微/纳器件粗糙表面间弯月面力及黏着力计算

微/纳器件表面微观粗糙结构间由于液体介质而引起的弯月面力和黏着力是导致器件精度降低乃至失效的主要原因之一。通过建立微/纳米尺度上球面-平面接触的物理模型,基于Young-Laplace方程和Reynolds润滑理论,分析得到粗糙表面接触分离过程中弯月面力和黏着力的计算公式。在此基础上,计算得到接触表面分离过程中的弯月面形状变化规律,并分别讨论了固体表面分离距离、液滴初始弯月面高度、固体表面润湿性能和分离时间等因素对弯月面力和黏着力的影响。研究结果为微/纳米表面抗黏着机理提供了理论依据。     

Heat transfer to non-Newtonian flows over a cylinder in cross flow

Over a range of 102<Re^*<5800, 6.5<Pr^*<79, and 0.6<n<1, circumferential wall temperatures for water and aqueous polymer (purely viscous) solution flows over a smooth cylinder were measured experimentally. The cylinder was heated by passing direct electric current through it. Aqueous solutions of Carbopol 934 and EZ1 were used as power-law non-Newtonian fluids. The peripherally averaged heat transfer coefficient for purely viscous non-Newtonian fluids, at any fixed flow rate, decreases with increasing polymer concentration. A new correlation is proposed for predicting the peripherally averaged Nusselt number for power-law fluid flows over a heated cylinder in cross flow.     

Pseudo plane stress mode II crack growth in plastic materials

The near tip field of mode II crack that grows in thin bodies with power hardening or perfectly plastic behavior is analyzed. It is shown that for power hardening behavior, the pseudo plane stress field possesses the logarithm singularity, i.e. σ (ln r)²/(n−1), (ln r)^{2n/(n − 1)}, where r is the distance from the crack tip, n the hardening exponent is σⁿ. When n → ∞ the solution reduced to that for the perfectly plastic case.     

Squeeze flow of a power-law fluid between two rigid spheres with wall slip

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Viscoelastic sink flow in a wedge for the UCM and Oldroyd-B models

The steady planar sink flow through wedges of angle π/α with α≥1/2 of the upper convected Maxwell (UCM) and Oldroyd-B fluids is considered. The local asymptotic structure near the wedge apex is shown to comprise an outer core flow region together with thin elastic boundary layers at the wedge walls. A class of similarity solutions is described for the outer core flow in which the streamlines are straight lines giving stress and velocity singularities of O(r⁻²) and O(r⁻¹), respectively, where r1 is the distance from the wedge apex. These solutions are matched to wall boundary layer equations which recover viscometric behaviour and are subsequently also solved using a similarity solution. The boundary layers are shown to be of thickness O(r²), their size being independent of the wedge angle. The parametric solution of this structure is determined numerically in terms of the volume flux Q and the pressure coefficient p₀, both of which are assumed furnished by the flow away from the wedge apex in the r=O(1) region. The solutions as described are sufficiently general to accommodate a wide variety of external flows from the far-field r=O(1) region. Recirculating regions are implicitly assumed to be absent.     

Uniqueness of positive solutions of Δu−u+up=0 in Rn

We establish the uniqueness of the positive, radially symmetric solution to the differential equation u–u+u^p=0 (with p>1) in a bounded or unbounded annular region in R ⁿ for all n1, with the Neumann boundary condition on the inner ball and the Dirichlet boundary condition on the outer ball (to be interpreted as decaying to zero in the case of an unbounded region). The regions we are interested in include, in particular, the cases of a ball, the exterior of a ball, and the whole space. For p=3 and n=3, this a well-known result of Coffman, which was later extended by McLeod & Serrin to general n and all values of p below a certain bound depending on n. Our result shows that such a bound on p is not needed. The basic approach used in this work is that of Coffman, but several of the principal steps in the proof are carried out with the help of Sturm's oscillation theory for linear second-order differential equations. Elementary topological arguments are widely used in the study.     

A singular perturbation problem of laminar flow in a uniformly porous channel with large injection and with an applied transverse magnetic field

Summary The problem of the steady flow of an electrically conducting viscous fluid through porous walls of a channel in the presence of an applied transverse magnetic field is considered. A solution for the case of small M ²/R (where M = Hartmann number, R = suction Reynolds number) with large blowing at the walls has been given by Terrill and Shrestha [3]. Their solution, on differentiating three times, is found to become infinite at the centre of the channel. Physically this means that there must be a viscous layer at the centre of the channel and Terrill and Shrestha are neglecting the shear layer. In this paper the solution given by Terrill and Shrestha is extended by obtaining an extra term of the series of expansion and the method of inner and outer expansion is used to obtain the complete solution which includes the viscous layer. The resulting series solutions are confirmed by numerical results.     

