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Register a new userShape transition and hydrodynamics of vesicles in tube flow
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The steady motion and deformation of a lipid-bilayer vesicle translating through a circular tube in low Reynolds number pressure-driven flow are investigated numerically using an axisymmetric boundary element method. This fluid-structure interaction problem is determined by three dimensionless parameters: reduced volume (a measure of the vesicle asphericity), geometric confinement (the ratio of the vesicle effective radius to the tube radius), and capillary number (the ratio of viscous to bending forces). The physical constraints of a vesicle -- fixed surface area and enclosed volume when it is confined in a tube -- determine critical confinement beyond which it cannot pass through without rupturing its membrane. The simulated results are presented in a wide range of reduced volumes [0.6, 0.98] for different degrees of confinement; the reduced volume of 0.6 mimics red blood cells. We draw a phase diagram of vesicle shapes and propose a shape transition line separating the parachute-like shape region from the bullet-like one in the reduced volume versus confinement phase space. We show that the shape transition marks a change in the behavior of vesicle mobility, especially for highly deflated vesicles. Most importantly, high-resolution simulations make it possible for us to examine the hydrodynamic interaction between the wall boundary and the vesicle surface at conditions of very high confinement, thus providing the limiting behavior of several quantities of interest, such as the thickness of lubrication film, vesicle mobility and its length, and the extra pressure drop due to the presence of the vesicle. This extra pressure drop holds implications for the rheology of dilute vesicle suspensions. Furthermore, we present various correlations and discuss a number of practical applications.
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Motivated by problems arising in the pneumatic actuation of controllers for micro-electromechanical systems (MEMS), labs-on-a-chip or biomimetic soft robots, and the study of microrheology of both gases and soft solids, we analyze the transient fluid--structure interaction (FSIs) between a viscoelastic tube conveying compressible flow at low Reynolds number. We express the density of the fluid as a linear function of the pressure, and we use the lubrication approximation to further simplify the fluid dynamics problem. On the other hand, the structural mechanics is governed by a modified Donnell shell theory accounting for Kelvin--Voigt-type linearly viscoelastic mechanical response. The fluid and structural mechanics problems are coupled through the tubes radial deformation and the hydrodynamic pressure. For small compressibility numbers and weak coupling, the equations are solved analytically via a perturbation expansion. Three illustrative problems are analyzed. First, we obtain exact (but implicit) solutions for the pressure for steady flow conditions. Second, we solve the transient problem of impulsive pressurization of the tubes inlet. Third, we analyze the transient response to an oscillatory inlet pressure. We show that an oscillatory inlet pressure leads to acoustic streaming in the tube, attributed to the nonlinear pressure gradient induced by the interplay of FSI and compressibility. Furthermore, we demonstrate an enhancement in the volumetric flow rate due to FSI coupling. The hydrodynamic pressure oscillations are shown to exhibit a low-pass frequency response (when averaging over the period of oscillations), while the frequency response of the tube deformation is similar to that of a band-pass filter.
We examine experimentally the deformation of flexible, microscale helical ribbons with nanoscale thickness subject to viscous flow in a microfluidic channel. Two aspects of flexible microhelices are quantified: the overall shape of the helix and the viscous frictional properties. The frictional coefficients determined by our experiments are consistent with calculated values in the context of resistive force theory. Deformation of helices by viscous flow is well-described by non-linear finite extensibility. Under distributed loading, the pitch distribution is non-uniform and from this, we identify both linear and non-linear behavior along the contour length of a single helix. Moreover, flexible helices are found to display reversible global to local helical transitions at high flow rate.
Laminar flow over a bubble mattress is expected to experience a significant reduction in friction since the individual surfaces of the bubbles are shear-free. However, if the bubbles are sufficiently curved, their protrusion into the fluid and along the flow direction can lead to an increase in friction as was recently demonstrated experimentally and computationally. We provide in this paper a simple model for this result. We consider a shear flow at low Reynolds number past a two-dimensional array of bubbles, and calculate analytically the effective slip length of the surface as function of the bubble geometry in the dilute limit. Our model is able to reproduce quantitatively the relationship between effective friction and bubble geometry obtained in numerical computations, and in particular: (a) The asymmetry in friction between convex and concave bubbles, and (b) the existence of a geometric transition from reduced to enhanced friction at a critical bubble protrusion angle.
When suspended particles are pushed by liquid flow through a constricted channel they might either pass the bottleneck without trouble or encounter a permanent clog that will stop them forever. However, they may also flow intermittently with great sensitivity to the neck-to-particle size ratio D/d. In this work, we experimentally explore the limits of the intermittent regime for a dense suspension through a single bottleneck as a function of this parameter. To this end, we make use of high time- and space-resolution experiments to obtain the distributions of arrest times T between successive bursts, which display power-law tails with characteristic exponents. These exponents compare well with the ones found for as disparate situations as the evacuation of pedestrians from a room, the entry of a flock of sheep into a shed or the discharge of particles from a silo. Nevertheless, the intrinsic properties of our system i.e. channel geometry, driving and interaction forces, particle size distribution seem to introduce a sharp transition from a clogged state to a continuous flow, where clogs do not develop at all. This contrasts with the results obtained in other systems where intermittent flow, with power-law exponents above two, were obtained.
Soft bodies flowing in a channel often exhibit parachute-like shapes usually attributed to an increase of hydrodynamic constraint (viscous stress and/or confinement). We show that the presence of a fluid membrane leads to the reverse phenomenon and build a phase diagram of shapes --- which are classified as bullet, croissant and parachute --- in channels of varying aspect ratio. Unexpectedly, shapes are relatively wider in the narrowest direction of the channel. We highlight the role of flow patterns on the membrane in this response to the asymmetry of stress distribution.
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