The stationary motion of a weakly deformed drop in the flow of a viscous fluid

The flow of a drop of viscous, incompressible fluid in another viscous, incompressible fluid is studied with values of the viscosities, densities, surface tension, and drop size which guarantee small deviation of the shape of the drop from spherical. The effect of the deviation on the character of the flow, the drag coefficient, etc. is considered. The cell model for the motion of a weakly deformed drop is investigated. An approximate formula is given for finding the drag coefficient in constrained flow. Some cases of nonisothermic motion of a spherical drop are studied.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 69, pp. 157–170, 1977.     

Stationary motion of a viscous drop taking into account its deformation

One investigates the stationary axisymmetric motion of a drop of a viscous incompressible fluid in the flow of a viscous incompressible fluid in the domain of moderate motion velocities (the Reynolds' number ～1–100), various surface tensions and relations between the viscosities inside and outside the drop. One gives a numerical algorithm for the computations. One gives some examples of flows for some values of the defining parameters.     

Deformation of a drop in a viscous stream and conditions of existence of its equilibrium form

The difference method is used for obtaining a solution of the problem of unsteady motion of a drop in a stream, taking into account its deformation under conditions of axial symmetry. The fluid inside and outside the drop is assumed viscous and incompressible. The stable forms of drop are represented for various Reynolds and Weber numbers of external stream. By analyzing the conditions for normal stresses at the drop boundary, the critical Weber number was obtained, which establishes the conditions of existence of equilibrium form of the drop.     

Numerical modeling of the equilibrium shapes of a ferrofluid drop in an external magnetic field

A numerical solution strategy for calculating equilibrium free surfaces of a magnetic fluid under the action of a magnetic field is proposed and applied to determine shapes of a linear magnetisable ferrofluid drop in a uniform magnetic field. Hysteresis phenomena for the drop deformation and the drop shapes with ends, close to conical, were observed numerically. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

精确计算Bingham流体圆管层流压降及速度分布规律的新方法

Bingham(宾汉)模型情况下,多采用通用公式进行圆管层流压降的解析计算,即将Bingham模型本构方程代入粘性流体圆管层流流动通用公式进行计算,仅能得到压降的解析解.新方法结合Bingham流体本构方程与运动方程,建立有关力学平衡方程,并运用代数方程的根式解理论对圆管层流流动时的非线性方程进行求解,可直接求得Bingham流体圆管层流压降及速度流核区半径的解析解,进一步可求得圆管层流速度解析解;Bingham流体圆管层流速度的直接影响因素为流量、塑性粘度和屈服值,研究发现速度流核宽度与屈服值成正比,与流量及塑性粘度成反比,且流核的宽度越大,流核区的速度越小.     

控制棒下落与流体流动的耦合状态方程及其保辛算法

针对核反应堆内控制棒下落问题,提出了描述控制棒下落与流体流动的耦合非线性状态方程。该状态方程对于落棒过程内不同的流体状态,具有统一的表达形式,可以很方便地处理不同工况下的落棒问题。为高效分析落棒过程,准确捕捉落棒过程内流动状态的突变,并保证时程积分的数值稳定,提出了一种基于时间步长自适应的保辛算法。数值算例表明,提出的数值模型可以采用较大的时间步长精确计算控制棒在下落过程中的位移、速度、加速度、落棒时间等关键数据,计算结果与商业软件所得结果高度吻合。     

Lattice Boltzmann modeling of wall-bounded ternary fluid flows

Starting from the phase-field perspective, we first formulate a novel wetting boundary condition to describe the interactions among ternary fluids and a solid and then we propose a boundary scheme for its implementation in the framework of the lattice Boltzmann (LB) method. This scheme for three-phase fluids can preserve the reduction consistency property of the diphasic case such that it can give physically relevant results. Combining this wetting boundary scheme and the LB ternary fluid model based on multicomponent phase-field theory, we simulated several ternary fluid flow problems involving a solid substrate, including the spreading of binary drops on a substrate, the spreading of a compound drop on a substrate, the capillary intrusion of ternary fluids, and the shear of a compound liquid drop on a substrate. The numerical results are found to be good agreement with the analytical solutions and some available results. Finally, as an application, we use the LB model coupled with the present wetting boundary scheme to numerically investigate the impact of a compound drop on a solid circular cylinder. It is found that the dynamics of a compound drop can be remarkably influenced by the wettability of the solid surface and the dimensionless Weber number.     

