126 research outputs found
Decoupling the effects of shear and extensional flows on the alignment of colloidal rods
Cellulose nanocrystals (CNC) can be considered as model colloidal rods and
have practical applications in the formation of soft materials with tailored
anisotropy. Here, we employ two contrasting microfluidic devices to
quantitatively elucidate the role of shearing and extensional flows on the
alignment of a dilute CNC dispersion. Characterization of the flow field by
micro-particle image velocimetry is coupled to flow-induced birefringence
analysis to quantify the deformation rate--alignment relationship. The
deformation rate required for CNC alignment is 4 smaller in extension
than in shear. Alignment in extension is independent of the deformation rate
magnitude, but is either 0 or 90 to the flow, depending on its
sign. In shear flow the colloidal rods orientate progressively towards
0 as the deformation rate magnitude increases. Our results decouple the
effects of shearing and extensional kinematics at aligning colloidal rods,
establishing coherent guidelines for the manufacture of structured soft
materials
Trouton-Noble paradox revisited
An apparent paradox is obtained in all previous treatments of the Trouton-Noble experiment; there is a three-dimensional torque in an inertial frame S in which a thin parallel-plate capacitor is moving, but there is no 3D torque in S', the rest frame of the capacitor. In this paper instead of using 3D quantities and their ``apparent'' transformations we deal with 4D geometric quantities their Lorentz transformations and equations with them. We introduce a new decomposition of the torque N (bivector) into 1-vectors N_{s} and N_{t}. It is shown that in the frame of ``fiducial'' observers, in which the observers who measure N_{s} and N_{t} are at rest, and in the standard basis, only the spatial components N_{s}^{i} and N_{t}^{i} remain, which can be associated with components of two 3D torques. In such treatment with 4D geometric quantities the mentioned paradox does not appear. The presented explanation is in a complete agreement with the principle of relativity and with the Trouton-Noble experiment without the introduction of any additional torque
Axiomatic geometric formulation of electromagnetism with only one axiom: the field equation for the bivector field F with an explanation of the Trouton-Noble experiment
In this paper we present an axiomatic, geometric, formulation of
electromagnetism with only one axiom: the field equation for the Faraday
bivector field F. This formulation with F field is a self-contained, complete
and consistent formulation that dispenses with either electric and magnetic
fields or the electromagnetic potentials. All physical quantities are defined
without reference frames, the absolute quantities, i.e., they are geometric
four dimensional (4D) quantities or, when some basis is introduced, every
quantity is represented as a 4D coordinate-based geometric quantity comprising
both components and a basis. The new observer independent expressions for the
stress-energy vector T(n)(1-vector), the energy density U (scalar), the
Poynting vector S and the momentum density g (1-vectors), the angular momentum
density M (bivector) and the Lorentz force K (1-vector) are directly derived
from the field equation for F. The local conservation laws are also directly
derived from that field equation. The 1-vector Lagrangian with the F field as a
4D absolute quantity is presented; the interaction term is written in terms of
F and not, as usual, in terms of A. It is shown that this geometric formulation
is in a full agreement with the Trouton-Noble experiment.Comment: 32 pages, LaTex, this changed version will be published in Found.
Phys. Let
Model for coiling and meandering instability of viscous threads
A numerical model is presented to describe both the transient and
steady-state dynamics of viscous threads falling onto a plane. The steady-state
coiling frequency w is calculated as a function of fall height H. In the case
of weak gravity, w ~ H^{-1} and w ~ H are obtained for lower and higher fall
heights respectively. When the effect of gravity is significant, the relation w
~ H^2 is observed. These results agree with the scaling laws previously
predicted. The critical Reynolds number for coil-uncoil transition is
discussed. When the gravity is weak, the transition occurs with hysteresis
effects. If the plane moves horizontally at a constant speed, a variety of
meandering oscillation modes can be observed experimentally. The present model
also can describe this phenomenon. The numerically obtained state diagram for
the meandering modes qualitatively agrees with the experiment.Comment: 12 pages, 10 figure
A discrete geometric approach for simulating the dynamics of thin viscous threads
We present a numerical model for the dynamics of thin viscous threads based
on a discrete, Lagrangian formulation of the smooth equations. The model makes
use of a condensed set of coordinates, called the centerline/spin
representation: the kinematical constraints linking the centerline's tangent to
the orientation of the material frame is used to eliminate two out of three
degrees of freedom associated with rotations. Based on a description of twist
inspired from discrete differential geometry and from variational principles,
we build a full-fledged discrete viscous thread model, which includes in
particular a discrete representation of the internal viscous stress.
Consistency of the discrete model with the classical, smooth equations is
established formally in the limit of a vanishing discretization length. The
discrete models lends itself naturally to numerical implementation. Our
numerical method is validated against reference solutions for steady coiling.
The method makes it possible to simulate the unsteady behavior of thin viscous
jets in a robust and efficient way, including the combined effects of inertia,
stretching, bending, twisting, large rotations and surface tension
Microdevices for extensional rheometry of low viscosity elastic liquids : a review
Extensional flows and the underlying stability/instability mechanisms are of extreme relevance to the efficient operation of inkjet printing, coating processes and drug delivery systems, as well as for the generation of micro droplets. The development of an extensional rheometer to characterize the extensional properties of low viscosity fluids has therefore stimulated great interest of researchers, particularly in the last decade. Microfluidics has proven to be an extraordinary working platform and different configurations of potential extensional microrheometers have been proposed. In this review, we present an overview of several successful designs, together with a critical assessment of their capabilities and limitations
Gene-Environment Interaction in the Etiology of Mathematical Ability Using SNP Sets
Mathematics ability and disability is as heritable as other cognitive abilities and disabilities, however its genetic etiology has received relatively little attention. In our recent genome-wide association study of mathematical ability in 10-year-old children, 10 SNP associations were nominated from scans of pooled DNA and validated in an individually genotyped sample. In this paper, we use a ‘SNP set’ composite of these 10 SNPs to investigate gene-environment (GE) interaction, examining whether the association between the 10-SNP set and mathematical ability differs as a function of ten environmental measures in the home and school in a sample of 1888 children with complete data. We found two significant GE interactions for environmental measures in the home and the school both in the direction of the diathesis-stress type of GE interaction: The 10-SNP set was more strongly associated with mathematical ability in chaotic homes and when parents are negative
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