1,721,078 research outputs found
Un modello analitico della fluodinamica del vitreo oculare liquefatto
No full textSi presenta un modello teorico della fluodinamica del vitreo oculare liquefatto indotta dai movimenti saccadici dell'occhio. Il vitreo è schematizzato come un fluido Newtoniano incomprimibile in moto irrotazionale. Nel caso di vitreo liquefatto l'ipotesi di irrotazionalità del moto risulta giustificata poiché, durante i brevi e rapidi movimenti saccadici, si ha la formazione di uno strato limite viscoso alla parete, il cui spessore risulta trascurabile rispetto
alle dimensioni del globo. La camera vitreale viene assimilata ad una
sfera debolmente deformata in modo da mettere in conto la rientranza
dovuta alla presenza del cristallino ed il fatto che l'asse antero-posteriore dell'occhio risulta, in condizioni fisiologiche, più corto rispetto a quello verticale ed a quello trasversale. Il problema per il potenziale della velocità assoluta viene risolto analiticamente in termini di armoniche sferiche. I risultati mostrano come la non sfericità del dominio generi nel vitreo un campo di moto caratterizzato da velocità significative e forte tridimensionalità. La distribuzione della velocità sul contorno suggerisce inoltre che l'irregolarità del dominio può modificare significativamente le
tensioni tangenziali sulla retina rispetto al caso di moto all'interno di una sfera. Il modello consente la valutazione delle pressioni dinamiche sul contorno che possono avere un ruolo nella patogenesi del distacco di retina. Un'analisi semplificata, relativa al caso di moto piano bidimensionale e rotazione impulsiva dell'occhio, mostra come lo strato limite alla parete tenda a separare, in prossimità del cristallino, per valori dell'angolo di rotazione superiori a circa 17°
An Analytical Model of the Dynamics of the Liquefied Vitreous Induced by Saccadic Eye Movements
No full textAn analytical model of the dynamics of the vitreous humour induced by saccadic movements within the eye globe is presented. The vitreous is treated as a weakly viscous Newtonian incompressible fluid, an assumption which is appropriate when the vitreous is liquefied or when it is replaced by aqueous humour after surgery. The thin viscous boundary layer generated during a
saccadic movement on the side wall is neglected and the flow field is assumed to be irrotational. The vitreous chamber is described as a weakly deformed sphere and this assumption allows a linear
treatment of the problem. An analytical solution is found in the form of an expansion of spherical harmonics. Results show that the non-spherical shape of the container generates a flow field charac-
terised by significant velocities and strong three-dimensionality. The model allows the computation of the dynamic pressure on the wall, which may play a role in the generation of retinal detachments.
Moreover, results suggest that the irregular shape of the globe may significantly modify tangential stresses on the boundary with respect to the case of motion within a sphere. A simplified analyti-
cal solution, for the case of two-dimensional flow within an impulsively rotated container, shows that boundary layer detachment is expected to occur for angles of rotation larger than a threshold value of 15◦ circa
Transition from migrating alternate bars to steady central bars in channels with variable width
No full textWe study the development process of free bars in straight
cohesionless channels subject to periodic width changes. The problem
is investigated both theoretically and experimentally. We first
consider the steady flow in a channel with low amplitude periodic
variations of the width. We than perform a linear stability analysis
of the latter flow. The main result is a linear dispersion
relationship which allows one to determine the correction to the
growth rate and migration speed of free bars due to width
variations. Theoretical results suggest that width variations may
inhibit the development of free bars and trigger the transition from
migrating to steady bars. The damping effect increases for increasing
values of Shields parameter; it also depends on the wavelength of
width variations. Theoretical findings agree almost qualitatively with
experimental observations performed in a laboratory flume
Su un problema di idroelasticità di rilievo per la dinamica del vitreo oculare
No full textSi studia il moto bidimensionale di un fluido posto all'interno di un cilindro rigido sottoposto a rotazioni periodiche intorno al proprio asse. Il cilindro è suddiviso longitudinalmente in due regioni da una membrana elastica tesa, posta in posizione diametrale; gli estremi della membrana sono fissati alle pareti del cilindro. Il presente contributo rappresenta il primo approccio allo studio della dinamica del vitreo oculare in presenza di una membrana vitrea. Il vitreo viene schematizzato come un fluido Newtoniano incomprimibile in moto irrotazionale e si linearizza il problema in virtù dell'ipotesi di piccola ampiezza delle rotazioni del contenitore. I risultati mettono in evidenza come le frequenze proprie di oscillazione della membrana risultino fortemente influenzate dalla presenza del vitreo. Si mostra inoltre come siano possibili fenomeni di risonanza per frequenze delle rotazioni del contenitore tipiche dei movimenti saccadici dell’occhio
