1,039 research outputs found
Model for Polymorphic Transitions in Bacterial Flagella
Many bacteria use rotating helical flagellar filaments to swim. The filaments
undergo polymorphic transformations in which the helical pitch and radius
change abruptly. These transformations arise in response to mechanical loading,
changes in solution temperature and ionic strength, and point substitutions in
the amino acid sequence of the protein subunits that make up the filament. To
explain polymorphism, we propose a new coarse-grained continuum rod theory
based on the quaternary structure of the filament. The model has two molecular
switches. The first is a double-well potential for the extension of a
protofilament, which is one of the eleven almost longitudinal columns of
subunits. Curved filament shapes occur in the model when there is a mismatch
strain, i.e. when inter-subunit bonds in the inner core of the filament prefer
a subunit spacing which is intermediate between the two spacings favored by the
double-well potential. The second switch is a double-well potential for twist,
due to lateral interactions between neighboring protofilaments. Cooperative
interactions between neighboring subunits within a protofilament are necessary
to ensure the uniqueness of helical ground states. We calculate a phase diagram
for filament shapes and the response of a filament to external moment and
force.Comment: 17 pages, 21 figure
Determining the Anchoring Strength of a Capillary Using Topological Defects
We consider a smectic-A* in a capillary with surface anchoring that favors
parallel alignment. If the bulk phase of the smectic is the standard
twist-grain-boundary phase of chiral smectics, then there will be a critical
radius below which the smectic will not have any topological defects. Above
this radius a single screw dislocation in the center of the capillary will be
favored. Along with surface anchoring, a magnetic field will also suppress the
formation of a screw dislocation. In this note, we calculate the critical field
at which a defect is energetically preferred as a function of the surface
anchoring strength and the capillary radius. Experiments at a few different
radii could thus determine the anchoring strength.Comment: Plain TeX (macros included), 8 pages, 2 included ps figures. Revision
includes a new figure and a textual modificatio
Swimming near Deformable Membranes at Low Reynolds Number
Microorganisms are rarely found in Nature swimming freely in an unbounded
fluid. Instead, they typically encounter other organisms, hard walls, or
deformable boundaries such as free interfaces or membranes. Hydrodynamic
interactions between the swimmer and nearby objects lead to many interesting
phenomena, such as changes in swimming speed, tendencies to accumulate or turn,
and coordinated flagellar beating. Inspired by this class of problems, we
investigate locomotion of microorganisms near deformable boundaries. We
calculate the speed of an infinitely long swimmer close to a flexible surface
separating two fluids; we also calculate the deformation and swimming speed of
the flexible surface. When the viscosities on either side of the flexible
interface differ, we find that fluid is pumped along or against the swimming
direction, depending on which viscosity is greater
Helical swimming in Stokes flow using a novel boundary-element method
We apply the boundary-element method to Stokes flows with helical symmetry,
such as the flow driven by an immersed rotating helical flagellum. We show that
the two-dimensional boundary integral method can be reduced to one dimension
using the helical symmetry. The computational cost is thus much reduced while
spatial resolution is maintained. We review the robustness of this method by
comparing the simulation results with the experimental measurement of the
motility of model helical flagella of various ratios of pitch to radius, along
with predictions from resistive-force theory and slender-body theory. We also
show that the modified boundary integral method provides reliable convergence
if the singularities in the kernel of the integral are treated appropriately.Comment: 30 pages, 10 figure
Locomotion of helical bodies in viscoelastic fluids: enhanced swimming at large helical amplitudes
The motion of a rotating helical body in a viscoelastic fluid is considered.
In the case of force-free swimming, the introduction of viscoelasticity can
either enhance or retard the swimming speed and locomotive efficiency,
depending on the body geometry, fluid properties, and the body rotation rate.