Calculation of viscous compressible gas flow past a corner

We consider the problem of calculating the parameters for supersonic viscous compressible gas flow past a corner (angle greater than ). The complete system of Navier-Stokes equations for the viscous compressible gas is solved in the small vicinity Q₁. (characteristic dimensionl~1/R) of the corner point. The conditions for smooth matching of the solution of the Navier-Stokes equations and the solution of the ideal gas or boundary layer equations are specified on the boundary of Q₁. All these solutions are a priori unknown, and the conditions for smooth matching reduce to certain differential equations on the boundary of Q₁. Here account is taken of the interaction of the flows near the wall surface and in the so-called outer region [1].We note that no a priori assumptions are made in Q₁ concerning the qualitative behavior of the solution, in contrast with other studies on viscous flow past a corner (for example, [2–4]).The Navier-Stokes system in Q₁ is solved numerically, using the difference scheme suggested in [5]. This scheme permits obtaining the steady-state solution by the asymptotic method for large Reynolds numbers R, and also has an approximation accuracy adequate to account for the effects of low viscosity and thermal conductivity.     

The skidding of an elliptic plate on a wet surface

A viscous fluid separates a massed, sliding, free elliptic plate and a smooth bottom plate. Due to the weight, the gap width between the plates decreases. The increased viscous drag eventually stops the skidding. The Navier-Stokes equations are expanded in terms of a small squeeze number. It is found that the gap width decrease as (time)^–1/2 and the maximum skidding distance depends on five nondimensional groups. An example shows it is easier for the elliptic plate to side longitudinally than laterally.     

存在填隙幂律流体时圆球间切向作用的近似解

在Reynolds润滑理论的基础上，导出了存在填隙幂律流体时，两刚性圆球有相对切向运动时流体压力的近似方程，并进一步求得了圆球所受阻力矩的近似积分表达式，给出了问题的数值解。结果发现幂流体的幂指数、颗粒间最小间隙以及颗粒的大小都是流体压力和颗粒间切向阻力的重要因素。与Godman等人的牛顿流体下圆球平行于平面缓慢运动时圆球所受阻力以及阻力矩的渐近解作的比较表明，本文的数值解优于渐近解。     

UNSTEADY DETACHED SEPARATION FROM A CIRCULAR CYLINDER PERFORMING ROTATIONAL OSCILLATIONS IN A UNIFORM VISCOUS INCOMPRESSIBLE FLOW

The origination of detached separation is studied on the basis of a numerical solution of the full Navier–Stokes equations. Fluxes of vorticity with different signs generated with twice the frequency of cylinder oscillation move from the cylinder to the outer surface of a detached liquid layer in the form of concentric rings. Near the critical layer between the attached layer and the main flow these rings are torn and crimped to the regions of separated vortices of the corresponding sign. The form of detached separated vortices is similar to that of vortices originating from a stationary circular cylinder in a uniform flow. Transition of the flow to a non-symmetric form with Karman vortex street generation at a Reynolds number (based on the radius) greater than 17 is revealed. This critical Reynolds number is smaller than that for a stationary circular cylinder in a viscous stream (where Re=20 has been determined to be a critical value) and corresponds to the Reynolds number extrapolated from the critical value for the stationary cylinder by increasing the cylinder radius by the attached layer thickness. The vorticity flux from the cylinder surface immediately into the separation region decreases as the frequency of cylinder oscillation increases. Violation of the flow potentiality in the detached separation region is the main cause of the vorticity generation on the outer surface of the attached liquid layer. © 1997 John Wiley & Sons, Ltd.     

Nonmonotonic relationship between the Reynolds number and the lift coefficient of a plate in a hypersonic rarefied gas flow

The aerodynamic coefficients of a plate in a hypersonic stream at low Reynolds numbers are studied over a wide range of similarity parameters. The dependence of the lift coefficientC _Y on the tangential force coefficient, the finite Mach number at the outer edge of the boundary layer and the velocity-slip and temperature-jump boundary conditions is taken into consideration. The nonmonotonic character of the relationship betweenC _Y and the Reynolds number, revealed previously in experiments, is explained within the framework of the viscous hypersonic interaction model.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 186–189, January–February, 1996.     

Computation of the two-dimensional viscous incompressible fluid flow with separation at the nlet edge around a cascade

A complex flow consisting of an outer inviscid stream, a dead-water separation domain, and a boundary layer, which interact strongly, is formed in viscous fluid flows with separation at the streamlined profile with high Re numbers. Different jet and vortex models of separation flow are known for an inviscid fluid; numerical, asymptotic, and integral methods [1–3] are used for a viscous fluid. The plane, stationary, turbulent flow through a turbine cascade by a constant-density fluid without and with separation from the inlet edge of the profile and subsequent attachment of the stream to the profile (a short, slender separation domain) is considered in this paper.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 34–44, May–June, 1978.     

