Initial stage of plate lifting from a water surface

This study deals with the flow induced by a rigid flat plate of finite length, initially touching a horizontal water surface, when it starts to move upwards with constant acceleration. In the present model, negative hydrodynamic pressures on the lower (wetted) surface of the plate are allowed, and thus, the water follows the plate due to the resulting suction force. The acceleration of the plate and the plate length are such that gravity, surface tension and viscous effects can be neglected during the early stages of the motion. Under these assumptions, the initial two-dimensional, potential flow caused by the plate lifting is obtained by using the small-time expansion of the velocity potential. This small-time solution is not valid close to the plate edges, as it predicts there singular flow velocities and unbounded displacements of the water-free surface. It is shown that close to the plate edges the flow is nonlinear and self-similar to leading order. This nonlinear flow is computed by the boundary-element method combined with a time-marching scheme. The numerical time-dependent solution approaches the self-similar local solution with time

Hydrodynamic forces in water exit problems

The three-dimensional steady problem of an elongated smooth body moving along the water free surface at a constant speed is considered within the 2D+T approximation. The corresponding unsteady two-dimensional problem describes both the water entry and the subsequent exit of a smooth contour from the water. The shape of the contour varies in time. The present paper is concerned with the exit stage. The draft of the body is small compared with the body length and beam. The hydrodynamic loads during the entry stage are evaluated by the original Wagner model of water impact. The linearized exit model (Korobkin, 2013) is generalized to account for time-dependent acceleration of the body and the body shape which also varies in time. The integral equation with respect to the size of the wetted area of the body is solved numerically. The theoretical predictions of the hydrodynamic forces acting on the body during its exit from the liquid are compared with the numerical results obtained by solving the Navier-Stokes equations. A simplified model of water exit with the body shape approximated by a parabolic contour with a time-dependent radius of curvature is proposed and validated. It is shown that the linearized water-exit model with non-linear correction terms predicts reasonably well the hydrodynamic loads

Theoretical analysis of time-dependent jetting on the surface of a thin moving liquid layer

Unsteady two-dimensional problem of a thin liquid layer with prescribed time-dependent influx into the layer, position of the influx section, and the thickness of the liquid at this section is studied by methods of asymptotic analysis. The ratio of the rate of the liquid thickness variation at the influx section to the influx velocity plays a role of a small parameter of the problem. The influx parameters are such that the flow in the thin layer is inertia dominated, with gravity, surface tension, and liquid viscosity being approximately negligible. Such flows were studied with respect to several applications, some of which are listed in the Introduction. One of the applications concerns with splashing during droplet impact onto a rigid substrate and related kinematic discontinuity propagating along the spray sheet, which is produced by the spreading droplet. This type of splashing was studied by Yarin and Weiss [“Impact of drops on solid surfaces: Self-similar capillary waves, and splashing as a new type of kinematic discontinuity,” J. Fluid Mech. 283, 141–173 (1995)] within a quasi-one-dimensional approach averaging the flow velocity over the layer thickness. We also start with the one-dimensional thin-layer approximation assuming the influx flow is accelerated. Such influx conditions lead to unbounded growth of the thickness of the liquid layer at a certain location and at a certain time instant within the one-dimensional approach. The present study recovers for the first time the structure of the flow close to this singularity using methods of asymptotic analysis. To this aim, the second-order outer solution, which is valid outside the region of the unbounded flow, is derived. The second-order outer solution is used to find proper stretched inner variables and the equations governing the inner flow at the leading order. It is shown that the inner free-surface flow in the stretched variables is two-dimensional, potential, non-linear, and independent of any parameters of the original problem

The response of a poroelastic ice plate to an external pressure

The response of a poroelastic ice cover to an external load is considered. The ice cover is modeled by a thin poroelastic floating plate within the linear theory of hydroelasticity. The porosity parameter is defined as the coefficient of proportionality of the velocity of liquid penetration into the plate and hydrodynamic pressure. The fluid under the plate is inviscid and incompressible. The flow caused by the ice deflection is potential. The external load is modeled by a localized smooth pressure. The two-dimensional problem of waves caused by a periodic external pressure on a floating porous-elastic plate is considered. The profiles of the generated waves are calculated for a given oscillation frequency of the amplitude of the external pressure. It was found that taking porosity into account leads to damping of oscillations in a distance from the external load

Dip-coating flow in the presence of two immiscible liquids

Dip coating is a common technique used to cover a solid surface with a thin liquid film, the thickness of which was successfully predicted by the theory developed in the 1940s by Landau & Levich (Acta Physicochem. URSS, vol. 17, 1942, pp. 141–153) and Derjaguin (Acta Physicochem. URSS, vol. 20, 1943, pp. 349–352). In this work, we present an extension of their theory to the case where the dipping bath contains two immiscible liquids, one lighter than the other, resulting in the entrainment of two thin films on the substrate. We report how the thicknesses of the coated films depend on the capillary number, on the ratios of the properties of the two liquids and on the relative thickness of the upper fluid layer in the bath. We also show that the liquid/liquid and liquid/gas interfaces evolve independently from each other as if only one liquid were coated, except for a very small region where their separation falls quickly to its asymptotic value and the shear stresses at the two interfaces peak. Interestingly, we find that the final coated thicknesses are determined by the values of these maximum shear stresses