Numerical solutions of the Oldroyd-B equations show how previous theoretical
predictions break down with increasing helical radius or with decreasing
filament thickness. Helices of large pitch angle show an increase in swimming
speed to a local maximum at a Deborah number of order unity. The numerical
results show how the small-amplitude theoretical calculations connect smoothly
to the large-amplitude experimental measurements
Enhancement of microorganism swimming speed in active matter
We study a swimming undulating sheet in the isotropic phase of an active
nematic liquid crystal. Activity changes the effective shear viscosity,
reducing it to zero at a critical value of activity. Expanding in the sheet
amplitude, we find that the correction to the swimming speed due to activity is
inversely proportional to the effective shear viscosity. Our perturbative
calculation becomes invalid near the critical value of activity; using
numerical methods to probe this regime, we find that activity enhances the
swimming speed by an order of magnitude compared to the passive case.Comment: 5 pages, 5 figure
Propulsion by a Helical Flagellum in a Capillary Tube
We study the microscale propulsion of a rotating helical filament confined by
a cylindrical tube, using a boundary-element method for Stokes flow that
accounts for helical symmetry. We determine the effect of confinement on
swimming speed and power consumption. Except for a small range of tube radii at
the tightest confinements, the swimming speed at fixed rotation rate increases
monotonically as the confinement becomes tighter. At fixed torque, the swimming
speed and power consumption depend only on the geometry of the filament
centerline, except at the smallest pitch angles for which the filament
thickness plays a role. We find that the `normal' geometry of
\textit{Escherichia coli} flagella is optimized for swimming efficiency,
independent of the degree of confinement. The efficiency peaks when the arc
length of the helix within a pitch matches the circumference of the cylindrical
wall. We also show that a swimming helix in a tube induces a net flow of fluid
along the tube.Comment: 13 pages, 5 figure
Wrinkling of a thin film on a nematic liquid crystal elastomer
Wrinkles commonly develop in a thin film deposited on a soft elastomer
substrate when the film is subject to compression. Motivated by recent
experiments [Agrawal et al., Soft Matter 8, 7138 (2012)] that show how wrinkle
morphology can be controlled by using a nematic elastomer substrate, we develop
the theory of small-amplitude wrinkles of an isotropic film atop a nematic
elastomer. The directors of the nematic elastomer are assumed to lie in a plane
parallel to the plane of the undeformed film. For uniaxial compression of the
film along the direction perpendicular to the elastomer directors, the system
behaves as a compressed film on an isotropic substrate. When the uniaxial
compression is along the direction of nematic order, we find that the soft
elasticity characteristic of liquid crystal elastomers leads to a critical
stress for wrinkling which is very small compared to the case of an isotropic
substrate. We also determine the wavelength of the wrinkles at the critical
stress, and show how the critical stress and wavelength depend on substrate
depth and the anisotropy of the polymer chains in the nematic elastomer
Locomotion and transport in a hexatic liquid crystal
The swimming behavior of bacteria and other microorganisms is sensitive to
the physical properties of the fluid in which they swim. Mucus, biofilms, and
artificial liquid-crystalline solutions are all examples of fluids with some
degree of anisotropy that are also commonly encountered by bacteria. In this
article, we study how liquid-crystalline order affects the swimming behavior of
a model swimmer. The swimmer is a one-dimensional version of G. I. Taylor's
swimming sheet: an infinite line undulating with small-amplitude transverse or
longitudinal traveling waves. The fluid is a two-dimensional hexatic
liquid-crystalline film. We calculate the power dissipated, swimming speed, and
flux of fluid entrained as a function of the swimmer's waveform as well as
properties of the hexatic film, such as the rotational and shear viscosity, the
Frank elastic constant, and the anchoring strength. The departure from
isotropic behavior is greatest for large rotational viscosity and weak
anchoring boundary conditions on the orientational order at the swimmer
surface. We even find that if the rotational viscosity is large enough, the
transverse-wave swimmer moves in the opposite direction relative to a swimmer
in an isotropic fluid
Dynamic supercoiling bifurcations of growing elastic filaments
Certain bacteria form filamentous colonies when the cells fail to separate
after dividing. In Bacillus subtilis, Bacillus thermus, and cyanobacteria, the
filaments can wrap into complex supercoiled structures as the cells grow. The
structures may be solenoids or plectonemes, with or without branches in the
latter case. Any microscopic theory of these morphological instabilities must
address the nature of pattern selection in the presence of growth, for growth
renders the problem nonautonomous and the bifurcations dynamic. To gain insight
into these phenomena, we formulate a general theory for growing elastic
filaments with bending and twisting resistance in a viscous medium, and study
an illustrative model problem: a growing filament with preferred twist, closed
into a loop. Growth depletes the twist, inducing a twist strain. The closure of
the loop prevents the filament from unwinding back to the preferred twist;
instead, twist relaxation is accomplished by the formation of supercoils.
Growth also produces viscous stresses on the filament which even in the absence
of twist produce buckling instabilities. Our linear stability analysis and
numerical studies reveal two dynamic regimes. For small intrinsic twist the
instability is akin to Euler buckling, leading to solenoidal structures, while
for large twist it is like the classic writhing of a twisted filament,
producing plectonemic windings. This model may apply to situations in which
supercoils form only, or more readily, when axial rotation of filaments is
blocked. Applications to specific biological systems are proposed.Comment: 35 pages, 11 figure
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