Modeling of particle layer detachment-Role of transient kinetic effects

Particle layers tend to build up on walls in many filtration and separation processes, calling for periodic removal in order to keep the apparatus running. Important factors are the adhesion of the layer on the substrate and the cohesion of the particles in the layer. Models describing such layer detachment generally assume constant and homogeneous conditions for the forces acting on the layer. But in reality detachment is extremely non-stationary concerning place and time, primarily due to changing conditions of the detaching forces on the one hand and changes in the particle layer morphology on the other. This paper describes a model and a simulation based on this model considering such transient kinetic effects, for which some computing results are presented and discussed.     

Modelling of particle layer detachment—Role of transient kinetic effects

Particle layers tend to build up on walls in many filtration and separation processes, calling for periodic removal in order to keep the apparatus running. Important factors are the adhesion of the layer on the substrate and the cohesion of the particles in the layer. Models describing such layer detachment generally assume constant and homogeneous conditions for the forces acting on the layer. But in reality detachment is extremely non-stationary concerning place and time, primarily due to changing conditi...     

Load sharing in bioinspired fibrillar adhesives with backing layer interactions and interfacial misalignment

Bio-inspired fibrillar adhesives rely on the utilization of short-range intermolecular forces harnessed by intimate contact at fibril tips. The combined adhesive strength of multiple fibrils can only be utilized if equal load sharing (ELS) is obtained at detachment. Previous investigations have highlighted that mechanical coupling of fibrils through a compliant backing layer gives rise to load concentration and the nucleation and propagation of interfacial flaws. However, misalignment of the adhesive and contacting surface has not been considered in theoretical treatments of load sharing with backing layer interactions. Alignment imperfections are difficult to avoid for a flat-on-flat interfacial configuration. In this work we demonstrate that interfacial misalignment can significantly alter load sharing and the kinematics of detachment in a model adhesive system. Load sharing regimes dominated by backing layer interactions and misalignment are revealed, the transition between which is controlled by the misalignment angle, fibril separation, and fibril compliance. In the regime dominated by misalignment, backing layer deformation can counteract misalignment giving rise to improved load sharing when compared to an identical fibrillar array with a rigid backing layer. This result challenges the conventional belief that stiffer (and thinner) backing layers consistently reduce load concentration among fibrils. Finally, we obtain analytically the fibril compliance distribution required to harness backing layer interactions to obtain ELS. Through fibril compliance optimization, ELS can be obtained even with misalignment. However, since misalignment is typically not deterministic, it is of greater practical significance that the array optimized for perfect alignment exhibits load sharing superior to that of a homogeneous array subject to misalignment. These results inform the design of fibrillar arrays with graded compliance capable of exhibiting improved load sharing over large areas.     

Dynamic detachment of a gas bubble from a solid flat substrate performing normal harmonic vibrations

This paper presents an investigation of the detachment of a bubble from a solid flat substrate according to a dynamic scenario, i. e., due to strong vibrations of the surface shape of the bubble caused by normal nonacoustic harmonic vibrations of the substrate. The Layzer’s model based on an analysis of single-mode solutions near the bubble top was used to study its detachment in microgravity, where the dynamics of the bubble surface is due to competition between liquid inertia forces and surface tension forces. Detachment of the bubble from the substrate was determined from the condition of its elongation during vibrations by a magnitude comparable to the radius of the bubble in equilibrium. The dependence of the vibration intensity required for the detachment of the bubble on the problem parameters was determined using a number of empirical assumptions. The volume of the detached bubbles was estimated.     

