1,720,969 research outputs found
Two-shape-tensor model for tumbling in nematic polymers and liquid crystals
Full text linkMost, but not all, liquid crystals tend to align when subject to shear flow, while most nematic polymeric liquid crystals undergo a tumbling instability, where the director rotates with the flow. The reasons of this instability remain elusive, as it is possible to find similar molecules exhibiting opposite behaviors. We propose a continuum theory suitable for describing a wide range of material behaviors, ranging form nematic elastomers to nematic polymers and nematic liquid crystals, where the material parameters have meaningful physical interpretations and the conditions for tumbling emerge clearly. There are two possible ways to relax the internal stress in a nematic material. The first is the reorganization of the polymer network, the second is the alignment of the network natural axis with respect to the principal direction of the effective strain. We show that tumbling occurs whenever the second mechanism is less efficient than the first. Furthermore, we provide a justification of the experimental fact that at high temperatures, in an isotropic phase, only flow alignment is observed and no tumbling is possible, even in polymers
Bifurcation analysis of pressure-induced detachment of a rod adhered to a plate
No full textWe study the lift of an elastica adhering to a flat rigid surface induced by a pressure difference. Adhesion is modelled by a cohesive force that decreases linearly with separation. Using a nonlinear local analysis, we determine the bifurcation diagram that governs the peeling process under quasi-static conditions. We show that the delamination emerges through a discontinuous transition: a normal form of the bifurcation diagram allows us to draw in a simple way the main physical mechanism, elucidating the local validity of the theory at the transition. We predict that the pressure, as a function of the detachment length, undergoes an initial drop followed by an approximately constant behaviour, while the detachment length at the transition is always finite and is roughly proportional to the elasto-adhesion length. This analysis can be the starting point to understand more complex-related problems that arise in fracture mechanics or in biology, such as testing of adhesives in a flowfield and the arterial dissection
Spontaneous flow in active nematics: Effects induced by annular confinement
No full textWithin the framework of continuum mechanics for materials with relaxation, this study investigates activity-induced laminar flow in an active nematic confined within an annular domain. Subsequent to the formulation of the problem as a nonlinear boundary value problem, a bifurcation analysis of the governing equation demonstrates that the critical threshold for the initiation of spontaneous flow is dependent on the aspect ratio (thickness-to-radius) of the domain. The influence of domain curvature is twofold: firstly, it facilitates the inception of spontaneous motion by reducing the critical threshold; secondly, it resolves the indeterminacy inherent in the planar geometry, wherein, at an equivalent critical threshold, two distinct flow configurations may manifest: a unidirectional flow or a configuration exhibiting two counter-propagating bands. In the annular geometry, the double-band configuration, characterized by a thicker inner layer, exhibits the lowest activation threshold. With an augmentation of either activity or curvature, the principal motion transitions towards a predominantly unidirectional flow, accompanied by a narrow counter-rotating band adjacent to the outer boundary, aligning with experimental observations of confined bacterial colonies
Strain energy storage and dissipation rate in active cell mechanics
Full text linkWhen living cells are observed at rest on a flat substrate, they can typically exhibit a rounded (symmetric) or an elongated (polarized) shape. Although the cells are apparently at rest, the active stress generated by the molecular motors continuously stretches and drifts the actin network, the cytoskeleton of the cell. In this paper we theoretically compare the energy stored and dissipated in this active system in two geometric configurations of interest: symmetric and polarized. We find that the stored energy is larger for a radially symmetric cell at low activation regime, while the polar configuration has larger strain energy when the active stress is beyond a critical threshold. Conversely, the dissipation of energy in a symmetric cell is always larger than that of a nonsymmetric one. By a combination of symmetry arguments and competition between surface and bulk stress, we argue that radial symmetry is an energetically expensive metastable state that provides access to an infinite number of lower-energy states, the polarized configurations
Spontaneous helical flows in active nematics lying on a cylindrical surface
