356 research outputs found
Droplet traffic in microfluidic networks: A simple model for understanding and designing
We propose a simple model to analyze the traffic of droplets in microfluidic
``dual networks''. Such functional networks which consist of two types of
channels, namely those accessible or forbidden to droplets, often display a
complex behavior characteristic of dynamical systems. By focusing on three
recently proposed configurations, we offer an explanation for their remarkable
behavior. Additionally, the model allows us to predict the behavior in
different parameter regimes. A verification will clarify fundamental issues,
such as the network symmetry, the role of the driving conditions, and of the
occurrence of reversible behavior. The model lends itself to a fast numerical
implementation, thus can help designing devices, identifying parameter windows
where the behavior is sufficiently robust for a devices to be practically
useful, and exploring new functionalities.Comment: accepted for publication in PR
Transverse electrokinetic and microfluidic effects in micro-patterned channels: lubrication analysis for slab geometries
Off-diagonal (transverse) effects in micro-patterned geometries are predicted
and analyzed within the general frame of linear response theory, relating
applied presure gradient and electric field to flow and electric current. These
effects could contribute to the design of pumps, mixers or flow detectors.
Shape and charge density modulations are proposed as a means to obtain sizeable
transverse effects, as demonstrated by focusing on simple geometries and using
the lubrication approximation.Comment: 9 pages, 7 figure
Wrinkling of pressurized elastic shells
We study the formation of localized structures formed by the point loading of an internally pressurized elastic shell. While unpressurized shells (such as a ping pong ball) buckle into polygonal structures, we show that pressurized shells are subject to a wrinkling instability. We present scaling laws for the critical indentation at which wrinkling occurs and the number of wrinkles formed in terms of the internal pressurization and material properties of the shell. These results are validated by numerical simulations. We show that the evolution of the wrinkle length with increasing indentation can be understood for highly pressurized shells from membrane theory. These results suggest that the position and number of wrinkles may be used in combination to give simple methods for the estimation of the mechanical properties of highly pressurized shells
Indentation of ellipsoidal and cylindrical elastic shells
Thin shells are found in nature at scales ranging from viruses to hens’ eggs; the stiffness of such shells is essential for their function. We present the results of numerical simulations and theoretical analyses for the indentation of ellipsoidal and cylindrical elastic shells, considering both pressurized and unpressurized shells. We provide a theoretical foundation for the experimental findings of Lazarus et al. [Phys. Rev. Lett. (submitted)] and for previous work inferring the turgor pressure of bacteria from measurements of their indentation stiffness; we also identify a new regime at large indentation. We show that the indentation stiffness of convex shells is dominated by either the mean or Gaussian curvature of the shell depending on the pressurization and indentation depth. Our results reveal how geometry rules the rigidity of shells
Rheological instability in a simple shear thickening model
We study the strain response to steady imposed stress in a spatially
homogeneous, scalar model for shear thickening, in which the local rate of
yielding \Gamma(l) of mesoscopic `elastic elements' is not monotonic in the
local strain l. Despite this, the macroscopic, steady-state flow curve (stress
vs. strain rate) is monotonic. However, for a broad class of \Gamma(l), the
response to steady stress is not in fact steady flow, but spontaneous
oscillation. We discuss this finding in relation to other theoretical and
experimental flow instabilities. Within the parameter ranges we studied, the
model does not exhibit rheo-chaos.Comment: 8 pages, 3 figs. Minor corrections made. To appear in Euro. Phys.
Let
The indentation of pressurized elastic shells: From polymeric capsules to yeast cells
Pressurized elastic capsules arise at scales ranging from the 10 m diameter pressure vessels used to store propane at oil refineries to the microscopic polymeric capsules that may be used in drug delivery. Nature also makes extensive use of pressurized elastic capsules: plant cells, bacteria and fungi have stiff walls, which are subject to an internal turgor pressure. Here we present theoretical, numerical and experimental investigations of the indentation of a linearly elastic shell subject to a constant internal pressure. We show that, unlike unpressurized shells, the relationship between force and displacement demonstrates two linear regimes. We determine analytical expressions for the effective stiffness in each of these regimes in terms of the material properties of the shell and the pressure difference. As a consequence, a single indentation experiment over a range of displacements may be used as a simple assay to determine both the internal pressure and elastic properties of capsules. Our results are relevant for determining the internal pressure in bacterial, fungal or plant cells. As an illustration of this, we apply our results to recent measurements of the stiffness of baker’s yeast and infer from these experiments that the internal osmotic pressure of yeast cells may be regulated in response to changes in the osmotic pressure of the external medium
Tension dynamics and viscoelasticity of extensible wormlike chains
The dynamic response of prestressed semiflexible biopolymers is characterized
by the propagation and relaxation of tension, which arises due to the near
inextensibility of a stiff backbone. It is coupled to the dynamics of contour
length stored in thermal undulations, but also to the local relaxation of
elongational strain. We present a systematic theory of tension dynamics for
stiff yet extensible wormlike chains. Our results show that even moderate
prestress gives rise to distinct Rouse-like extensibility signatures in the
high-frequency viscoelastic response.Comment: 4 pages, 1 figure; corrected typo
Current reversals in a rocking ratchet: dynamical vs symmetry-breaking mechanisms
Directed transport in ratchets is determined by symmetry-breaking in a system
out of equilibrium. A hallmark of rocking ratchets is current reversals: an
increase in the rocking force changes the direction of the current. In this
work for a bi-harmonically driven spatially symmetric rocking ratchet we show
that a class of current reversal is precisely determined by symmetry-breaking,
thus creating a link between dynamical and symmetry-breaking mechanisms
A simple model for heterogeneous flows of yield stress fluids
Various experiments evidence spatial heterogeneities in sheared yield stress
fluids. To account for heterogeneities in the velocity gradient direction, we
use a simple model corresponding to a non-monotonous local constitutive curve
and study a simple shear geometry. Different types of boundary conditions are
considered. Under controlled macroscopic shear stress , we find
homogeneous flow in the bulk and a hysteretic macroscopic stress - shear rate
curve. Under controlled macroscopic shear rate , shear banding is
predicted within a range of values of . For small shear rates,
stick slip can also be observed. These qualitative behaviours are robust when
changing the boundary conditions.Comment: 13 pages, 13 figure
Monte Carlo simulations of copolymers at homopolymer interfaces: Interfacial structure as a function of the copolymer density
By means of extensive Monte Carlo simulations of the bond fluctuation model,
we study the effect of adding AB diblock copolymers on the properties of an
interface between demixed homopolymer phases. The parameters are chosen such
that the homopolymers are strongly segregated, and the whole range of copolymer
concentrations in the two phase coexistence region is scanned. We compare the
``mushroom'' regime, in which copolymers are diluted and do not interact with
each other, with the ``wet brush'' regime, where copolymers overlap and
stretch, but are still swollen by the homopolymers. A ``dry brush'' regime is
never entered for our choice of chain lengths. ``Intrinsic'' profiles are
calculated using a block analysis method introduced by us in earlier work. We
discuss density profiles, orientational profiles and contact number profiles.
In general, the features of the profiles are similar at all copolymer
concentrations, however, the profiles in the concentrated regime are much
broader than in the dilute regime. The results compare well with
self-consistent field calculations.Comment: to appear in J. Chem. Phy
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