Application of Lattice-Boltzmann Method for Analysing Detachment of Micron-Sized Particles from Carrier Particles in Turbulent Flows

Numerical calculations based on the Lattice-Boltzmann method were performed for a particle cluster consisting of a large spherical carrier particle covered with hundreds of small spherical drug particles. This cluster, fixed in space within a cubic computational domain, was exposed to turbulent plug airflow with predefined intensity. Such a situation is found in dry powder inhalers where carrier particles blended with fine drug powder are dispersed in a highly turbulent flow with the objective of detaching the drug powder for pulmonary delivery. Turbulence was generated by a digital filtering technique applied to the inflow velocity boundary condition. This technique was first validated by analysing the turbulence intensity at 15 fluid nodes along the stream-wise direction of the computational domain. The size ratio between the drug and carrier particle was 5 μ m/100 μ m, and the coverage degree of the carrier by the small particles was 50%, which is a typical value for carrier particle blending. The range of carrier particle Reynolds numbers considered was between 80 and 200, typical values found in inhaler devices. Exemplarily, at Re = 200 turbulence intensity was varied from 0.3% to 9.0%. The systematic increase of the mean flow (i.e. 80 < Re <200) resulted in varying turbulence intensities from 20 to 9%. These simulations provided the temporal evolution of the fluid dynamic forces on the drug particles in dependence of their angular position on the carrier in order to estimate the possibility of drug particle detachment. For turbulent conditions (i.e. Re = 200 and I = 9.0%) the maximum fluid forces on the drug particles were found to be about 10-times larger than found in laminar flow. The fluctuations in the forces were found to be higher than the flow velocity fluctuations due to the modification of the boundary layer around the cluster and instabilities triggered by the turbulent flow. There are three possibilities for detaching the drug powder, namely, through lift-off and sliding or rolling. Lift-off was found to be of minor importance due to the observed small normal fluid forces even at Re = 200 and I = 9.0%. The probability of sliding and rolling detachment in dependence of the angular position was estimated based on measured adhesion properties, i.e. van der Waals force, adhesion surface energy and friction coefficient. The remarkable rise of detachment probability for both effects due to the action of turbulence is an important finding of this study. In accordance with laminar flow, rolling detachment occurs before sliding, however in turbulent conditions over the entire carrier particle. The present studies improve the understanding of drug particle detachment from carrier particles in an inhaler device. The results will be the basis for developing Lagrangian detachment models that eventually should allow the optimisation of dry powder inhalators through computational fluid dynamics.     

Closed-form solutions of the pull-in instability in nano-cantilevers under electrostatic and intermolecular surface forces

In this paper, a distributed parameter model is used to study the pull-in instability of cantilever type nanomechanical switches subjected to intermolecular and electrostatic forces. In modeling of the electrostatic force, the fringing field effect is taken into account. The model is nonlinear due to the inherent nonlinearity of the intermolecular and electrostatic forces. The nonlinear differential equation of the model is transformed into the integral form by using the Green’s function of the cantilever beam. Closed-form solutions are obtained by assuming an appropriate shape function for the beam deflection to evaluate the integrals. The pull-in parameters of the switch are computed under the combined effects of electrostatic and intermolecular forces. Electrostatic microactuators and freestanding nanoactuators are considered as special cases of our study. The detachment length and the minimum initial gap of freestanding nano-cantilevers, which are the basic design parameters for NEMS switches, are determined. The results of the distributed parameter model are compared with the lumped parameter model.     

MEASUREMENT OF ADHESION FORCES IN AIR WITH THE VIBRATION METHOD

The vibration method represents a practical method for the measurement of adhesion forces and adhesion force distributions. This method causes sinusoidally altemating stresses and yields detachment and contact forces between particles and substrate of the same order of magnitude. Alternating contact forces of the vibration method can cause an adhesion force intensification through flattening of asperities. The measuring principle of the vibration method and the analysis of experimental results are described in the article. Normal adhesion forces (pull-off forces) are measured using the vibration method and the colloidal probe technique. The results of both methods show good agreement for small particle sizes. The influence of the detachment force direction is shown by comparing tangential and normal adhesion forces measured using particle reentrainment in a turbulent air flow and the vibration method, respectively. The surface roughness of the substrate and the relative humidity are shown to significantly influence the measured adhesion forces. For the calculation of the adhesion forces, an approach by Rabinovich was combined with approximations of plastic micro asperity flattening. The Rabinovich approach accounts for roughness effects on the van der Waals force by incorporating the rms roughness of the interacting surfaces. rms-values of the particles and substrates were measured with atomic force microscopy at different scanning areas.     

