Hydrodynamic boundary conditions and dynamic forces between bubbles and surfaces

Dynamic forces between a 50 microm radius bubble driven towards and from a mica plate using an atomic force microscope in electrolyte and in surfactant exhibit different hydrodynamic boundary conditions at the bubble surface. In added surfactant, the forces are consistent with the no-slip boundary condition at the mica and bubble surfaces. With no surfactant, a new boundary condition that accounts for the transport of trace surface impurities explains variations of dynamic forces at different speeds and provides a direct connection between dynamic forces and surface transport effects at the air-water interface.     

Limits of the hydrodynamic no-slip boundary condition

A controversial point in fluid dynamics is to distinguish the relative importance of surface roughness and fluid-surface intermolecular interactions in determining the boundary condition. Here hydrodynamic forces were compared for flow of Newtonian fluids past surfaces of variable roughness but similar, poorly wetted, surface chemistry. The critical shear stress and shear rate to observe deviations from predictions using the no-slip boundary condition increased nearly exponentially with increasing roughness and diverged at approximately 6 nm rms roughness. We conclude that local intermolecular interactions dominated when the surface was very smooth, but roughness dominated otherwise. This quantifies the limits of both ideas.     

粘性涡方法在多圆柱绕流数值模拟中的应用

用粘性涡方法求解了涡量速度形式的二维不可压缩Navier—Stokes方程．利用分步方法分别求解无粘的对流运动和粘性扩散，粘性扩散用随机走步方法来处理，利用涡量交换技术来满足无滑移边界条件，同时为进一步减少计算量，在求解对流速度时，采用了多极子展开法加速技术使得计算量由N2的量级减少到NlogN的量级．数值模拟了单圆柱和双圆柱纵向排列的绕流流场．     

A Boundary Condition-Implemented Immersed Boundary-Lattice Boltzmann Method and Its Application for Simulation of Flows Around a Circular Cylinder

A boundary condition-implemented immersed boundary-lattice Boltzmann method (IB-LBM) is presented in this work. The present approach is an improvement to the conventional IB-LBM. In the conventional IB-LBM, the no-slip boundary condition is only approximately satisfied. As a result, there is flow penetration to the solid boundary. Another drawback of conventional IB-LBM is the use of Dirac delta function interpolation, which only has the first order of accuracy. In this work, the no-slip boundary condition is directly implemented, and used to correct the velocity at two adjacent mesh points from both sides of the boundary point. The velocity correction is made through the second-order polynomial interpolation rather than the first-order delta function interpolation. Obviously, the two drawbacks of conventional IB-LBM are removed in the present study. Another important contribution of this paper is to present a simple way to compute the hydrodynamic forces on the boundary from Newton's second law. To validate the proposed method, the two-dimensional vortex decaying problem and incompressible flow over a circular cylinder are simulated. As shown in the present results, the flow penetration problem is eliminated, and the obtained results compare very well with available data in the literature.     

Nanorheology: An investigation of the boundary condition at hydrophobic and hydrophilic interfaces

It has been shown that the flow of a simple liquid over a solid surface can violate the so-called no-slip boundary condition. We investigate the flow of polar liquids, water and glycerol, on a hydrophilic Pyrex surface and a hydrophobic surface made of a Self-Assembled Monolayer of OTS (octadecyltrichlorosilane) on Pyrex. We use a Dynamic Surface Force Apparatus (DSFA) which allows one to study the flow of a liquid film confined between two surfaces with a nanometer resolution. No-slip boundary conditions are found for both fluids on hydrophilic surfaces only. Significant slip is found on the hydrophobic surfaces, with a typical length of one hundred nanometers. Received 21 December 2001 and Received in final form 3 August 2002 RID="a" ID="a"e-mail: ccottin@dpm.univ-lyon1.fr RID="b" ID="b"Present address.     

Dynamics of thin free liquid films stabilized with ionic surfactants

To study the dynamics of free liquid films which are stabilized with ionic surfactants, an electrohydrodynamic theory is developed. The long-range interaction forces, namely the repulsive force arising from the overlap of diffuse electric double layers and the attractive Van der Waals-London force, are described by the Maxwell stress tensor with its related field equations and the Van der Waals potential. The short-range surface force has a normal Laplace component and a tangential surface tension gradient component. The total set of first-order equations and their boundary conditions, which describes the capillary waves on the surfaces and the induced flow motion in the film, has been solved. The dispersion relation for the “squeezing mode” is obtained. The cases of no-slip condition and the long-wavelength limit have been studied in more detail. The testability of the dispersion relation using laser beat spectroscopy is reported.     