Analysis and experiments on the spreading dynamics of a viscoelastic drop

We study the spreading dynamics of a sessile viscoelastic drop on a horizontal surface, where a simplified Phan–Thien–Tanner (sPTT) model is considered to represent the rheology of viscoelastic drop. We have adopted a macroscopic approach to obtain the temporal evolution of the spreading drop, while to establish the efficacy of the theoretical model, we have validated the results obtained from the mathematical formulation with the experimental results for both the Newtonian (Si-oil) and viscoelastic (PDMS and aqueous solution of CMC and glycerin) drops. Following the framework of Seaver–Berg approximation, the spherical shape of the drop is assumed as a cylindrical disk here. We observe from this study that an increment in the elasticity of the fluid enhances the velocity gradient and increases the viscous dissipation in the drop volume, leading to a reduction in the spreading rate.     

Wave propagation analysis in buried pipe conveying fluid

A study of wave propagation in buried pipe conveying fluid is presented in the paper. The Flüggle shell model is adopted for pipe and surrounding solid is modeled as elastic matrix by using Winkle model. Wave dispersion curves of a buried vacant pipe and a pipe conveying fluid are obtained numerically by considering coupling conditions. Results show that wave velocity exhibits sharp drop points in dispersion curves, and remains to an identical values before and after the points for both of vacant pipe and pipe conveying fluid. Effects of wall thickness, elastic matrix properties and fluid velocity are also discussed.     

Problem of the motion of two viscous incompressible fluids separated by a closed free interface

A local existence theorem for the problem of unsteady motion of a drop in a viscous incompressible capillary fluid is proved in Sobolev spaces. A linearized problem with known closed interface is also studied in Holder spaces of functions.     

Pendant drop formation of shear-thinning and yield stress fluids

A volume-of-fluid numerical method is used to predict the dynamics of shear-thinning liquid drop formation in air from a circular orifice. The validity of the numerical calculation is confirmed for a Newtonian liquid by comparison with experimental measurements. For particular values of Weber number and Froude number, predictions show a more rapid pinch-off, and a reduced number of secondary droplets, with increasing shear-thinning. Also a minimum in the limiting drop length occurs for the smallest Weber number as the zero-shear viscosity is varied. At the highest viscosity, the drop length is reduced due to shear-thinning, whereas at lower viscosities there is little effect of shear-thinning. The evolution of predicted drop shape, drop thickness and length, and the configuration at pinch-off are discussed for shear-thinning drops. The evolution of a drop of Bingham yield stress liquid is also considered as a limiting case. In contrast to the shear-thinning cases, it exhibits a plug flow prior to necking, an almost step-change approach to pinch-off of a “torpedo” shaped drop following the onset of necking, and a much smaller neck length; no secondary drops are formed. The results demonstrate the potential of the numerical model as a design tool in tailoring the fluid rheology for controlling drop formation behaviour.     

Asymptotic analysis of a thin fluid layer-elastic plate interaction problem

We study the nonstationary flow of an incompressible fluid in a thin rectangle with an elastic plate as the upper part of the boundary. The flow is governed by a time-dependent pressure drop and an external force and it is modeled by Stokes equations. The dynamic of this fluid–structure interaction problem is studied in the limit when the thickness of the fluid domain tends to zero. Using the asymptotic techniques, we obtain for the effective plate displacement a sixth-order parabolic equation with a non standard boundary conditions. Results on existence, uniqueness and regularity of the solution are proved. The approximation is justified through a weak convergence theorem.     