Criteria for the detachment of a three-dimensional boundary layer

On the assumption that the character of the flow in a specified section of the boundary layer depends solely on the behavior of the external flow in the immediate vicinity of the section under consideration, criteria are derived for the detachment of laminar and turbulent boundary layers in the case of three-dimensional flow. The detachment criteria so found are a consequence of the necessary condition for the detachment of a three-dimensional boundary layer deduced earlier [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 50–54, July–August, 1970.     

Electrically-excited (electroosmotic) flows in microchannels for mixing applications

We propose an asymptotic model for quite general liquid microchannel flows in the presence of electrical double layers (EDLs). The model provides an “inner” solution for the wall layer, which reflects the dominant balance between electrical forces and viscous forces (tangentially), respectively between electrical forces and pressure and viscous forces (normally). The electrically-neutral core of the flow is governed by the standard Navier–Stokes equations, providing the “outer” solution. The asymptotic matching of both solutions provides a method for the simplified numerical treatment of such EDLs. The superposition of the solutions in both regions then allows to infer an approximate solution, valid within the entire domain.Based on this model, we apply external oscillatory electrical fields to excite secondary flows (i) in microchannels with an internal obstacle or (ii) in folded (meander) microchannels. These secondary flows are demonstrated to greatly enhance the mixing of two liquids flowing in a layered fashion through these microchannels. Thus, electrical excitation has considerable potential if micromixers for ionic liquids are designed within electrically-insulating (e.g. plastics, glass) substrates.     

Modelling of fluidelastic instability in a square inline tube array including the boundary layer effect

Flow-induced vibration (FIV) is a design concern in many engineering applications such as tube bundles in heat exchangers. When FIV materializes, it often results in fatigue and/or fretting wear of the tubes, leading to their failure. Three cross-flow excitation mechanisms are responsible for such failures: random turbulence excitation, Strouhal periodicity, and fluidelastic instability. Of these three mechanisms, fluidelastic instability has the greatest potential for destruction. Because of this, a large amount of research has been conducted to understand and predict this mechanism. This paper presents a time domain model to predict the fluidelastic instability forces in a tube array. The proposed model accounts for temporal variations in the flow separation. The unsteady boundary layer is solved numerically and coupled with the structure model and the far field flow model. It is found that including the boundary layer effect results in a lower stability threshold. This is primarily due to a larger fluidelastic force effect on the tube. The increase in the fluidelastic effect is attributed to the phase difference between the boundary layer separation point motion and the tube motion. It is also observed that a non-linear limit cycle is predicted by the proposed model.     

Vapour bubble growth and detachment at the wall of shear flow

N-pentane micro-bubbles are created on a small heated film flushed-mounted at the lower wall of a horizontal channel. The bubble growth and detachment in the shear flow are filmed with a high-speed video camera. The time evolutions of the bubble radius and bubble centre position are measured from image processing. The growth rate is determined and compared to models of the literature. The experimental results are also used to estimate the different forces acting on the bubble during its growth and after its detachment.     

颗粒流润滑过程中粉末层的微观破坏形式和机理分析

将松散的石墨粉末导入到面接触摩擦副间隙中,对粉末层形成和破坏过程的宏、微观现象进行了跟踪和分析.通过对粉末层的电子、光学显微镜观察及能谱分析发现粉末层典型的生命周期包含完整、轻微破损、严重剥落和完全破坏4个阶段.利用光学显微镜观察到粉末层的鼓包、部分剥落、分层剥落和擦伤等微观现象,这些现象代表粉末层不同阶段的破坏状态和磨损程度.鼓包、部分剥落、分层剥落是粉末层破坏的早期形式.擦伤是粉末层破坏的严重形式,表明上试件和下试件发生了表面的直接接触并产生磨损,通常能够在粉末层完全破坏之前观察到.     

