Balance Of Normal Forces Research Articles

Film Shape Research of Slipper Bearing in Axial Piston Pump Based on Genetic Algorithms

In the process of axial piston pump working, centrifugal moment causes slipper bearing to tilt and wedge oil film could be formed between the slipper and swashplate. The film shape corresponds with its pressure field. By force equilibrium analysis, the calculation of film shape can be simplified as a single objective optimization problem with two decision variables, which uses the normal force balance and the flow equilibrium as equality constraints and treats the slipper tilt angle and the azimuth angle as inequality constraints.The Niche Genetic Algorithm was applied to solve this problem. The results showed that using this method the optimum solution can be gained and the convergence speed is relatively fast. A precision 3-D film shapes can be obtained, which can afford new reference to the design of the slipper bearing.

Convergence of a family of Galerkin discretizations for the Stokes-Darcy coupled problem

In this paper we analyze the well-posedness (unique solvability, stability, and Cea’s estimate) of a family of Galerkin schemes for the coupling of fluid flow with porous media flow. Flows are governed by the Stokes and Darcy equations, respectively, and the corresponding transmission conditions are given by mass conservation, balance of normal forces, and the Beavers-Joseph-Saffman law. We consider the usual primal formulation in the Stokes domain and the dual-mixed one in the Darcy region, which yields a compact perturbation of an invertible mapping as the resulting operator equation. We then apply a classical result on projection methods for Fredholm operators of index zero to show that use of any pair of stable Stokes and Darcy elements implies the well-posedness of the corresponding Stokes-Darcy Galerkin scheme. This extends previous results showing well-posedness only for BernardiRaugel and Raviart-Thomas elements. In addition, we show that under somewhat more demanding hypotheses, an alternative approach that makes no use of compacteness arguments, can also be applied. Finally, we provide several numerical results illustrating the good performance of the Galerkin method for different geometries of the problem using the MINI element and the Raviart-Thomas subspace of lowest order.

A residual-based a posteriori error estimator for a fully-mixed formulation of the Stokes–Darcy coupled problem

In this paper we develop an a posteriori error analysis of a new fully mixed finite element method for the coupling of fluid flow with porous media flow in 2D. Flows are governed by the Stokes and Darcy equations, respectively, and the corresponding transmission conditions are given by mass conservation, balance of normal forces, and the Beavers–Joseph–Saffman law. We consider dual-mixed formulations in both media, which yields the pseudostress and the velocity in the fluid, together with the velocity and the pressure in the porous medium, and the traces of the porous media pressure and the fluid velocity on the interface, as the resulting unknowns. The set of feasible finite element subspaces includes Raviart–Thomas elements of lowest order and piecewise constants for the velocities and pressures, respectively, in both domains, together with continuous piecewise linear elements for the traces. We derive a reliable and efficient residual-based a posteriori error estimator for the coupled problem. The proof of reliability makes use of the global inf–sup condition, Helmholtz decompositions in both media, and local approximation properties of the Clément interpolant and Raviart–Thomas operator. On the other hand, inverse inequalities, the localization technique based on element-bubble and edge-bubble functions, and known results from previous works, are the main tools for proving the efficiency of the estimator. Finally, some numerical results confirming the theoretical properties of this estimator, and illustrating the capability of the corresponding adaptive algorithm to localize the singularities of the solution, are reported.

Analysis of fully-mixed finite element methods for the Stokes-Darcy coupled problem

