21 research outputs found
Deformation of a flexible fiber in a viscous flow past an obstacle
We study the deformation and transport of elastic fibers in a viscous
Hele-Shaw flow with curved streamlines. The variations of the global velocity
and orientation of the fiber follow closely those of the local flow velocity.
The ratios of the curvatures of the fibers by the corresponding curvatures of
the streamlines reflect a balance between elastic and viscous forces: this
ratio is shown experimentally to be determined by a dimensionless {\it Sperm
number} combining the characteristic parameters of the flow (transverse
velocity gradient, viscosity, fiber diameter/cell gap ratio) and those of the
fiber (diameter, effective length, Young's modulus). For short fibers, the
effective length is that of the fiber; for long ones, it is equal to the
transverse characteristic length of the flow. For , the
ratio of the curvatures increases linearly with ; For ,
the fiber reaches the same curvature as the streamlines
A novel approach to rigid spheroid models in viscous flows using operator splitting methods
Calculating cost-effective solutions to particle dynamics in viscous flows is
an important problem in many areas of industry and nature. We implement a
second-order symmetric splitting method on the governing equations for a rigid
spheroidal particle model with torques, drag and gravity. The method splits the
operators into a vector field that is conservative and one that takes into
account the forces of the fluid. Error analysis and numerical tests are
performed on perturbed and stiff particle-fluid systems. For the perturbed
case, the splitting method greatly improves the solution accuracy, when
compared to a conventional multi-step method, and the global error behaves as
for roughly equal computational cost. For stiff
systems, we show that the splitting method retains stability in regimes where
conventional methods blow up. In addition, we show through numerical
experiments that the global order is reduced from
in the non-stiff regime to in
the stiff regime.Comment: 24 pages, 6 figures (13 if you count sub figs), all figures are in
colou
Large-scale simulation of steady and time-dependent active suspensions with the force-coupling method
We present a new development of the force-coupling method (FCM) to address
the accurate simulation of a large number of interacting micro-swimmers. Our
approach is based on the squirmer model, which we adapt to the FCM framework,
resulting in a method that is suitable for simulating semi-dilute squirmer
suspensions. Other effects, such as steric interactions, are considered with
our model. We test our method by comparing the velocity field around a single
squirmer and the pairwise interactions between two squirmers with exact
solutions to the Stokes equations and results given by other numerical methods.
We also illustrate our method's ability to describe spheroidal swimmer shapes
and biologically-relevant time-dependent swimming gaits. We detail the
numerical algorithm used to compute the hydrodynamic coupling between a large
collection () of micro-swimmers. Using this methodology, we
investigate the emergence of polar order in a suspension of squirmers and show
that for large domains, both the steady-state polar order parameter and the
growth rate of instability are independent of system size. These results
demonstrate the effectiveness of our approach to achieve near continuum-level
results, allowing for better comparison with experimental measurements while
complementing and informing continuum models.Comment: 37 pages, 21 figure
Fast and spectrally accurate summation of 2-periodic Stokes potentials
We derive a Ewald decomposition for the Stokeslet in planar periodicity and a
novel PME-type O(N log N) method for the fast evaluation of the resulting sums.
The decomposition is the natural 2P counterpart to the classical 3P
decomposition by Hasimoto, and is given in an explicit form not found in the
literature. Truncation error estimates are provided to aid in selecting
parameters. The fast, PME-type, method appears to be the first fast method for
computing Stokeslet Ewald sums in planar periodicity, and has three attractive
properties: it is spectrally accurate; it uses the minimal amount of memory
that a gridded Ewald method can use; and provides clarity regarding numerical
errors and how to choose parameters. Analytical and numerical results are give
to support this. We explore the practicalities of the proposed method, and
survey the computational issues involved in applying it to 2-periodic boundary
integral Stokes problems
Aerodynamics of long fibres settling in air at 10<Re<100
The aerodynamics of long aspect ratio nylon fibrous particles has been investigated experimentally whilst settling in air under super dilute conditions without any influence of secondary flows and at fibre Reynolds numbers of 10–100 based on fibre length. Measurement of the orientations and velocities of fibrous particles is undertaken by two-dimensional Particle Tracking Velocimetry (PTV), based on the two end-points. A statistical evaluation of fibres' mean vertical and horizontal components of settling velocities, angular velocity, orientation, number density is presented and used to assess particle aerodynamics.Guo Q. Qi, Graham J. Nathan, Richard M. Kels
Large-scale simulation of steady and time-dependent active suspensions with the force-coupling method
We present a new development of the force-coupling method (FCM) to address the accurate simulation of a large number of interacting micro-swimmers. Our approach is based on the squirmer model, which we adapt to the FCM framework, resulting in a method that is suitable for simulating semi-dilute squirmer suspensions. Other effects, such as steric interactions, are considered with our model. We test our method by comparing the velocity field around a single squirmer and the pairwise interactions between two squirmers with exact solutions to the Stokes equations and results given by other numerical methods. We also illustrate our method’s ability to describe spheroidal swimmer shapes and biologically-relevant time-dependent swimming gaits. We detail the numerical algorithm used to compute the hydrodynamic coupling between a large collection (10^4–10^5) of micro-swimmers. Using this methodology, we investigate the emergence of polar order in a suspension of squirmers and show that for large domains, both the steady-state polar order parameter and the growth rate of instability are independent of system size. These results demonstrate the effectiveness of our approach to achieve near continuum-level results, allowing for better comparison with experimental measurements while complementing and informing continuum models
Methods for suspensions of passive and active filaments
Flexible filaments and fibres are essential components of important complex
fluids that appear in many biological and industrial settings. Direct
simulations of these systems that capture the motion and deformation of many
immersed filaments in suspension remain a formidable computational challenge
due to the complex, coupled fluid--structure interactions of all filaments, the
numerical stiffness associated with filament bending, and the various
constraints that must be maintained as the filaments deform. In this paper, we
address these challenges by describing filament kinematics using quaternions to
resolve both bending and twisting, applying implicit time-integration to
alleviate numerical stiffness, and using quasi-Newton methods to obtain
solutions to the resulting system of nonlinear equations. In particular, we
employ geometric time integration to ensure that the quaternions remain unit as
the filaments move. We also show that our framework can be used with a variety
of models and methods, including matrix-free fast methods, that resolve low
Reynolds number hydrodynamic interactions. We provide a series of tests and
example simulations to demonstrate the performance and possible applications of
our method. Finally, we provide a link to a MATLAB/Octave implementation of our
framework that can be used to learn more about our approach and as a tool for
filament simulation