The Newton drag law for bodies formed by intersecting surfaces

The Newtonian shock layer theory for smooth surfaces has been developed in [1–7]. However, if a body consists of two intersecting surfaces, on each of which there is a regular shock layer, these two layers will interact at the line of intersection. Considering that the shock layer is hypersonic, we can again apply the Newton scheme to the impact of the particles with the second surface. As a result, concentrated forces arise at the line of intersection. An indication of the possibility of the appearance of such forces is given in [2]. In the following we present a method of calculating the concentrated forces and indicate the real flow of which they are the analogy.     

Multiscale Modeling of Colloid and Fluid Dynamics in Porous Media Including an Evolving Microstructure

We consider colloidal dynamics and single-phase fluid flow within a saturated porous medium in two space dimensions. A new approach in modeling pore clogging and porosity changes on the macroscopic scale is presented. Starting from the pore scale, transport of colloids is modeled by the Nernst?CPlanck equations. Here, interaction with the porous matrix due to (non-)DLVO forces is included as an additional transport mechanism. Fluid flow is described by incompressible Stokes equations with interaction energy as forcing term. Attachment and detachment processes are modeled by a surface reaction rate. The evolution of the underlying microstructure is captured by a level set function. The crucial point in completing this model is to set up appropriate boundary conditions on the evolving solid?Cliquid interface. Their derivation is based on mass conservation. As a result of an averaging procedure by periodic homogenization in a level set framework, on the macroscale we obtain Darcy??s law and a modified averaged convection?Cdiffusion equation with effective coefficients due to the evolving microstructure. These equations are supplemented by microscopic cell problems. Time- and space-dependent averaged coefficient functions explicitly contain information of the underlying geometry and also information of the interaction potential. The theoretical results are complemented by numerical computations of the averaged coefficients and simulations of a heterogeneous multiscale scenario. Here, we consider a radially symmetric setting, i.e., in particular we assume a locally periodic geometry consisting of circular grains. We focus on the interplay between attachment and detachment reaction, colloidal interaction forces, and the evolving microstructure. Our model contributes to the understanding of the effects and processes leading to porosity changes and pore clogging from a theoretical point of view.     

Leading edge vortex formation and detachment on a flat plate undergoing simultaneous pitching and plunging motion: Experimental and computational study

This study focuses on the formation and detachment of a leading edge vortex (LEV) appearing on an airfoil when its effective angle of attack is dynamically changed, inducing additional forces and moments on the airfoil. Experimental measurements of the time-resolved velocity field using Particle Image Velocimetry (PIV) are complemented by a computational study using an URANS (Unsteady Reynolds-Averaged Navier–Stokes) framework. In this framework a transition-sensitive Reynolds-stress model of turbulence, proposed by Maduta et al. (2018), which combines the near-wall Reynolds-Stress model by Jakirlic and Maduta (2015) and a phenomenological transition model governing the pre-turbulent kinetic energy by Walters and Cokljat (2008), is employed. Combined pitching and plunging kinematics of the investigated flat plate airfoil enable the effective inflow angle to be arbitrarily prescribed. A qualitative assessment of flow fields and a quantitative comparison of LEV characteristics in terms of its center position and circulation as well as an investigation of the mechanism causing the vortex to stop accumulating circulation revealed close agreement between the experimental and simulation results. Further considerations of the lift contribution from the pressure and suction side of the airfoil to the overall lift indicates that the qualitative lift evolution is reproduced even if the pressure side contribution is neglected. This reveals important characteristics of such airfoil dynamics, which can be exploited in future experimental studies, where direct aerodynamic force and moment measurements are greatly inhibited by dominating inertial forces.     

Effect of vortex shedding in unsteady aerodynamic forces for a low Reynolds number stationary wing at low angle of attack

This study elucidates the relation between wake vortex shedding and aerodynamic force fluctuations for a low Reynolds number wing from time resolved particle image velocimetry (TR-PIV) experimental measurements. The results reveal a periodic lift and drag variation within the shedding cycle and resolve the frequencies of those fluctuations from a proper orthogonal decomposition (POD) and power spectral density (PSD) analysis. To show the effect of vortex shedding on the body force fluctuations, the evolution of instantaneous aerodynamic forces is compared to the pressure field of the fluid flow and to the vortical structures in the wake of the airfoil. A six step model describing the vortex-force relation is proposed. It shows that changes in lift such as maximum lift and minimum lift are associated with the detachment of a vortex. It also shows that the minimum or local minimum drag value is obtained at the onset formation of a vortex on the airfoil wake. Similarly, the maximum or local maximum drag is obtained at the onset formation of the saddle on the airfoil wake. The model further explains the asymmetry observed in the unsteady drag force evolution. The model can be used to optimize flow control and fluid-structure interaction applications.     

