Shape Diagram of Vesicles in Poiseuille Flow

Coupier, Gwennou; Farutin, Alexander; Minetti, Christophe; Podgorski, Thomas; Misbah, Chaouqi

doi:10.1103/physrevlett.108.178106

Cited by 81 publications

(104 citation statements)

References 40 publications

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“…The top views of the droplets become more asymmetric between the front and the rear, while they remain symmetric between the top and bottom. The shape of the droplet is similar to that of the vesicles obtained by Coupier et al 45 for low Re. Negative curvature regions at the rear appear at Re = 19.3.…”

Section: Resultssupporting

confidence: 70%

Inertial migration of deformable droplets in a microchannel

Chen

Xue

Zhang³

et al. 2014

Physics of Fluids

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The microfluidic inertial effect is an effective way of focusing and sorting droplets suspended in a carrier fluid in microchannels. To understand the flow dynamics of microscale droplet migration, we conduct numerical simulations on the droplet motion and deformation in a straight microchannel. The results are compared with preliminary experiments and theoretical analysis. In contrast to most existing literature, the present simulations are three-dimensional and full length in the streamwise direction and consider the confinement effects for a rectangular cross section. To thoroughly examine the effect of the velocity distribution, the release positions of single droplets are varied in a quarter of the channel cross section based on the geometrical symmetries. The migration dynamics and equilibrium positions of the droplets are obtained for different fluid velocities and droplet sizes. Droplets with diameters larger than half of the channel height migrate to the centerline in the height direction and two equilibrium positions are observed between the centerline and the wall in the width direction. In addition to the well-known Segré-Silberberg equilibrium positions, new equilibrium positions closer to the centerline are observed. This finding is validated by preliminary experiments that are designed to introduce droplets at different initial lateral positions. Small droplets also migrate to two equilibrium positions in the quarter of the channel cross section, but the coordinates in the width direction are between the centerline and the wall. The equilibrium positions move toward the centerlines with increasing Reynolds number due to increasing deformations of the droplets. The distributions of the lift forces, angular velocities, and the deformation parameters of droplets along the two confinement direction are investigated in detail. Comparisons are made with theoretical predictions to determine the fundamentals of droplet migration in microchannels. In addition, existence of the inner equilibrium position is linked to the quartic velocity distribution in the width direction through a simple model for the slip angular velocities of droplets.

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Section: Resultssupporting

confidence: 70%

Inertial migration of deformable droplets in a microchannel

Chen

Xue

Zhang³

et al. 2014

Physics of Fluids

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“…We show the steady state deformation in Figure 2 for Ca = 0.05, 0.3, 0.6. The steady state is nearly spherical for stiff capsules, whereas, by increasing the capillary number, it develops a frontrear asymmetry and displays first a bullet-like, and then a croissant-like shape [41,43,44]. We refer to the shape as "croissant" rather than "parachute" following the convention in [41,44] according to which a "parachute" shape is perfectly axisymmetric.…”

Section: Resultsmentioning

confidence: 99%

“…The steady state is nearly spherical for stiff capsules, whereas, by increasing the capillary number, it develops a frontrear asymmetry and displays first a bullet-like, and then a croissant-like shape [41,43,44]. We refer to the shape as "croissant" rather than "parachute" following the convention in [41,44] according to which a "parachute" shape is perfectly axisymmetric. This is not the case here since the capsule either sees the periodic boundary conditions in z and the walls in y or adapts to the duct square crosssection [43,45].…”

Section: Resultsmentioning

confidence: 99%

Motion of an elastic capsule in a constricted microchannel

et al. 2015

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We study the motion of an elastic capsule through a microchannel characterized by a localized constriction. We consider a capsule with a stress-free spherical shape and impose its steady state configuration in an infinitely long straight channel as the initial condition for our calculations. We report how the capsule deformation, velocity, retention time, and maximum stress of the membrane are affected by the capillary number, Ca, and the constriction shape. We estimate the deformation by measuring the variation of the three-dimensional surface area and a series of alternative quantities easier to extract from experiments. These are the Taylor parameter, the perimeter and the area of the capsule in the spanwise plane. We find that the perimeter is the quantity that reproduces the behavior of the three-dimensional surface area the best. This is maximum at the centre of the constriction and shows a second peak after it, whose location depends on the Ca number. We observe that, in general, area-deformation correlated quantities grow linearly with Ca, while velocity-correlated quantities saturate for large Ca but display a steeper increase for small Ca. The velocity of the capsule divided by the velocity of the flow displays, surprisingly, two different qualitative behaviors for small and large capillary numbers. Finally, we report that longer constrictions and spanwise wall bounded (versus spanwise periodic) domains cause larger deformations and velocities. If the deformation and velocity in the spanwise wall bounded domains are rescaled by the initial equilibrium deformation and velocity, their behavior is undistinguishable from that in a periodic domain. In contrast, a remarkably different behavior is reported in sinusoidally shaped and smoothed rectangular constrictions indicating that the capsule dynamics is particularly sensitive to abrupt changes in the cross section. In a smoothed rectangular constriction larger deformations and velocities occur over a larger distance.

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“…Although there is some experimental evidence that surfactant-covered drops can undergo asymmetric deformation and breakup, the phenomenon has never been rigorously studied. An experimental validation of the steady asymmetric vesicle shapes also needs to be systematically carried out, although this may be a difficult task; for example, the vesicle 'slippers' in Poiseuille flow have proven elusive to experimental observation (Coupier et al 2012). Finally, external fields other than flow, e.g.…”

Section: Futurementioning

confidence: 99%

“…In simple shear, a vesicle deforms into an ellipsoid which can either tank-tread, keeping the orientation steady, or tumble. In Poiseuille flow, vesicles typically migrate towards the flow centreline where they assume axisymmetric bulletor parachute-like shapes (Coupier et al 2012).…”

Section: Introductionmentioning

confidence: 99%

Asymmetric shapes and pearling of a stretched vesicle

Vlahovska

2014

J. Fluid Mech.

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Closed bilayer membranes (vesicles) display a plethora of non-spherical shapes under equilibrium conditions, unlike drops and bubbles which are kept spherical by surface tension. Even more complex behaviour arises under applied flow. Intriguingly, a vesicle can adopt asymmetric shapes even under symmetric forcing such as uniaxial extensional flow. Narasimhan, Spann & Shaqfeh (J. Fluid Mech., vol. 750, 2014, pp. 144-190) explain the mechanism of this peculiar instability and trace its origin to the tension which develops in the area-incompressible membrane in response to the applied stress. The authors also show that this mechanism is relevant to the pearling of tubular vesicles. This study raises many questions, e.g. whether other soft particles with load-dependent tension such as capsules can undergo similar shape transformations.

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Shape Diagram of Vesicles in Poiseuille Flow

Cited by 81 publications

References 40 publications

Inertial migration of deformable droplets in a microchannel

Inertial migration of deformable droplets in a microchannel

Motion of an elastic capsule in a constricted microchannel

Asymmetric shapes and pearling of a stretched vesicle

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