Influence of anionic surfactant on stability of nanoparticles in aqueous solutions

Dispersion and aggregation of nanoparticles in aqueous solutions are important factors for safe and effective application of nanoparticles, for instance, in the oil industry. As conventional oil reserves are depleted, it is necessary to advance chemical enhanced oil recovery (cEOR) techniques to develop unconventional oil reservoirs. Nanoparticles modified by surfactants can be a promising reagent in cEOR. These nanomaterials can reduce interfacial tension and change the wettability of reservoir rock, which leads to an increase in oil recovery. However, the application of nanoparticles is limited by their substantial aggregation in aqueous solutions. The purpose of this work is to select nanoparticles for obtaining stable sols in water in the presence of an anionic surfactant and to optimize the conditions (pH) for further modifying the nanoparticles with the anionic surfactant. Sodium dodecyl sulfate (SDS) is used as an anionic surfactant. The aggregation of oxide and carbon nanoparticles in water and anionic surfactant solutions was studied by laser diffraction, dynamic and electrophoretic light scattering methods. Most of the studied nanoparticles in water form aggregates with bi-, three- and polymodal particle size distributions. TiO2 nanoparticles obtained by plasma dynamic synthesis form the most stable sols in anionic surfactant solutions. The range of 5–7 pH is defined as optimal for their modification with surfactants. The stability of carbon nanoparticles in aqueous solutions increases significantly in the presence of a surfactant. The obtained results form the basis for further research on the modification of marked nanoparticles in surfactant solutions

Three-dimensional steep wave impact on a vertical plate with an open rectangular section

The present study treats the three-dimensional hydrodynamic slamming problem on a vertical plate subjected to the impact of a steep wave moving towards the plate with a constant velocity. The problem is complicated significantly by assuming that there is a rectangular opening on the plate which allows a discharge of the liquid. The analysis is conducted analytically assuming linear potential theory. The examined configuration determines two boundary value problems with mixed conditions which fully are taken into account. The mathematical process assimilates the plate with a degenerate elliptical cylinder allowing the employment of elliptical harmonics that ensure the satisfaction of the free-surface boundary condition of the front face of the steep wave, away from the plate. This assumption leads to an additional boundary value problem with mixed conditions in the vertical direction. The associated problem involves triple trigonometrical series and it is solved through a transformation into integral equations. To tackle the boundary value problem in the vertical direction a perturbation technique is employed. Extensive numerical calculations are presented as regards the variation of the velocity potential on the plate at the instant of the impact which reveals the influence of the opening. The theory is extended to the computation of the total impulse exerted on the plate using pressure-impulse theory

Three-dimensional steep wave impact on a vertical cylinder

In the present study we investigate the 3-D hydrodynamic slamming problem on a vertical cylinder due to the impact of a steep wave that is moving with a steady velocity. The linear theory of the velocity potential is employed by assuming inviscid, incompressible fluid and irrotational flow. As the problem is set in 3-D space, the employment of the Wagner condition is essential. The set of equations we pose, is presented as a mixed boundary value problem for Laplace's equation in 3-D. Apart from the mixed-type of boundary conditions, the problem is complicated by considering that the region of wetted surface of the cylinder is a set whose boundary depends on the vertical coordinate on the cylinder up to the free-surface. We make some simple assumptions at the start but otherwise we proceed analytically. We find closed-form relations for the hydrodynamic variables, namely the time dependent potential, the pressure impulse, the shape of the wave front (from the contact point to beyond the cylinder) and the slamming force

Catching Element Formation In The Act

Gamma-ray astronomy explores the most energetic photons in nature to address some of the most pressing puzzles in contemporary astrophysics. It encompasses a wide range of objects and phenomena: stars, supernovae, novae, neutron stars, stellar-mass black holes, nucleosynthesis, the interstellar medium, cosmic rays and relativistic-particle acceleration, and the evolution of galaxies. MeV gamma-rays provide a unique probe of nuclear processes in astronomy, directly measuring radioactive decay, nuclear de-excitation, and positron annihilation. The substantial information carried by gamma-ray photons allows us to see deeper into these objects, the bulk of the power is often emitted at gamma-ray energies, and radioactivity provides a natural physical clock that adds unique information. New science will be driven by time-domain population studies at gamma-ray energies. This science is enabled by next-generation gamma-ray instruments with one to two orders of magnitude better sensitivity, larger sky coverage, and faster cadence than all previous gamma-ray instruments. This transformative capability permits: (a) the accurate identification of the gamma-ray emitting objects and correlations with observations taken at other wavelengths and with other messengers; (b) construction of new gamma-ray maps of the Milky Way and other nearby galaxies where extended regions are distinguished from point sources; and (c) considerable serendipitous science of scarce events -- nearby neutron star mergers, for example. Advances in technology push the performance of new gamma-ray instruments to address a wide set of astrophysical questions.Comment: 14 pages including 3 figure