In this paper we analyze fully-mixed finite element methods for the coupling of fluid flow with porous media flow in 2D. Flows are governed by the Stokes and Darcy equations, respectively, and the corresponding transmission conditions are given by mass conservation, balance of normal forces, and the Beavers-Joseph-Saffman law. The fully-mixed concept employed here refers to the fact that we consider dual-mixed formulations in both media, which means that the main unknowns are given by the pseudostress and the velocity in the fluid, together with the velocity and the pressure in the porous medium. In addition, the transmission conditions become essential, which leads to the introduction of the traces of the porous media pressure and the fluid velocity as the associated Lagrange multipliers. We apply the Fredholm and Babuška-Brezzi theories to derive sufficient conditions for the unique solvability of the resulting continuous and discrete formulations. In particular, we show that the existence of uniformly bounded discrete liftings of the normal traces simplifies the derivation of the corresponding stability estimates. A feasible choice of subspaces is given by Raviart-Thomas elements of lowest order and piecewise constants for the velocities and pressures, respectively, in both domains, together with continuous piecewise linear elements for the Lagrange multipliers. Finally, several numerical results illustrating the good performance of the method with these discrete spaces, and confirming the theoretical rate of convergence, are provided.

A Residual-Based A Posteriori Error Estimator for the Stokes–Darcy Coupled Problem

In this paper we develop an a posteriori error analysis of a new conforming mixed finite element method for the coupling of fluid flow with porous media flow. The flows are governed by the Stokes and Darcy equations, respectively, and the transmission conditions are given by mass conservation, balance of normal forces, and the Beavers-Joseph-Saffman law. The finite element subspaces consider Bernardi-Raugel and Raviart-Thomas elements for the velocities, piecewise constants for the pressures, and continuous piecewise linear elements for a Lagrange multiplier defined on the interface. We derive a reliable and efficient residual-based a posteriori error estimator for this coupled problem. The proof of reliability makes use of suitable auxiliary problems, diverse continuous inf-sup conditions satisfied by the bilinear forms involved, and local approximation properties of the Clement interpolant and Raviart-Thomas operator. On the other hand, Helmholtz decomposition, inverse inequalities, and the localization technique based on triangle-bubble and edge-bubble functions are the main tools for proving the efficiency of the estimator. Up to minor modifications, our analysis can be extended to other finite element subspaces yielding a stable Galerkin scheme.

A conforming mixed finite-element method for the coupling of fluid flow with porous media flow

We consider a porous medium entirely enclosed within a fluid region and present a well-posed conforming mixed finite-element method for the corresponding coupled problem. The interface conditions refer to mass conservation, balance of normal forces and the Beavers-Joseph-Saffman law, which yields the introduction of the trace of the porous medium pressure as a suitable Lagrange multiplier. The finite-element subspaces defining the discrete formulation employ Bernardi-Raugel and Raviart-Thomas elements for the velocities, piecewise constants for the pressures and continuous piecewise-linear elements for the Lagrange multiplier. We show stability, convergence and a priori error estimates for the associated Galerkin scheme. Finally, we provide several numerical results illustrating the good performance of the method and confirming the theoretical rates of convergence.

Discussion on Young's Equation Based on Interfacial Jump Condition

The Young's equation describes the interfacial equilibrium condition of a liquid droplet on a smooth solid surface. This relation is derived by Thomas Young in 1805. It has been discussed until today after his work. In general, the Young's equation is discussed from the viewpoint of thermo-dynamics. However, there is no answer which elucidates the normal force balance σlg sin θ in the Young's equation. From the hydrodynamics point of view, there is a momentum jump condition at a gas-liquid interface. This jump condition is derived based on mechanical balance by using mathematical procedure such as Stoke's theorem and the differential geometry. In this study, we reconsider the Young's equation from this momentum jump condition point of view. Finally, we dynamics. However, there is no answer which elucidates the normal force balance σlg sin θ in the Young's equation. From the hydrodynamics point of view, there is a momentum jump condition at a gas-liquid interface. This jump condition is derived based on mechanical balance by using mathematical procedure such as Stoke's theorem and the differential geometry. In this study, we reconsider the Young's equation from this momentum jump condition point of view. Finally, we derive the revised Young's equation in which there is the normal force term (σlg sin θ). Then, we evaluate the revised Young's equation by comparing the analytical solution with the experimental data reported by Amirfazli. Moreover, we discuss on the line tension and the contact angle for a lens