Drag and Separation Flow Past Solid Sphere with Porous Shell at Moderate Reynolds Number

Axisymmetric viscous, two-dimensional steady and incompressible fluid flow past a solid sphere with porous shell at moderate Reynolds numbers is investigated numerically. There are two dimensionless parameters that govern the flow in this study: the Reynolds number based on the free stream fluid velocity and the diameter of the solid core, and the ratio of the porous shell thickness to the square root of its permeability. The flow in the free fluid region outside the shell is governed by the Navier–Stokes equation. The flow within the porous annulus region of the shell is governed by a Darcy model. Using a commercially available computational fluid dynamics (CFD) package, drag coefficient and separation angle have been computed for flow past a solid sphere with a porous shell for Reynolds numbers of 50, 100, and 200, and for porous parameter in the range of 0.025–2.5. In all simulation cases, the ratio of b/a was fixed at 1.5; i.e., the ratio of outer shell radius to the inner core radius. A parametric equation relating the drag coefficient and separation point with the Reynolds number and porosity parameter were obtained by multiple linear regression. In the limit of very high permeability, the computed drag coefficient as well as the separation angle approaches that for a solid sphere of radius a, as expected. In the limit of very low permeability, the computed total drag coefficient approaches that for a solid sphere of radius b, as expected. The simulation results are presented in terms of viscous drag coefficient, separation angles and total drag coefficient. It was found that the total drag coefficient around the solid sphere as well as the separation angle are strongly governed by the porous shell permeability as well as the Reynolds number. The separation point shifts toward the rear stagnation point as the shell permeability is increased. Separation angle and drag coefficient for the special case of a solid sphere of radius r = a was found to be in good agreement with previous experimental results and with the standard drag curve.     

UNSTEADY CONFINED VISCOUS FLOWS WITH OSCILLATING WALLS AND MULTIPLE SEPARATION REGIONS OVER A DOWNSTREAM-FACING STEP

This paper presents computational solutions for unsteady viscous flows in channels with a downstream-facing step, followed by an oscillating floor. These solutions of the unsteady Navier–Stokes equations are obtained with a time-integration method using artificial compressibility in a fixed computational domain, which is obtained via a time-dependent coordinate transformation from the fluid domain with moving boundaries. The computational method is first validated for steady viscous flows past a downstream-facing step by comparison with previous numerical solutions and experimental results. This method is then used to obtain solutions for unsteady viscous flows with multiple separation regions over a downstream-facing step with oscillating walls, for which there are no previously known solutions. Thus, the present results may be used as benchmark solutions for the unsteady viscous flows with multiple separation regions between fixed and oscillating walls.     

Flow of soft solids squeezed between planar and spherical surfaces

The force to squeeze a Herschel–Bulkley material without slip between two approaching surfaces of various curvature is calculated. The Herschel–Bulkley yield stress requires an infinite force to make plane–plane and plane–concave surfaces touch. However, for plane–convex surfaces this force is finite, which suggests experiments to access the mesoscopic thickness region (1–100 m) of non-Newtonian materials using squeeze flow between a plate and a convex lens. Compared to the plane–parallel surfaces that are used most often for squeeze flow, the dependence of the separation h and approach speed V on the squeezing-time is more complicated. However, when the surfaces become close, a simplification occurs and the near-contact approach speed is found to vary as V h⁰ if the Herschel–Bulkley index is n<1/3, and V h^(3n-1)/(2n) if n 1/3. Using both plane–plane and plane–convex surfaces, concordant measurements are made of the Herschel–Bulkley index n and yield stress ₀ for two soft solids. Good agreement is also found between ₀ measured by the vane and by each squeeze-flow method. However, one of the materials shows a limiting separation and a V(h) behaviour not predicted by theory for h<10 m, possibly owing to an interparticle structure of similar lengthscale.     

The effect of T-stress on crack–inclusion interaction under mode I loading

A closed-form solution has been developed to predict the effect of T-stress on the crack–inclusion interaction. As validated by several numerical examples, the approximate solution has satisfactory accuracy for different inclusion shapes and modulus ratios between inclusion and matrix under different T-stress levels. Thus the role of T-stress in crack–inclusion interaction can be predicted quantitatively.     

Near tip field for pseudo Mode II crack growth: Power law hardening material

The asymptotic behavior of stress and strain near the tip of a Mode II crack growing in power law hardening material is analyzed by assuming that the crack grows straight ahead even though tests show otherwise. The results show that the stress and strain possess the singularities of (ln r)^2/(n−1) and (ln r)^2n/(n−1) respectively. The distance from the crack tip is r, and n is the hardening exponent, i.e. σⁿ. The amplitudes of the stress and strain near the crack tip are determined by the asymptotic analysis.