Topographic expressions of bars in channels with variable width
No full textA three dimensional quasi-analytical model is introduced to determine the flow field and the altimetric response of movable-bed channels subject to periodic
width variations. The basic assumptions underlying the analysis are those of small amplitude of width variations and wide channel, so that non linear effects and side walt effects are neglected. The aim of the work is to determine the conditions under which the channel is planimetrically stable or unstable, i.e. it tends to damp (or enhance) a given initial (infinitesimal) perturbation
of the channel width due to bank erosion. A simple bank erosion model is adopted whereby the rate of bank retreat is related to the excess shear stress at the banks. Theoretical results suggest that the equilibrium bottom profile is mainly constituted by two components. The first component represents a purely longitudinal bottom deformation, which induces deposition at the widest section and scour at the constraint, where the cross sectionally averaged velocity attains its maximum value. The second component is mainly originated by three dimen-
sional effects and induces a transverse deformation of the bed in the form of a central bar. Its relative position with respect to the former component changes with the length of width variations: under suitable conditions the flow divergence induced by the central bar leads to a maximum velocity at the banks in wide sections, which implies that width variations tend to amplify
Finite amplitude Faraday waves induced by a random forcing
No full textIn the present contribution we study the waves arising on the free surface of a liquid in a rectangular container undergoing vertical oscillations. Our aim in the work is to investigate the role of a random forcing characterized by a narrow-band spectrum on the wave amplitude close to subharmonic resonant conditions. The analysis is carried out theoretically by means of a weakly nonlinear analysis, assuming the ratio a 0 between the acceleration of the tank and the gravitational acceleration to be small. We consider irrotational flow and take into account viscous effects by adding a linear dissipative term to the amplitude equation following Miles ‘‘Nonlinear Faraday resonance,’’ J. Fluid Mech. 146, 285 1984. Comparing the results with those obtained in the case
of a monochromatic forcing, it appears that the range of unstable frequencies significantly widens. This finding agrees with the theoretical results found in the linear context by Zhang, Casademunt and Vinals ‘‘Study of the parametric oscillator driven by a narrow band noise to model the response of a fluid surface to time-dependent accelerations,’’ Phys. Fluids A 5, 3147 1993. The maximum
equilibrium amplitude of the free surface waves for the random forcing case turns out to be smaller than that of the monochromatic forcing and it decreases as the spectrum width is increased
Eye rotation induced dynamics of a Newtonian fluid within the vitreous cavity: the effect of the chamber shape
No full textThe dynamics of the vitreous body induced by eye rotations is studied
experimentally. In particular, we consider the case in which the vitreous cavity is filled by a Newtonian fluid, either because the vitreous is liquefied or because it has been replaced, after vitrectomy, by a viscous fluid. We employ a rigid Perspex container which models, in a magnified scale, the vitreous cavity of the human eye. The shape of the cavity closely resembles that of the real vitreous chamber; in particular, the anterior part of the container is concave in order to model the presence of the eye lens. The container
is filled with glycerol and is mounted on the shaft of a computer-controlled motor which rotates according to a periodic time law. PIV (particle image velocimetry) measurements are taken on the equatorial plane orthogonal to the axis of rotation. The experimental measurements show that the velocity field is strongly influenced by the deformed geometry of the domain. In particular, the formation of a vortex in the vicinity of the lens, which migrates in time towards
