36 research outputs found
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Off-plane motion of an oblate capsule in a simple shear flow
This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.We investigate the mechanical equilibrium state of an oblate capsule when its revolution axis is
initially off the shear plane. We consider an oblate capsule with an aspect ratio of 0.5 and a strain-hardening
membrane. The three-dimensional fluid-structure interaction problem is solved numerically by coupling a
finite element method with a boundary integral method. The capsule converges towards the same mechanical
equilibrium state whatever the initial orientation. This equilibrium depends on the capillary number Ca, which
compares the viscous to the elastic forces and on the viscosity ratio between the internal and external fluids.
For = 1, the tumbling and swinging motions, observed when the revolution axis is initially in the shear plane,
are mechanically stable until Ca 1; when Ca is further increased, the capsule assumes the rolling motion
that is observed when its revolution axis is initially aligned with the vorticity axis. When is increased, the tumbling-to-swinging transition appears for higher Ca and the swinging-to-rolling transition for lower Ca. For
5, the swinging regime completely disappears: depending on Ca, it is then either the tumbling or the rolling motion that is the mechanical equilibrium state
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Online fabrication and characterization of capsule populations with a flow-focusing microfluidic system
This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.We have designed a microfluidic system that combines a double flow-focusing setup for calibrated capsule fabrication with a microchannel for the characterization of their mechanical properties. The double flow-focusing system consists of a first Y junction to create the microdroplets and of a second Y junction to introduce the cross-linking agent allowing the membrane formation. The human serum albumin (HSA) aqueous solution for the dispersed solution, hydrophobic phase for the continuous solution and cross-linking agent solution are introduced by means of syringe pumps. A wavy channel after the second junction allows to control the reticulation time. A cylindrical microchannel then enables to deform and characterize the capsules formed. The mechanical properties of the capsule membrane are obtained by inverse analysis (Chu et al. 2011). The results show that the drop size increases with the flow rate ratio between the central and lateral channels and does not change much regardless of the flow rate of the reticulation phase. The mean shear modulus of the capsules fabricated after 23 s of reticulation is of the order of the surface tension of HSA solution with Dragoxat indicating that the reticulation time is too short to form an elastic membrane around the droplet. When the reticulation time is increased to 60 s, the membrane shear modulus is multiplied by a factor of 3 confirming that a solid membrane has formed around the drop
Accelerated boundary integral method for multiphase flow in non-periodic geometries
An accelerated boundary integral method for Stokes flow of a suspension of
deformable particles is presented for an arbitrary domain and implemented for
the important case of a planar slit geometry. The computational complexity of
the algorithm scales as O(N) or ), where is proportional to the
product of number of particles and the number of elements employed to
discretize the particle. This technique is enabled by the use of an alternative
boundary integral formulation in which the velocity field is expressed in terms
of a single layer integral alone, even in problems with non-matched
viscosities. The density of the single layer integral is obtained from a
Fredholm integral equation of the second kind involving the double layer
integral. Acceleration in this implementation is provided by the use of General
Geometry Ewald-like method (GGEM) for computing the velocity and stress fields
driven by a set of point forces in the geometry of interest. For the particular
case of the slit geometry, a Fourier-Chebyshev spectral discretization of GGEM
is developed. Efficient implementations employing the GGEM methodology are
presented for the resulting single and the double layer integrals. The
implementation is validated with test problems on the velocity of rigid
particles and drops between parallel walls in pressure driven flow, the Taylor
deformation parameter of capsules in simple shear flow and the particle
trajectory in pair collisions of capsules in shear flow. The computational
complexity of the algorithm is verified with results from several large scale
multiparticle simulations.Comment: Journal of Computational Physics, to appea
Effective swimming strategies in low Reynolds number flows
The optimal strategy for a microscopic swimmer to migrate across a linear
shear flow is discussed. The two cases, in which the swimmer is located at
large distance, and in the proximity of a solid wall, are taken into account.
It is shown that migration can be achieved by means of a combination of sailing
through the flow and swimming, where the swimming strokes are induced by the
external flow without need of internal energy sources or external drives. The
structural dynamics required for the swimmer to move in the desired direction
is discussed and two simple models, based respectively on the presence of an
elastic structure, and on an orientation dependent friction, to control the
deformations induced by the external flow, are analyzed. In all cases, the
deformation sequence is a generalization of the tank-treading motion regimes
observed in vesicles in shear flows. Analytic expressions for the migration
velocity as a function of the deformation pattern and amplitude are provided.
The effects of thermal fluctuations on propulsion have been discussed and the
possibility that noise be exploited to overcome the limitations imposed on the
microswimmer by the scallop theorem have been discussed.Comment: 14 pages, 5 figure
Spherical capsules in three-dimensional unbounded Stokes flows: effect of the membrane constitutive law and onset of buckling
The dynamic response of an initially spherical capsule subject to different externally imposed flows is examined. The neo-Hookcan and Skalak et al. (Biophys. J., vol. 13 (1973), pp. 245-264) constitutive laws are used for the description of the membrane mechanics, assuming negligible bending resistance. The viscosity ratio between the interior and exterior fluids of the capsule is taken to be unity and creeping-flow conditions are assumed to prevail. The capillary number epsilon is the basic dimensionless number of the problem, which measures the relative importance of viscous and elastic forces. The boundary-element method is used with bi-cubic B-splines as basis functions in order to discretize the capsule surface by a structured mesh. This guarantees continuity of second derivatives with respect to the position of the Lagrangian particles used for tracking the location of the interface at each time step and improves the accuracy of the method. For simple shear flow and hyperbolic flow, an interval in 8 is identified within which stable equilibrium shapes are obtained. For smaller values of E, steady shapes are briefly captured, but they soon become unstable owing to the development of compressive tensions in the membrane near the equator that cause the capsule to buckle. The post-buckling state of the capsule is conjectured to exhibit small folds around the equator similar to those reported by Walter et al. Colloid Polymer Sci. Vol. 278 (2001), pp. 123-132 for polysiloxane microcapsules. For large values of 6, beyond the interval of stability, the membrane has two tips along the direction of elongation where the deformation is most severe, and no equilibrium shapes could be identified. For both regions outside the interval of stability, the membrane model is not appropriate and bending resistance is essential to obtain realistic capsule shapes. This pattern persists for the two constitutive laws that were used, with the Skalak et al. law producing a wider stability interval than the neo-Hookean law owing to its strain hardening nature