Hydrostatic equilibrium

About: Hydrostatic equilibrium is a research topic. Over the lifetime, 2451 publications have been published within this topic receiving 62172 citations.

Exact solution of the hydrodynamic focusing driven by hydrostatic pressure

Abstract: Microfluidic nanoprecipitation makes use of hydrodynamic focusing (HF) to accurately control the diffusive mixing of reactants. Both stability and precise handling of flow streams are essential for this application. However, flow stability is hardly attained when fluids are supplied by syringe pumps, due to the unavoidable fluctuations associated to the driving mechanical system. The alternative use of hydrostatic pressure is constantly increasing in microfluidic laboratories, though precise mathematical descriptions have not been reported so far. This paper presents a quantitative model for the HF driven by gravity in slit microchannels. The model analytically predicts the focusing width of the sample stream from the relative heights of the sample and sheath reservoirs. Fluids with different densities and viscosities are considered, which impact on the pressure provided by the hydrostatic columns, as well as on the flow pattern of HF. Theoretical predictions were successfully validated against experimental data. Flow-focusing experiments were carried out in hybrid PMMA/OCA chips with slit microchannels, using fluids with different physicochemical properties. Finally, a color reaction induced by pH-shift was implemented as a practical example. Different levels of diffusive mixing and reaction were attained along the focused stream by varying the relative heights of the fluid columns, precisely as predicted by calculations. The model thus provides a rational basis for the design of HF experiments using hydrostatics.

Moore–Gibson–Thompson Stability Model in a Two-Temperature Photonic Semiconductor Excited Medium Affected by Rotation and Initial Stress

Abstract: In this paper, the two-temperature theory is used to examine a novel model that generalizes the Moore–Gibson–Thompson (MGT) effect according to two-dimensional electronic/thermoelastic deformation. The main equations for a semiconductor medium in the context of the impact of rotation are explained in terms of the impact of the initial hydrostatic stress at the free surface. The normal-mode approach is used to derive the precise formulae for the fundamental physical quantities (i.e., normal displacement, normal load stress, electronic diffusion (carrier density), dynamic and conductive temperature distribution) under the influence of the two-temperature coefficient. The comparison with the base state is performed using linear stability analysis. To make some comparisons based on the various values of thermal memories, the influence of a number of novel parameters is applied to each of our primary physical quantities, such as the rotation parameter and the initial stress. An example of the main fields’ perturbation is also obtained and graphically described.

Numerical Study on Constant-Flow Hydrostatic Water Bearing for a Machine-Tool Table

Abstract: Precision machine tools using hydrostatic water bearings are superior to those using hydrostatic oil bearings in terms of environmental protection, worker’s safety, and cost. As for hydrostatic water bearings, a constant-flow type is more suitable than a constant-pressure type. However, the hydrostatic water bearings applied for machine tools are few cases, and there are only a few reports concerning the constant-flow bearings. In this study, sustaining force of the constant-flow hydrostatic water bearing pad is computed numerically by using ANSYS FLUENT. Then the solutions evaluated by the simple analytical models, which were proposed previously, are examined by comparing them with the numerical result. Additionally, an improved analytical model is proposed.

Hydrostatics of Spherical thin Films

Abstract: The hydrostatic approach is applied to spherical films to define the film tension and the surface tensions of the two interfaces and to generalize the definition of the disjoining pressure to the case of systems with curved surfaces. Equations relating the thermodynamic parameters with the components of the pressure tensor are derived.

An Efficient Hydrodynamic Model for Surface Waves

Abstract: In the present study,a semi-implicit finite difference model for non-hydrostatic,free-surface flows is analyzed and discussed.The governing equations are the three-dimensional free-surface Reynolds-averaged Navier-Stokes equations defined on a general,irregular domain of arbitrary scale.At outflow,a combination of a sponge layer technique and a radiation boundary condition is applied to minimize wave reflection.The equations are solved with the fractional step method where the hydrostatic pressure component is determined first,while the non-hydrostatic component of the pressure is computed from the pressure Poisson equation in which the coefficient matrix is positive definite and symmetric.The advection and horizontal viscosity terms are discretized by use of a semi-Lagrangian approach.The resulting model is computationally efficient and unrestricted to the CFL condition.The developed model is verified against analytical solutions and experimental data,with excellent agreement.