic Cross Junctions. arXiv admin note: substantial text overlap with
arXiv:1508.0014
Effects of viscoelasticity on droplet dynamics and break-up in microfluidic T-Junctions: a lattice Boltzmann study
The effects of viscoelasticity on the dynamics and break-up of fluid threads
in microfluidic T-junctions are investigated using numerical simulations of
dilute polymer solutions at changing the Capillary number (\mbox {Ca}), i.e.
at changing the balance between the viscous forces and the surface tension at
the interface, up to \mbox{Ca} \approx 3 \times 10^{-2}. A Navier-Stokes (NS)
description of the solvent based on the lattice Boltzmann models (LBM) is here
coupled to constitutive equations for finite extensible non-linear elastic
dumbbells with the closure proposed by Peterlin (FENE-P model). We present the
results of three-dimensional simulations in a range of \mbox{Ca} which is
broad enough to characterize all the three characteristic mechanisms of breakup
in the confined T-junction, i.e. , and regimes. The various model parameters of the FENE-P constitutive
equations, including the polymer relaxation time and the finite
extensibility parameter , are changed to provide quantitative details on
how the dynamics and break-up properties are affected by viscoelasticity. We
will analyze cases with (DV), where
viscoelastic properties are confined in the dispersed (d) phase, as well as
cases with (MV), where viscoelastic properties
are confined in the continuous (c) phase. Moderate flow-rate ratios of the two phases are considered in the present study. Overall, we
find that the effects are more pronounced in the case with MV, as the flow
driving the break-up process upstream of the emerging thread can be sensibly
perturbed by the polymer stresses.Comment: 16 pages, 14 figures; This Work applies the Numerical Methodology
described in arXiv:1406.2686 to the Problem of Droplet Generation in
Microfluidic T-Junctions. arXiv admin note: substantial text overlap with
arXiv:1508.0055
Deformation and break-up of viscoelastic droplets in confined shear flow
The deformation and break-up of Newtonian/viscoelastic droplets are studied
in confined shear flow. Our numerical approach is based on a combination of
Lattice-Boltzmann models (LBM) and finite difference schemes, the former used
to model two immiscible fluids with variable viscous ratio, and the latter used
to model the polymer dynamics. The kinetics of the polymers is introduced using
constitutive equations for viscoelastic fluids with finitely extensible
non-linear elastic dumbbells with Peterlin's closure (FENE-P). We quantify the
droplet response by changing the polymer relaxation time , the maximum
extensibility of the polymers, and the degree of confinement, i.e. the
ratio of the droplet diameter to gap spacing. In unconfined shear flow, the
effects of droplet viscoelasticity on the critical Capillary number
\mbox{Ca}_{\mbox{\tiny{cr}}} for break-up are moderate in all cases studied.
However, in confined conditions a different behaviour is observed: the critical
Capillary number of a viscoelastic droplet increases or decreases, depending on
the maximum elongation of the polymers, the latter affecting the extensional
viscosity of the polymeric solution. Force balance is monitored in the
numerical simulations to validate the physical picture.Comment: 34 Pages, 13 Figures. This Work applies the Numerical Methodology
described in arXiv:1406.2686 to the Problem of Droplet Break-up in confined
microchannel
Interaction Pressure Tensor for a class of Multicomponent Lattice Boltzmann models
We present a theory to obtain the pressure tensor for a class of non-ideal
multicomponent lattice Boltzmann models, thus extending the theory presented by
Shan (X. Shan, Phys. Rev. E 77, 066702 (2008)) for single component fluids. We
obtain the correct form of the pressure tensor directly on the lattice and the
resulting equilibrium properties are shown to agree very well with those
measured from numerical simulations. Results are compared with those of
alternative theories.Comment: 7 Pages, 5 figure
Avalanche statistics during coarsening dynamics
We study the coarsening dynamics of a two dimensional system via lattice
Boltzmann numerical simulations. The system under consideration is a biphasic
system consisting of domains of a dispersed phase closely packed together in a
continuous phase and separated by thin interfaces. Such system is elastic and
typically out of equilibrium. The equilibrium state is attained via the
coarsening dynamics, wherein the dispersed phase slowly diffuses through the
interfaces, causing domains to change in size and eventually rearrange
abruptly. The effect of rearrangements is propagated throughout the system via
the intrinsic elastic interactions and may cause rearrangements elsewhere,
resulting in intermittent bursts of activity and avalanche behaviour. Here we
aim at quantitatively characterizing the corresponding avalanche statistics
(i.e. size, duration, inter-avalanche time). Despite the coarsening dynamics is
triggered by an internal driving mechanism, we find quantitative indications
that such avalanche statistics displays scaling-laws very similar to those
observed in the response of disordered materials to external loads
A note on the effective slip properties for microchannel flows with ultra-hydrophobic surfaces
A type of super-hydrophobic surface consists of a solid plane boundary with
an array of grooves which, due to the effect of surface tension, prevent a
complete wetting of the wall. The effect is greatest when the grooves are
aligned with the flow. The pressure difference between the liquid and the gas
in the grooves causes a curvature of the liquid surface resisted by surface
tension. The effects of this surface deformation are studied in this paper. The
corrections to the effective slip length produced by the curvature are analyzed
theoretically and a comparison with available data and related mathematical
models is presented.Comment: 19 pages, 5 figure
Hybrid Lattice Boltzmann/Finite Difference simulations of viscoelastic multicomponent flows in confined geometries
We propose numerical simulations of viscoelastic fluids based on a hybrid
algorithm combining Lattice-Boltzmann models (LBM) and Finite Differences (FD)
schemes, the former used to model the macroscopic hydrodynamic equations, and
the latter used to model the polymer dynamics. The kinetics of the polymers is
introduced using constitutive equations for viscoelastic fluids with finitely
extensible non-linear elastic dumbbells with Peterlin's closure (FENE-P). The
numerical model is first benchmarked by characterizing the rheological
behaviour of dilute homogeneous solutions in various configurations, including
steady shear, elongational flows, transient shear and oscillatory flows. As an
upgrade of complexity, we study the model in presence of non-ideal
multicomponent interfaces, where immiscibility is introduced in the LBM
description using the "Shan-Chen" model. The problem of a confined viscoelastic
(Newtonian) droplet in a Newtonian (viscoelastic) matrix under simple shear is
investigated and numerical results are compared with the predictions of various
theoretical models. The proposed numerical simulations explore problems where
the capabilities of LBM were never quantified before.Comment: 32 Pages, 11 Figure
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