Tunable-slip boundaries for coarse-grained simulations of fluid flow

On the micro- and nanoscale, classical hydrodynamic boundary conditions such as the no-slip condition no longer apply. Instead, the flow profiles exhibit "slip" at the surface, which is characterized by a finite slip length (partial slip). We present a new, systematic way of implementing partial-slip boundary conditions with arbitrary slip length in coarse-grained computer simulations. The main idea is to represent the complex microscopic interface structure by a spatially varying effective viscous force. An analytical equation for the resulting slip length can be derived for planar and for curved surfaces. The comparison with computer simulations of a DPD (dissipative particle dynamics) fluid shows that this expression is valid from full slip to no slip.     

A curved no-slip boundary condition for the lattice Boltzmann method

We present a generalization of the no-slip boundary condition by Lätt et al. [J. Lätt, B. Chopard, O. Malaspinas, M. Deville, A. Michler, Straight velocity boundaries in the lattice Boltzmann method, Physical Review E 77 (5) (2008) 056703] from straight to curved geometries for the lattice Boltzmann Bhatnager–Gross–Krook method (LBGK). The boundary condition is based on a reconstruction of the populations from the density, velocity and rate of strain. For curved boundaries, the reconstruction reduces the question of accuracy to a technical issue of interpolation. We present a method of interpolation allowing a very accurate representation of the curved boundary. The resulting boundary condition is verified for three different test cases: Taylor–Couette flow in-between rotating cylinders, laminar flow around a cylinder and flow past an impulsively started cylinder, demonstrating its second order accuracy and low error constant. The present boundary is stable for relaxation frequencies close to two.     

Time-dependent and outflow boundary conditions for Dissipative Particle Dynamics

We propose a simple method to impose both no-slip boundary conditions at fluid-wall interfaces and at outflow boundaries in fully developed regions for Dissipative Particle Dynamics (DPD) fluid systems. The procedure to enforce the no-slip condition is based on a velocity-dependent shear force, which is a generalized force to represent the presence of the solid-wall particles and to maintain locally thermodynamic consistency. We show that this method can be implemented in both steady and time-dependent fluid systems and compare the DPD results with the continuum limit (Navier-Stokes) results. We also develop a force-adaptive method to impose the outflow boundary conditions for fully developed flow with unspecified outflow velocity profile or pressure value. We study flows over the backward-facing step and in idealized arterial bifurcations using a combination of the two new boundary methods with different flow rates. Finally, we explore the applicability of the outflow method in time-dependent flow systems. The outflow boundary method works well for systems with Womersley number of O(1), i.e., when the pressure and flowrate at the outflow are approximately in-phase.     

The influence of slip on the peristaltic motion of a third order fluid in an asymmetric channel

In this investigation, the peristaltic flow of a third order fluid in an asymmetric channel is considered in the presence of a slip condition. The series solution of the stream function and longitudinal pressure gradient is given under long wave length and low Reynolds number approximations. Pressure rise and frictional forces per wave length are analyzed through numerical integration. Pumping and trapping phenomena are examined and the obtained results are compared with those of no-slip condition. Comparison is made with the results of no-slip and viscous fluid cases.     

基于浸入边界-多松弛时间格子玻尔兹曼通量求解法的流固耦合算法研究

针对流固耦合问题,发展了基于浸入边界-多松弛时间格子玻尔兹曼通量求解法(immersed boundary method multi-relaxation-time lattice Boltzmann flux solver,IB-MRT-LBFS)的弱耦合算法.依据多尺度Chapman-Enskog展开,建立不可压宏观方程状态变量和通量与格子玻尔兹曼方程中粒子密度分布函数之间的关系;采用强制浸入边界法处理流固界面使固壁表面满足无滑移边界条件,根据修正的速度求解动量方程力源项;结构运动方程采用四阶龙格-库塔法求解.格子模型与浸入边界法的引入使流固耦合计算可以在笛卡尔网格下进行,无需生成贴体网格及运用动网格技术,简化了计算过程.数值模拟了单圆柱横向涡激振动、单圆柱及串列双圆柱双自由度涡激振动问题.结果表明,IB-MRT-LBFS能够准确预测圆柱涡激振动的锁定区间、振动响应、受力情况以及捕捉尾流场结构形态,验证了该算法在求解流固耦合问题的有效性和可行性.     

A Kato Type Theorem for the Inviscid Limit of the Navier-Stokes Equations with a Moving Rigid Body

The issue of the inviscid limit for the incompressible Navier-Stokes equations when a no-slip condition is prescribed on the boundary is a famous open problem. A result by Kato (Math Sci Res Inst Publ 2:85?C98, 1984) says that convergence to the Euler equations holds true in the energy space if and only if the energy dissipation rate of the viscous flow in a boundary layer of width proportional to the viscosity vanishes. Of course, if one considers the motion of a solid body in an incompressible fluid, with a no-slip condition at the interface, the issue of the inviscid limit is as least as difficult. However it is not clear if the additional difficulties linked to the body??s dynamic make this issue more difficult or not. In this paper we consider the motion of a rigid body in an incompressible fluid occupying the complementary set in the space and we prove that a Kato type condition implies the convergence of the fluid velocity and of the body velocity as well, which seems to indicate that an answer in the case of a fixed boundary could also bring an answer to the case where there is a moving body in the fluid.     