the core of the domain, is invariably observed. The vortex path is tracked in time by means of a vortex identification technique and it is found that it is significantly influenced by the Womersley number of the flow. Particle trajectories are computed from the PIV measurements. Particles initially located at different positions on the equatorial horizontal plane (perpendicular to the axis of rotation) tend to concentrate in narrow regions adjacent to the lens, thus suggesting the existence, in such regions, of a vertical fluid ejection. Such a strong flow three-dimensionality, which is essentially induced by the irregular shape of the domain, may play a significant role in the mixing processes taking place inside the eye globe. The tangential stresses acting on the rigid boundary of the domain are also computed from the experimental measurements showing that regions subject to particularly intense stresses exist along the boundary close to the lens
Channel bifurcation in braided rivers: Equilibrium configurations and stability
No full textWe investigate the equilibrium configurations and the stability of river bifurcations in gravel braided networks. Within the context of a one-dimensional approach, the nodal point conditions play a crucial rule, as pointed out by Wang et al. [1995] who propose an empirical relationship relating water and sediment flow rates into the downstream branches. In the present paper, an alternative formulation of nodal point conditions is proposed based on a quasi two-dimensional approach. The results show that, if the Shields parameter of the upstream channel is large enough, the system only admits of one solution with both branches open, which is invariably stable. As the Shields parameter of the upstream channel decreases, two further stable solutions appear characterized by a different partition of water discharge into the downstream branches: in this case, the previous solution becomes unstable. Theoretical findings are confirmed by the numerical solution of the nonlinear one-dimensional equations
Shape Change of the Vitreous Chamber Influences Retinal Detachment and Reattachment Processes: Is Mechanical Stress during Eye Rotations a Factor?
No full textPurpose. We aim to understand how mechanical causation influences retinal detachment and reattachment processes. In particular, myopes suffer retinal detachment more frequently than emmetropes, and following a retinal detachment, scleral buckling promotes retinal reattachment. We test the hypothesis that stresses arising from saccadic eye rotations are involved in the processes, and that the alteration in the stress due to the change in the vitreous chamber geometry is sufficient to explain the phenomena.
Methods. The vitreous chamber of the eye has an approximately spherical shape and it is filled with vitreous humor. We developed a mathematical model, treating the vitreous chamber in emmetropic and myopic eyes as a spheroid and in eyes subjected to scleral buckling as a sphere with a circumferential indentation. We assume that the eye performs prescribed small-amplitude, periodic, torsional rotations and we solve semi-analytically for the fluid pressure, velocity, and stress distributions.
Results. The shape of the vitreous chamber has a large effect on the retinal stress. The vitreous and the retina of a highly myopic eye continuously experience shear stresses significantly higher than those of an emmetropic eye. An eye fitted with a scleral buckle experiences large stress levels localized around the buckle.
Conclusions. Our results provide a mechanical explanation for the more frequent occurrence of posterior vitreous detachment and retinal detachment in myopic eyes. To understand how the stress distribution in a buckled eye facilitates reattachment, an additional model of the details of the reattachment process should be coupled to this model
Oscillatory motion of a viscoelastic fluid within a spherical cavity
No full textWe study the motion of a viscoelastic fluid within a rigid spherical cavity with the aim of improving understanding of the motion of the vitreous humour in the human eye. The flow of vitreous humour leads to traction on the retina, which, once the retina is torn or damaged, can cause it to detach from the choroid, leading to loss of sight if left untreated. In the first part of the paper we investigate the relaxation behaviour of the fluid, the transient flow that would be observed in the stationary sphere starting from non-stationary initial conditions. For a general viscoelastic fluid we calculate the growth rates and eigenfunctions associated with the system, and we discuss two particular rheological models of the vitreous humour taken from the literature. In the second part of the paper we consider forced oscillations of the fluid, due to small-amplitude rotations of the sphere about a diameter, representing saccades of the eyeball. We conclude with a discussion of the possible occurrence of resonant
phenomena and their clinical relevance
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