Forced Convection and Sedimentation Past a Flat Plate

The steady laminar flow of a well-mixed suspension of monodisperse solid spheres, convected steadily past a horizontal flat plate and sedimenting under the action of gravity, is examined. It is shown that, in the limit as Re approaches infinity and epsilon approaches 0, where Re is the bulk Reynolds number and epsilon is the ratio of the particle radius a to the characteristic length scale L, the analysis for determining the particle concentration profile has several aspects in common with that of obtaining the temperature profile in forced-convection heat transfer from a wall to a fluid stream moving at high Reynolds and Prandtl numbers. Specifically, it is found that the particle concentration remains uniform throughout the O(Re(exp -1/2)) thick Blasius boundary layer except for two O(epsilon(exp 2/3)) thin regions on either side of the plate, where the concentration profile becomes non-uniform owing to the presence of shear-induced particle diffusion which balances the particle flux due to convection and sedimentation. The system of equations within this concentration boundary layer admits a similarity solution near the leading edge of the plate, according to which the particle concentration along the top surface of the plate increases from its value in the free stream by an amount proportional to X(exp 5/6), with X measuring the distance along the plate, and decreases in a similar fashion along the underside. But, unlike the case of gravity settling on an inclined plate in the absence of a bulk flow at infinity considered earlier, here the concentration profile remains continuous everywhere. For values of X beyond the region near the leading edge, the particle concentration profile is obtained through the numerical solution of the relevant equations. It is found that, as predicted from the similarity solution, there exists a value of X at which the particle concentration along the top side of the plate attains its maximum value phi(sub m) and that, beyond this point, a stagnant sediment layer will form that grows steadily in time. This critical value of X is computed as a function of phi(sub s), the particle volume fraction in the free stream. In contrast, but again in conformity with the similarity solution, for values of X sufficiently far removed from the leading edge along the underside of the plate, a particle-free region is predicted to form adjacent to the plate. This model, with minor modifications, can be used to describe particle migration in other shear flows, as, for example, in the case of crossflow microfiltration

Forecasting the Long-Term Effects of the Pandemic on Children: Towards a COVID-Generation

This study focuses on mapping the existing effects of the pandemic and the measures taken to address it on the mental health of children in order to investigate the long-term consequences that it is expected to have. For infants, preschool, school and adolescent children it seems that intense stress develops for different reasons. As adults these children may experience an increased incidence of anxiety, depressive, obsessive–compulsive and personality disorders, while they are also expected to develop a strong External Locus of Control, low Faith in the Just World and low happiness. At the same time, an absence of distinction within the limits of the physical and digital world is expected. As for children with special educational needs, they are particularly affected due to the pandemic, as early diagnosis and the development of interventions to improve their educational and psychosocial progress are hampered and this might have negative long-term effects on their development. In overall, these negative effects and related experiences seem to be homogeneous across humanity for those who are currently minors and are expected to lead to the view of an autonomous generation, the COVID-generation

Static response of coated microbubbles:Modeling simulations and parameter estimation

AbstractThe mechanical response of contrast agent microbubbles subject to a static load was investigated in force-deformation curves. Asymptotic relations are fitted with experimental AFM measurements of polymeric microbubbles available in the literature. The elastic modulus and shell thickness are estimated based on the transition from the classical linear (Reissner) to the nonlinear (Pogorelov) regime. The estimated value of the elastic modulus is in the order of GPa and the shell thickness in the order of nm, in good agreement with independent estimates. Numerical simulations recover the above transition and identify a third regime, dominated by the compressibility of the enclosed gas

Modulation of the secondary Bjerknes force in multi-bubble systems

The behaviours of insonated bubble clusters are regulated by the secondary Bjerknes force between bubble pairs. While the force has been investigated extensively for two-bubble systems, the modulation of the force by nearby bubbles remains unclear. This problem is investigated in this paper by theoretical analyses and numerical simulations of a three bubble system. For weak oscillations, the third bubble is found to have strong effects when its radius is close to the resonant radius. The equilibrium distance between the bubble pair is reduced when the radius of the third bubble is smaller than the resonant threshold, and increased when it is larger. For strong oscillations of bubbles with radii of a few microns, the third bubble reduces the magnitude of the force, hence increasing the equilibrium distance. The modulation effects depend strongly on the relative sizes of the bubbles. Stronger effects can be produced when the third bubble is placed closer to the smaller bubble in the bubble pair. The findings highlight the need for a more accurate parametrization of the secondary Bjerknes force in the simulation and manipulation of bubble clusters

On an isoperimetric problem with a competing non-local term. II. The general case

This paper is the continuation of [H. Kn\"upfer and C. B. Muratov, Commun. Pure Appl. Math. (2012, to be published)]. We investigate the classical isoperimetric problem modified by an addition of a non-local repulsive term generated by a kernel given by an inverse power of the distance. In this work, we treat the case of general space dimension. We obtain basic existence results for minimizers with sufficiently small masses. For certain ranges of the exponent in the kernel we also obtain non-existence results for sufficiently large masses, as well as a characterization of minimizers as balls for sufficiently small masses and low spatial dimensionality. The physically important special case of three space dimensions and Coulombic repulsion is included in all the results mentioned above. In particular, our work yields a negative answer to the question if stable atomic nuclei at arbitrarily high atomic numbers can exist in the framework of the classical liquid drop model of nuclear matter. In all cases the minimal energy scales linearly with mass for large masses, even if the infimum of energy may not be attained