No full textWithin the framework of the two-dimensional Ericksen-Leslie model, we explore the effect of geometric confinement on the spontaneous flow of active nematic gels. The nematic particles are assumed to flow on a cylindrical surface, while a degenerate tangential anchoring is enforced. Using the linear approximation of the motion equations, we show that there is a close interplay among extrinsic curvature, flow, director alignment, and activity. We find that the extrinsic curvature promotes the director alignment parallel to the cylindrical axis and is responsible for raising the critical threshold with respect to the flat case. Our analysis reveals a very rich scenario where the key quantities are the activity coefficient, the tumbling parameter, and the anisotropic viscosity ratio. Thus, solutions can exhibit a double periodicity in both the azimuthal and axial variables. As a consequence, the velocity field can make a finite angle with the cylinder axis and the active flow winds on the surface with a helical pattern, while the director oscillates around the cylinder generators. Our results can be validated on thin layers of nematic gels placed between two concentric cylinders and suggest which material properties are most suited for the design of active microfluidic devices
Elementary Mechanics of the Mitral Valve
Full text linkWe illustrate a bare-bones mathematical model that is able to account for the elementary mechanics of the mitral valve when the leaflets of the valve close under the systolic pressure. The mechanical model exploits the aspect ratio of the valve leaflets that are represented as inextensible rods, subject to the blood pressure, with one fixed endpoint (on the endocardium) and an attached wire anchored to the papillary muscle. Force and torque balance equations are obtained exploiting the principle of virtual work, where the first contact point between rods is identified by the Weierstrass-Erdmann condition of variational nature. The chordae tendineae are modeled as a force applied to the free endpoint of the flaps. Different possible boundary conditions are investigated at the mitral annulus, and, by an asymptotic analysis, we demonstrate that in the pressure regime of interest generic boundary conditions generate a tensional boundary layer. Conversely, a specific choice of the boundary condition inhibits the generation of high tensional gradients in a small layer
ELEMENTARY MECHANICS OF THE MITRAL VALVE
Full text linkWe illustrate a bare-bones mathematical model that is able to account for the elementary mechanics of the mitral valve when the leaflets of the valve close under the systolic pressure. The mechanical model exploits the aspect ratio of the valve leaflets that are represented as inextensible rods, subject to the blood pressure, with one fixed endpoint (on the endocardium) and an attached wire anchored to the papillary muscle. Force and torque balance equations are obtained exploiting the principle of virtual work, where the first contact point between rods is identified by the Weierstrass-Erdmann condition of variational nature. The chordae tendineae are modeled as a force applied to the free endpoint of the flaps. Different possible boundary conditions are investigated at the mitral annulus, and, by an asymptotic analysis, we demonstrate that in the pressure regime of interest generic boundary conditions generate a tensional boundary layer. Conversely, a specific choice of the boundary condition inhibits the generation of high tensional gradients in a small layer
Dehydration-induced mechanical instabilities in active elastic spherical shells
Full text linkActive elastic instabilities are common phenomena in the natural world, where they have the character of sudden mechanical morphings. Frequently, the driving force of the instability mechanisms has a chemo-mechanical nature, which makes the instabilities very different from the standard elastic instabilities. In this paper, we describe and study the active elastic instability occurring in a swollen spherical closed shell, confining a water-filled cavity, during a dehydration process. We set up a few numerical experiments based on a stress-diffusion model to give an insight into the phenomenon. Then, we present a study that looks at the chemo-mechanical problem and, through a few simplifying assumptions, allows us to derive a semi-analytical model of the phenomenon. It takes into account both the stress state and the water concentration in the walls of the shell at the onset of the instability. Moreover, it considers the invariance of the cavity volume at the onset of instability, which is due to the impossibility of instantaneously changing the cavity volume filled with water. Eventually, it is shown that the semi-analytic model matches very well the outcomes of the numerical experiments far from the initial regime; the ranges of validity of the approximated analytical model are also discussed
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