16 research outputs found
Flexible filament in time-periodic viscous flow: shape chaos and period three
We study a single, freely--floating, inextensible, elastic filament in a
linear shear flow: . In our
model: the elastic energy depends only on bending; the rate-of-strain,
is a periodic function of time, ; and the
interaction between the filament and the flow is approximated by a local
isotropic drag force. Based on the shape of the filament we find five different
dynamical phases: straight, buckled, periodic (with period two, period three,
period four, etc), chaotic, and one with chaotic transients. In the chaotic
phase, we show that the iterative map for the angle, which the end-to-end
vector of the filament makes with the tangent its one end, has period three
solutions; hence it is chaotic. Furthermore, in the chaotic phase the flow is
an efficient mixer.Comment: 7 pages, 5 figures, 2 table
Passively parallel regularized stokeslets
Stokes flow, discussed by G.G. Stokes in 1851, describes many microscopic
biological flow phenomena, including cilia-driven transport and flagellar
motility; the need to quantify and understand these flows has motivated decades
of mathematical and computational research. Regularized stokeslet methods,
which have been used and refined over the past twenty years, offer significant
advantages in simplicity of implementation, with a recent modification based on
nearest-neighbour interpolation providing significant improvements in
efficiency and accuracy. Moreover this method can be implemented with the
majority of the computation taking place through built-in linear algebra,
entailing that state-of-the-art hardware and software developments in the
latter, in particular multicore and GPU computing, can be exploited through
minimal modifications ('passive parallelism') to existing MATLAB computer code.
Hence, and with widely-available GPU hardware, significant improvements in the
efficiency of the regularized stokeslet method can be obtained. The approach is
demonstrated through computational experiments on three model biological flows:
undulatory propulsion of multiple C. Elegans, simulation of progression and
transport by multiple sperm in a geometrically confined region, and left-right
symmetry breaking particle transport in the ventral node of the mouse embryo.
In general an order-of-magnitude improvement in efficiency is observed. This
development further widens the complexity of biological flow systems that are
accessible without the need for extensive code development or specialist
facilities.Comment: 21 pages, 7 figures, submitte
Local drag of a slender rod parallel to a plane wall in a viscous fluid
The viscous drag on a slender rod by a wall is important to many biological and industrial systems. This drag critically depends on the separation between the rod and the wall and can be approximated asymptotically in specific regimes, namely far from, or very close to, the wall, but is typically determined numerically for general separations. In this article we determine an asymptotic representation of the local drag for a slender rod parallel to a wall which is valid for all separations. This is possible through matching the behavior of a rod close to the wall and a rod far from the wall. We show that the leading order drag in both these regimes has been known since 1981 and that they can be used to produce a composite representation of the drag which is valid for all separations. This is in contrast to a sphere above a wall, where no simple uniformly valid representation exists. We estimate the error on this composite representation as the separation increases, discuss how the results could be used as resistive-force theory, and demonstrate their use on a two-hinged swimmer above a wall
Rotation of a low-Reynolds-number watermill: theory and simulations
Recent experiments have demonstrated that small-scale rotary devices
installed in a microfluidic channel can be driven passively by the underlying
flow alone without resorting to conventionally applied magnetic or electric
fields. In this work, we conduct a theoretical and numerical study on such a
flow-driven "watermill" at low Reynolds number, focusing on its hydrodynamic
features. We model the watermill by a collection of equally-spaced rigid rods.
Based on the classical resistive force (RF) theory and direct numerical
simulations, we compute the watermill's instantaneous rotational velocity as a
function of its rod number , position and orientation. When , the
RF theory predicts that the watermill's rotational velocity is independent of
and its orientation, implying the full rotational symmetry (of infinity
order), even though the geometrical configuration exhibits a lower-fold
rotational symmetry; the numerical solutions including hydrodynamic
interactions show a weak dependence on and the orientation. In addition, we
adopt a dynamical system approach to identify the equilibrium positions of the
watermill and analyse their stability. We further compare the theoretically and
numerically derived rotational velocities, which agree with each other in
general, while considerable discrepancy arises in certain configurations owing
to the hydrodynamic interactions neglected by the RF theory. We confirm this
conclusion by employing the RF-based asymptotic framework incorporating
hydrodynamic interactions for a simpler watermill consisting of two or three
rods and we show that accounting for hydrodynamic interactions can
significantly enhance the accuracy of the theoretical predictions