Static and dynamic response of a fluid-fluid interface to electric point and line charge

We consider the behaviour of a dielectric fluid-fluid interface in the presence of a strong electric field from a point charge and line charge, respectively, both statically and, in the latter case, dynamically. The fluid surface is elevated above its undisturbed level until balance is reached between the electromagnetic lifting force, gravity and surface tension. We derive ordinary differential equations for the shape of the fluid-fluid interface which are solved numerically with standard means, demonstrating how the elevation depends on field strength and surface tension coefficient. In the dynamic case of a moving line charge, the surface of an inviscid liquid-liquid interface is left to oscillate behind the moving charge after it has been lifted against the force of gravity. We show how the wavelength of the oscillations depends on the relative strength of the forces of gravity and inertia, whereas the amplitude of the oscillations is a nontrivial function of the velocity at which the line charge moves.Comment: 19 pages, 6 figures version accepted for publication in Annals of Physic

Three-dimensional stability of free convection vortices in the presence of a magnetic field

Three-dimensional (3D) stability of 2D vortical flow of a liquid metal in a cavity of square cross section is examined. Vortices are produced as a result of free convection and internal heating in the cavity in the presence of a magnetic field. Low-magnetic-Reynolds-number equations are used for the base flow and stability formulation. Finite element methodology is used to discretize the problem. Efficient calculation of the dominant eigenvalues is afforded by the Arnoldi method, while neutral stability diagrams are constructed using continuation techniques. The number of vortices exhibited by the base flow switches from one to two as the internal heating crosses a threshold value. The dominant instability mechanism is the Gortler instability in the case of a single vortex and elliptical instability in the case of two vortices. In elliptic instability, axial vorticity is symmetric, it is characterized by two lobed structures aligned with one of the two principal directions of strain and the dominant eigenmode assumes the form of a traveling wave. The magnetic field opposes buoyancy, alters the direction of maximal strain by accentuating wall shear layers in comparison with the vortex pair in the core and leads to smaller frequencies at criticality

Numerical Study of a Liquid Metal Oscillating inside a Pore in the Presence of Lorentz and Capillary Forces

In order to ensure stable power exhaust and to protect the walls of fusion reactors, liquid metals that are fed to the wall surface through a capillary porous system (CPS) are considered as alternative plasma-facing components (PFCs). However, operational issues like drop ejection and plasma contamination may arise. In this study, the unsteady flow of a liquid metal inside a single pore of the CPS in the presence of Lorentz forces is investigated. A numerical solution is performed via the finite element methodology coupled with elliptic mesh generation. A critical magnetic number is found (Bondm = 4.5) below which the flow after a few oscillations reaches a steady state with mild rotational patterns. Above this threshold, the interface exhibits saturated oscillations. As the Lorentz force is further increased, Bondm > 5.8, a Rayleigh–Taylor instability develops as the interface is accelerated under the influence of the increased magnetic pressure and a finite time singularity is captured. It is conjectured that eventually, drop ejection will take place that will disrupt cohesion of the interface and contaminate the surrounding medium. Finally, the dynamic response of different operating fluids is investigated, e.g., gallium, and the stabilizing effect of increased electrical conductivity and surface tension is demonstrated

Numerical study of the interaction between a pulsating coated microbubble and a rigid wall. II. Trapped pulsation

The dynamic response of an encapsulated bubble subject to an acoustic disturbance in a wall restricted flow is investigated, when the viscous forces of the surrounding liquid are accounted for. The Galerkin finite element methodology is employed and the elliptic mesh generation technique is used for updating the mesh. As the bubble accelerates towards the wall, the dominant force balance is between Bjerknes forces and the viscous drag that develops. In this process a prolate shape is acquired by the bubble, due to excessive compression at the equator region. When the bubble reaches the wall lubrication pressure develops in the near wall region that resists further approach. As long as the sound amplitude remains below a threshold value determined by the onset of parametric shape mode excitation saturated, or "trapped,"pulsations are performed around a certain small distance from the wall. The balance between Bjerknes attraction and the lubrication pressure that arises due to shell bending along the flattened shell portion that faces the wall generates an oblate shape. Elongation is now observed along the equatorial plane where a local liquid overpressure is established generating large tensile strain. The time-averaged deflection of the microbubble at the pole that lies close to the wall is determined by the bending and stretching resistances of the shell in the manner described by Reissner's linear law for a static compressive load on an elastic shell, corrected for the effect of surface tension. The oscillatory part of the bubble motion in that same region, the contact region, follows the forcing frequency and consists of a pressure driven and a shear flow in the form of a Stokes layer where a significant amount of instantaneous wall shear is generated. The thickness of the film that occupies the Stokes layer is on the order of a few tenths of nm and is determined by the balance between liquid and shell tangential viscous stresses. The steady streaming effect on the wall shear is absent owing to the negligible phase difference between the volume and center of mass pulsations. © 2021 American Physical Society