1,287 research outputs found
Hydrodynamics of Suspensions of Passive and Active Rigid Particles: A Rigid Multiblob Approach
We develop a rigid multiblob method for numerically solving the mobility
problem for suspensions of passive and active rigid particles of complex shape
in Stokes flow in unconfined, partially confined, and fully confined
geometries. As in a number of existing methods, we discretize rigid bodies
using a collection of minimally-resolved spherical blobs constrained to move as
a rigid body, to arrive at a potentially large linear system of equations for
the unknown Lagrange multipliers and rigid-body motions. Here we develop a
block-diagonal preconditioner for this linear system and show that a standard
Krylov solver converges in a modest number of iterations that is essentially
independent of the number of particles. For unbounded suspensions and
suspensions sedimented against a single no-slip boundary, we rely on existing
analytical expressions for the Rotne-Prager tensor combined with a fast
multipole method or a direct summation on a Graphical Processing Unit to obtain
an simple yet efficient and scalable implementation. For fully confined
domains, such as periodic suspensions or suspensions confined in slit and
square channels, we extend a recently-developed rigid-body immersed boundary
method to suspensions of freely-moving passive or active rigid particles at
zero Reynolds number. We demonstrate that the iterative solver for the coupled
fluid and rigid body equations converges in a bounded number of iterations
regardless of the system size. We optimize a number of parameters in the
iterative solvers and apply our method to a variety of benchmark problems to
carefully assess the accuracy of the rigid multiblob approach as a function of
the resolution. We also model the dynamics of colloidal particles studied in
recent experiments, such as passive boomerangs in a slit channel, as well as a
pair of non-Brownian active nanorods sedimented against a wall.Comment: Under revision in CAMCOS, Nov 201
A boundary element regularised Stokeslet method applied to cilia and flagella-driven flow
A boundary element implementation of the regularised Stokeslet method of
Cortez is applied to cilia and flagella-driven flows in biology.
Previously-published approaches implicitly combine the force discretisation and
the numerical quadrature used to evaluate boundary integrals. By contrast, a
boundary element method can be implemented by discretising the force using
basis functions, and calculating integrals using accurate numerical or analytic
integration. This substantially weakens the coupling of the mesh size for the
force and the regularisation parameter, and greatly reduces the number of
degrees of freedom required. When modelling a cilium or flagellum as a
one-dimensional filament, the regularisation parameter can be considered a
proxy for the body radius, as opposed to being a parameter used to minimise
numerical errors. Modelling a patch of cilia, it is found that: (1) For a fixed
number of cilia, reducing cilia spacing reduces transport. (2) For fixed patch
dimension, increasing cilia number increases the transport, up to a plateau at
cilia. Modelling a choanoflagellate cell it is found that the
presence of a lorica structure significantly affects transport and flow outside
the lorica, but does not significantly alter the force experienced by the
flagellum.Comment: 20 pages, 7 figures, postprin
Biological Fluid Mechanics Under the Microscope: A Tribute to John Blake
John Blake (1947--2016) was a leader in fluid mechanics, his two principal
areas of expertise being biological fluid mechanics on microscopic scales and
bubble dynamics. He produced leading research and mentored others in both
Australia, his home country, and the UK, his adopted home. This article reviews
John Blake's contributions in biological fluid mechanics, as well as giving the
author's personal viewpoint as one of the many graduate students and
researchers who benefitted from his supervision, guidance and inspiration. The
key topics from biological mechanics discussed are: `squirmer' models of
protozoa, the method of images in Stokes flow and the `blakelet' solution,
discrete cilia modelling via slender body theory, physiological flows in
respiration and reproduction, blinking stokeslets in microorganism feeding,
human sperm motility, and embryonic nodal cilia.Comment: 23 pages, 11 figures. Submitted versio
- …