Effect of Viscosities on Mixing in A Patterned Micro Mixer

The effect of viscosity and viscosity difference and boundary patterned slip on mixing in a micro mixer has been numerically studied using lattice Boltzmann method （LBM）. The slip and no-slip ratio is not constant and varies irregularly, and viscosity is altered by changing the relaxation time in LBE equation. The slip boundary condition is simulated by specular reflection boundary and the no-slip boundary condition is simulated by bounce back boundary. It has been found that it is feasible to optimize the micro mixer design by combining the viscosity effect and boundary patterned ratio altogether.     

A mesh-dependent model for applying dynamic contact angles to VOF simulations

Typical VOF algorithms rely on an implicit slip that scales with mesh refinement, to allow contact lines to move along no-slip boundaries. As a result, solutions of contact line phenomena vary continuously with mesh spacing; this paper presents examples of that variation. A mesh-dependent dynamic contact angle model is then presented, that is based on fundamental hydrodynamics and serves as a more appropriate boundary condition at a moving contact line. This new boundary condition eliminates the stress singularity at the contact line; the resulting problem is thus well-posed and yields solutions that converge with mesh refinement. Numerical results are presented of a solid plate withdrawing from a fluid pool, and of spontaneous droplet spread at small capillary and Reynolds numbers.     

Can nanoscale surface charge heterogeneity really explain colloid detachment from primary minima upon reduction of solution ionic strength?

This study theoretically examined colloid detachment from primary minima with ionic strength (IS) reduction on heterogeneous collector surfaces. The chemically and physically heterogeneous collector surfaces were modeled as a planar surface carrying nanoscale patches of different zeta potentials and nanoscale pillars/hemispheroids, respectively. The surface element integration technique was used to calculate interaction energies between colloid and collector surfaces. Two boundary conditions for the double-layer interaction energy were considered, namely constant surface potential (CSP), and linear superposition approximation (LSA). In contrast to prevailing opinions in the literature, our results show that colloids attached on the chemically heterogeneous surface cannot be detached by IS reduction under CSP condition due to an increase of the adhesive force/torque with decreasing IS. Detachment from chemically heterogeneous surfaces by IS reduction can occur under LSA condition only when the flow velocity is very high. In contrast, the presence of nanoscale physical heterogeneity can cause colloid detachment from primary minima by IS reduction under both CSP and LSA conditions at flow velocities commonly used in experimental studies because of a significant reduction in the adhesive forces/torques.     

Large variation in the boundary-condition slippage for a rarefied gas flowing between two surfaces

We study the slippage of a gas along mobile rigid walls in the sphere-plane confined geometry and find that it varies considerably with pressure. The classical no-slip boundary condition valid at ambient pressure changes continuously to an almost perfect slip condition in a primary vacuum. Our study emphasizes the key role played by the mean free path of the gas molecules on the interaction between a confined fluid and solid surfaces and further demonstrates that the macroscopic hydrodynamics approach can be used with confidence even in a primary vacuum environment where it is intuitively expected to fail.     

Generic flow profiles induced by a beating cilium

We describe a multipole expansion for the low-Reynolds-number fluid flows generated by a localized source embedded in a plane with a no-slip boundary condition. It contains 3 independent terms that fall quadratically with the distance and 6 terms that fall with the third power. Within this framework we discuss the flows induced by a beating cilium described in different ways: a small particle circling on an elliptical trajectory, a thin rod and a general ciliary beating pattern. We identify the flow modes present based on the symmetry properties of the ciliary beat.     

Cubic Auto-Catalysis Reactions in Three-Dimensional Nanofluid Flow Considering Viscous and Joule Dissipations Under Thermal Jump

In this problem, simultaneous effects of Joule and viscous dissipationin three-dimensional flow of nanoliquid have been addressed in slip flow regime under timedependent rotational oscillations. Silver nanoparticles are submerged in the base fluid (water)due to their chemical and biological features. To increment the novelty, effects of cubicautocatalysis chemical reactions and radiative heat transfer have been incorporated in therelated boundary layer equations. Dimensionless partial differential system is solved byemploying the proposed implicit finite difference approach. Convergence conditions andstability criteria are obtained to ensure the convergence and accuracy of solutions.A comparative analysis is proposed for no-slip nanofluid flow (NSNF) and slip nanofluid flow(SNF). Variations in skin-friction coefficients, Sherwood and Nusselt numbers against physicalparameters are tabulated. It is investigated that velocity slip and temperature jump significantlycontrol drag forces and rate of heat transfer.     

No-slip hydrodynamic boundary condition for hydrophilic particles

We describe measurement and interpretation of the force acting on a smooth hydrophilic glass particle during rapid (1-100 microm s(-1) approach to, and separation from, a hydrophilic glass plate in viscous concentrated aqueous sucrose solutions (0.001 Pa s相似文献