The initial stages of gravity driven flows

Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2011Includes bibliographical references (leaves: 47)Text in English; Abstract: Turkish and Englishix, 59 leavesDuring the initial stage of dam breaking; the liquid flow and the free surface shape are investigated. We used small-time approximation for this investigation and derived the leading order solution of classical dam-break problem. But this solution is not valid in a small vicinity of the corner point (the intersection point between the initially vertical free surface and the horizontal rigid bottom). The dimension of this vicinity is estimated with the help of a local analysis of the this outer solution close to the corner point. Streched local coordinates are used in this vicinity to resolve the flow singularity and to derive the leading order inner solution (which describes the formation of the jet flow along the bottom) and the correction to the leading order. This asymptotic solution obtained is expected to be helpful in the analysis of developed gravity driven flows

Oscillations of weakly viscous conducting liquid drops in a strong magnetic field

We analyse small-amplitude oscillations of a weakly viscous electrically conducting liquid drop in a strong uniform DC magnetic field. An asymptotic solution is obtained showing that the magnetic field does not affect the shape eigenmodes, which remain the spherical harmonics as in the non-magnetic case. Strong magnetic field, however, constrains the liquid flow associated with the oscillations and, thus, reduces the oscillation frequencies by increasing effective inertia of the liquid. In such a field, liquid oscillates in a two-dimensional (2D) way as solid columns aligned with the field. Two types of oscillations are possible: longitudinal and transversal to the field. Such oscillations are weakly damped by a strong magnetic field - the stronger the field, the weaker the damping, except for the axisymmetric transversal and inherently 2D modes. The former are overdamped because of being incompatible with the incompressibility constraint, whereas the latter are not affected at all because of being naturally invariant along the field. Since the magnetic damping for all other modes decreases inversely with the square of the field strength, viscous damping may become important in a sufficiently strong magnetic field. The viscous damping is found analytically by a simple energy dissipation approach which is shown for the longitudinal modes to be equivalent to a much more complicated eigenvalue perturbation technique. This study provides a theoretical basis for the development of new measurement methods of surface tension, viscosity and the electrical conductivity of liquid metals using the oscillating drop technique in a strong superimposed DC magnetic field.Comment: 17 pages, 3 figures, substantially revised (to appear in J. Fluid Mech.

Reexamination of Hagen-Poiseuille flow: shape-dependence of the hydraulic resistance in microchannels

We consider pressure-driven, steady state Poiseuille flow in straight channels with various cross-sectional shapes: elliptic, rectangular, triangular, and harmonic-perturbed circles. A given shape is characterized by its perimeter P and area A which are combined into the dimensionless compactness number C = P^2/A, while the hydraulic resistance is characterized by the well-known dimensionless geometrical correction factor alpha. We find that alpha depends linearly on C, which points out C as a single dimensionless measure characterizing flow properties as well as the strength and effectiveness of surface-related phenomena central to lab-on-a-chip applications. This measure also provides a simple way to evaluate the hydraulic resistance for the various shapes.Comment: 4 pages including 3 figures. Revised title, as publishe

Active shape correction of a thin glass/plastic X-ray mirror

Optics for future X-ray telescopes will be characterized by very large aperture and focal length, and will be made of lightweight materials like glass or plastic in order to keep the total mass within acceptable limits. Optics based on thin slumped glass foils are currently in use in the NuSTAR telescope and are being developed at various institutes like INAF/OAB, aiming at improving the angular resolution to a few arcsec HEW. Another possibility would be the use of thin plastic foils, being developed at SAO and the Palermo University. Even if relevant progresses in the achieved angular resolution were recently made, a viable possibility to further improve the mirror figure would be the application of piezoelectric actuators onto the non-optical side of the mirrors. In fact, thin mirrors are prone to deform, so they require a careful integration to avoid deformations and even correct forming errors. This however offers the possibility to actively correct the residual deformation. Even if other groups are already at work on this idea, we are pursuing the concept of active integration of thin glass or plastic foils with piezoelectric patches, fed by voltages driven by the feedback provided by X-rays, in intra-focal setup at the XACT facility at INAF/OAPA. In this work, we show the preliminary simulations and the first steps taken in this project

Electrostatic and electrokinetic contributions to the elastic moduli of a driven membrane

We discuss the electrostatic contribution to the elastic moduli of a cell or artificial membrane placed in an electrolyte and driven by a DC electric field. The field drives ion currents across the membrane, through specific channels, pumps or natural pores. In steady state, charges accumulate in the Debye layers close to the membrane, modifying the membrane elastic moduli. We first study a model of a membrane of zero thickness, later generalizing this treatment to allow for a finite thickness and finite dielectric constant. Our results clarify and extend the results presented in [D. Lacoste, M. Cosentino Lagomarsino, and J. F. Joanny, Europhys. Lett., {\bf 77}, 18006 (2007)], by providing a physical explanation for a destabilizing term proportional to \kps^3 in the fluctuation spectrum, which we relate to a nonlinear ($E^2$) electro-kinetic effect called induced-charge electro-osmosis (ICEO). Recent studies of ICEO have focused on electrodes and polarizable particles, where an applied bulk field is perturbed by capacitive charging of the double layer and drives flow along the field axis toward surface protrusions; in contrast, we predict "reverse" ICEO flows around driven membranes, due to curvature-induced tangential fields within a non-equilibrium double layer, which hydrodynamically enhance protrusions. We also consider the effect of incorporating the dynamics of a spatially dependent concentration field for the ion channels.Comment: 22 pages, 10 figures. Under review for EPJ

Inconsistencies in the Notions of Acoustic Stress and Streaming

Inviscid hydrodynamics mediates forces through pressure and other, typically irrotational, external forces. Acoustically induced forces must be consistent with arising from such a pressure field. The use of "acoustic stress" is shown to have inconsistencies with such an analysis and generally arise from mathematical expediency but poor overall conceptualization of such systems. This contention is further supported by the poor agreement of experiment in many such approaches. The notion of momentum as being an intrinsic property of sound waves is similarly found to be paradoxical. Through an analysis that includes viscosity and attenuation, we conclude that all acoustic streaming must arise from vorticity introduced by viscous forces at the driver or other solid boundaries and that calculations with acoustic stress should be replaced with ones using a nonlinear correction to the overall pressure field

Assessing the outcome of orthognathic surgery by three-dimensional soft tissue analysis

Studies of orthognathic surgery often focus on pre-surgical versus post-surgical changes in facial shape. In contrast, this study provides an innovative comparison between post-surgical and control shape. Forty orthognathic surgery patients were included, who underwent three different types of surgical correction: Le Fort I maxillary advancement, bilateral sagittal split mandibular advancement, and bimaxillary advancement surgery. Control facial images were captured from volunteers from local communities in Glasgow, with patterns of age, sex, and ethnic background that matched those of the surgical patients. Facial models were fitted and Procrustes registration and principal components analysis used to allow quantitative analysis, including the comparison of group mean shape and mean asymmetry. The primary characteristic of the difference in shape was found to be residual mandibular prognathism in the group of female patients who underwent Le Fort I maxillary advancement. Individual cases were assessed against this type of shape difference, using a quantitative scale to aid clinical audit. Analysis of the combined surgical groups provided strong evidence that surgery reduces asymmetry in some parts of the face such as the upper lip region. No evidence was found that mean asymmetry in post-surgical patients is greater than that in controls