DYNAMICS OF A SUBMERGED AND INCLINED CONCENTRIC PIPE SYSTEM WITH INTERNAL AND EXTERNAL FLOWS

In this paper, we formulate a mathematical model to study the dynamics of submerged and inclined concentric pipes with different lengths. The governing equations of motion for the inner pipe are derived under small deformation assumptions and with the consideration of gravitational forces, turbulent boundary layer thickness of external flow, fluid frictional forces, and inertia effects. We obtain discretized dynamical equations using spatial finite-difference schemes and calculate the resonant frequencies of a particular pipe system design. In addition, by varying the operating conditions, we identify a few critical parameters pertaining to the proper design of such pipe systems.     

Modified Particle Detachment Model for Colloidal Transport in Porous Media

Particle detachment from the rock during suspension transport in porous media was widely observed in laboratory corefloods and for flows in natural reservoirs. A new mathematical model for detachment of particles is based on mechanical equilibrium of a particle positioned on the internal cake or matrix surface in the pore space. The torque balance of drag, electrostatic, lifting and gravity forces, acting on the particle from the matrix and the moving fluid, is considered. The torque balance determines maximum retention concentration during the particle capture. The particle torque equilibrium is determined by the dimensionless ratio between the drag and normal forces acting on the particle. The maximum retention function of the dimensionless ratio (dislodging number) closes system of governing equations for colloid transport with particle release. One-dimensional problem of coreflooding by suspension accounting for limited particle retention, controlled by the torque sum, allows for exact solution under the assumptions of constant filtration coefficient and porosity. The explicit formulae permit the calculation of the model parameters (maximum retention concentration, filtration and formation damage coefficients) from the history of the pressure drop across the core during suspension injection. The values for maximum retention concentration, as obtained from two coreflood tests, have been matched with those calculated by the torque balance on the micro scale.     

Effect of the deformation in the inertia forces on the inverse dynamics of planar flexible mechanical systems

The inverse dynamics problem for articulated structural systems such as robotic manipulators is the problem of the determination of the joint actuator forces and motor torques such that the system components follow specified motion trajectories. In many of the previous investigations, the open loop control law was established using an inverse dynamics procedure in which the centrifugal and Coriolis inertia forces are linearized such that these forces in the flexible model are the same as those in the rigid body model. In some other investigations, the effect of the nonlinear centrifugal and Coriolis forces is neglected in the analysis and control system design of articulated structural systems. It is the objective of this investigation to study the effect of the linearization of the centrifugal and Coriolis forces on the nonlinear dynamics of constrained flexible mechanical systems. The virtual work of the inertia forces is used to define the complete nonlinear centrifugal and Coriolis force model. This nonlinear model that depends on the rate of the finite rotation and the elastic deformation of the deformable bodies is used to obtain the solution of the inverse dynamics problem, thus defining the joint torques that produce the desired motion trajectories. The effect of the linearization of the mass matrix as well as the centrifugal and Coriolis forces on the obtained feedforward control law is examined numerically. The results presented in this investigation are obtained using a slider crank mechanism with a flexible connecting rod.     

Boundary layers in highly anisotropic plane elasticity

The boundary layer method proposed by Everstine and Pipkin for the analysis of highly anisotropic materials, such as fibre-reinforced materials, in elastic plane strain is developed and extended also to include plane stress. It is applied to problems of point forces acting on half-planes, and to two crack problems. The boundary layer solutions are compared with known exact solutions in anisotropic elasticity, and it is found that the boundary layer theory gives good results for elastic constants typical of a carbon fibre reinforced resin.