On a Time-Dependent Fluid-Solid Coupling in 3D with Nonstandard Boundary Conditions

We study the motion of a Stokes fluid through an elastic half cylinder with thickness. The fluid is driven by a small time-dependent pressure drop between the outflow and the inflow sections. Nonstandard boundary conditions are imposed at the tube’s ends and we consider small displacements of the elastic structure, such that the domains involved are not moving in time. We prove existence and uniqueness of a weak solution for this three dimensional fluid-elastic structure interaction problem. Under appropriate regularity assumptions on the data we obtain strong energy estimates and show the existence of a pressure with improved properties.     

Effect of a deicing fluid on the durability of carbon/epoxy composites

The degradation of mechanical properties and the moisture absorption of a carbon/epoxy composite is studied through immersion of specimens in two common types of glycol-based (corn-based and synthetic) deicing fluids at two temperatures. Test results indicate that the effects of the fluids are similar at room temperature, while at elevated temperatures, the specimens immersed in the corn-based deicing fluid show a greater drop in the tensile strength. Moreover, gravimetric analysis results show a mass gain in all specimens, with a significantly lower gain from the corn-based deicing fluid than from the synthetic one at the two temperatures selected in this study.     

Regularization of a discrete scheme governing the three-dimensional evolution of a fluid-fluid interface

A regularized discrete scheme is developed that describes the three-dimensional evolution of the interface between fluids with different viscosities and densities in the Leibenzon-Muskat model. The regularization is achieved by smoothing the kernel of the singular integral involved in the differential equation governing the moving interface. The discrete scheme is tested by solving the problem of a drop of one fluid evolving in a translational flow of another.     

非牛顿流体偏心环空螺旋流的解析解

石油和化工中许多问题需要求解非牛顿流体偏心环空螺旋流。本文全面地研究了幂律流体和宾汉流体在偏心环空中层流螺旋流的流动规律与流动状态的判别。在理论上,根据流体力学原理,运用数学方法,在作者同心环空螺旋流的理论基础上,通过对偏心环空螺旋流流场的无限细分法,给出了该流场的视粘度分布、速度分布、流量和压降方程,进而建立了判别流态的稳定性参数。     

On an extremal property of the Poiseuille flow between two coaxial cylinders

Some extremal property is established of the axial stationary flow of a Newtonian fluid between two concentric cylinders. It is shown that the ratio of the flow rate through the cross-section of an eccentric gap to the pressure drop (along the axis) reaches its minimum when the eccentricity equals zero; i.e., the minimum of the ratio is realized for the Poiseuille flow.     

考虑毛管形状的幂律流体等效渗透率计算方法(英文)

While studying the flow of oil and gas in the reservoir, it is not realistic that capillary with circular section is only used to express the pores. It is more representative to simulate porous media pore with kinds of capillary with triangle or rectangle section etc. In the condition of the same diameter, when polymer for oil displacement flows in the porous medium, there only exists shear flow which can be expressed with power law model. Based on fluid flow-pressure drop equation in single capillary, this paper gives a calculation method of equivalent permeability of power law fluid of single capillary and capillary bundles with different sections.     

Steady streaming around a spherical drop displaced from the velocity antinode in an acoustic levitation field

The steady (acoustic) streaming associated with a sphericaldrop displaced from the velocity antinode of a standing waveis studied. The ratio of the particle size to the acoustic wavelengthis treated as small but non-zero, and the solution is developedin the form of a two-term expansion in terms of the correspondingsmallness parameter. The drop viscosity is assumed to be muchhigher than that of the surrounding fluid, which is the casefor a drop in a gas medium. There are essentially three distinctregions where the steady streaming flow is analysed: insidethe drop (internal circulation), in the Stokes shear-wave layerat the surface on the gas side, and the gas outside the Stokeslayer (the outer streaming region). Solutions for the internalcirculation and the outer streaming are obtained in the limitof small Reynolds number. Despite the gas-to-liquid viscosity ratio being small, the outerstreaming may be dramatically affected by the fact that thesphere is liquid as opposed to solid. The parameter that measuresthe effect of liquidity is essentially the viscosity ratio dividedby the relative (to the particle size) thickness of the Stokeslayer. The case of a solid sphere is recovered by letting thisparameter go to zero.