A COMPUTATIONAL METHOD FOR GENERATING THE FREE-SURFACE NECK-DOWN PROFILE FOR GLASS FLOW IN OPTICAL FIBER DRAWING

A combined analytical and numerical approach, based on the transport equations and surface force balance, has been developed for the generation of the neck-down profile of an optical fiber during the drawing process. This is a fairly complex but important circumstance, which involves modeling the flow of glass under large temperature differences and large changes in viscosity and cross-sectional area. An axisymmetric, laminar flow is assumed in the glass and in the circulating inert gases. The governing transport equations are solved employing a finite difference method. The radially lumped axial velocity, the normal force balance, and the vertical momentum equations are used to obtain a correction scheme for the neck-down profile. After a new corrected profile is obtained, the full governing equations are solved for the flow and heat transfer, considering both radiation and convection transport. This process is continued until the necking shape does not change from one iteration to the next. The necking shape obtained is validated by comparisons with experimental results available in the literature. Also, the robustness of the numerical scheme is verified by starting with different initial profiles, each of which yielded the same final shape. It is verified that for the converged solution, the draw tension is essentially constant throughout the necking region, as expected. Among the interesting results obtained are the limitations imposed on fiber diameter and speed for feasible drawing conditions. A strong dependence of the profile on the temperature distribution in the glass is observed. The effects of other important physical parameters on the profile are determined.

A three-component force vector cell for in vitro quantification of the force exerted by the papillary muscle on the left ventricular wall

Recent clinical studies indicate that functional mitral regurgitation, which is a common complication in patients who suffer from ischemic heart disease, is related to an increase in the tethering forces acting on the mitral valve leaflets. Alterations in the valvular assembly, displacement of the papillary muscles or dilatation of the mitral valve annulus can disrupt the normal force balance on the mitral leaflets and result in an abnormal coaptation geometry with incomplete mitral leaflet closure. The force balance imposed on the mitral leaflets is created by the coapting forces generated by the transmitral pressure difference and the tethering forces at the leaflet attachments. A unique force vector cell capable of accurately measuring the three-component force vector applied by the papillary muscle on the left-ventricular wall was designed and manufactured to permit quantification of the alteration in the force balance acting on the mitral leaflets, and to allow for the study of the influence of papillary muscle displacement on mitral regurgitation.

A thermodynamic and biomechanical theory of cell adhesion Part I: General formulism

The equilibrium thermodynamics calculus of cell adhesion developed by Bell et al. (1984, Biophys. J. 45, 1051-1064) has been extended to the general non-equilibrium case. In contrast to previous models which could only compute the end results of equilibrium states, the present theory is able to calculate the kinetic process of evolution of adhesion, which may or may not approach towards equilibrium. Starting from a basic constitutive hypothesis for Helmholtz free energy, equations of balance of normal forces, energy balance at the edge of the contact area and rate of entropy production are derived using an irreversible thermodynamics approach, in which the restriction imposed by the Second Law of Thermodynamics takes the place of free energy minimization used by Bell et al. (1984). An explicit expression for adhesion energy density is derived for the general transient case as the difference of the usable work transduced from chemical energy liberation from bond formation of specific crosslinking molecules and the repulsive potential of non-specific interactions. This allows the energy balance to be used as an independent boundary equation rather than a practical way of computing the adhesion energy. Jump conditions are obtained from the conservation of crosslinking molecules across the edge of adhesion region which is treated as a singular curve. The bond formation and lateral motion of the crosslinking molecules are assumed to obey a set of reaction-diffusion equations. These equations and the force balance equation within the contact area, plus the jump conditions and the energy balance equation at the edge form a well-posed moving boundary problem which determines the propagation of the adhesion boundary, the separation distance between the two cell membranes over the contact area as well as the distributions of the crosslinking molecules on the cell surfaces. The behavior of the system depends on the relative importance of virtual convection, lateral diffusion and bond formation of the crosslinking molecules at the edge of the adhesion region, according to which two types of rate limiting cases are discussed, viz, reaction-limited and diffusion-limited processes.