The effects of slip velocity at a membrane surface on blood flow in the microcirculation

Closed-form solutions are presented for blood flow in the microcirculation by taking into account the influence of slip velocity at the membrane surface. In this study, the convective inertia force is neglected in comparison with that of blood viscosity on the basis of the smallness of the Reynolds number of the flow in microcirculation. The permeability property of the blood vessel is based on the well known Starling's hypothesis [11]. The effects of slip coefficient on the velocity and pressure fields are clearly depicted.

Experimental Investigation On The Slip Between Oil And Water In Horizontal Pipes

This work is devoted to study of the slip phenomenon between phases in water-oil two-phase flow in horizontal pipes. The emphasis is placed on the effects of input fluids flow rates, pipe diameter and viscosities of oil phase on the slip. Experiments were conducted to measure the holdup in two horizontal pipes with 0.05 m diameter and 0.025 m diameter, respectively, using two different viscosities of white oil and tap water as liquid phases. Results showed that the ratios of in situ oil to water velocity at the pipe of small diameter are higher than those at the pipe of big diameter when having same input flow rates. At low input water flow rate, there is a large deviation on the holdup between two flow systems with different oil viscosities and the deviation becomes gradually smaller with further increased input water flow rate. (C) 2008 Elsevier Inc. All rights reserved.

The effect of wall-slip formation on the rheological behaviour of lead-free solder pastes

Wall-slip plays an important role in the flow behaviour of solder paste materials. The wall-slip arises due to the various attractive and repulsive forces acting between the solder particles and the walls of the measuring geometry. These interactions could lead to the presence of a thin liquid layer adjacent to the wall, which causes slippage. The aim of this study is to investigate the influence of the solder paste formulation on wall-slip formation and its effect on the printability of these pastes material. A wall slip model is utilised to calculate the true viscosity and slip velocity for the lead-free solder pastes samples used in this study. The difference in the measured viscosity and the true viscosity could indicate wall-slip formation between the solder pastes and the parallel plate. Sample P1 showed a higher slip velocity compared to sample P2. The slip velocity calculated for the solder pastes could be used as a performance indicator to understand the paste release characteristics in the stencil printing process.

The generalized Onsager model for the secondary flow in a high-speed rotating cylinder

The generalizations of the Onsager model for the radial boundary layer and the Carrier-Maslen model for the end-cap axial boundary layer in a high-speed rotating cylinder are formulated for studying the secondary gas flow due to wall heating and due to insertion of mass, momentum and energy into the cylinder. The generalizations have wider applicability than the original Onsager and Carrier-Maslen models, because they are not restricted to the limit A >> 1, though they are restricted to the limit R e >> 1 and a high-aspect-ratio cylinder whose length/diameter ratio is large. Here, the stratification parameter A = root m Omega(2)R(2)/2k(B)T). This parameter A is the ratio of the peripheral speed, Omega R, to the most probable molecular speed, root 2k(B)T/m, the Reynolds number Re = rho w Omega R(2)/mu, where m is the molecular mass, Omega and R are the rotational speed and radius of the cylinder, k(B) is the Boltzmann constant, T is the gas temperature, rho(w) is the gas density at wall, and mu is the gas viscosity. In the case of wall forcing, analytical solutions are obtained for the sixth-order generalized Onsager equations for the master potential, and for the fourth-order generalized Carrier-Maslen equation for the velocity potential. For the case of mass/momentum/energy insertion into the flow, the separation-of-variables procedure is used, and the appropriate homogeneous boundary conditions are specified so that the linear operators in the axial and radial directions are self-adjoint. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order and second-order in the radial and axial directions for the Onsager equation, and fourth-order and second-order in the axial and radial directions for the Carrier-Maslen equation) are determined. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations. The comparison reveals that the boundary conditions in the simulations and analysis have to be matched with care. The commonly used `diffuse reflection' boundary conditions at solid walls in DSMC simulations result in a non-zero slip velocity as well as a `temperature slip' (gas temperature at the wall is different from wall temperature). These have to be incorporated in the analysis in order to make quantitative predictions. In the case of mass/momentum/energy sources within the flow, it is necessary to ensure that the homogeneous boundary conditions are accurately satisfied in the simulations. When these precautions are taken, there is excellent agreement between analysis and simulations, to within 10 %, even when the stratification parameter is as low as 0.707, the Reynolds number is as low as 100 and the aspect ratio (length/diameter) of the cylinder is as low as 2, and the secondary flow velocity is as high as 0.2 times the maximum base flow velocity. The predictions of the generalized models are also significantly better than those of the original Onsager and Carrier-Maslen models, which are restricted to thin boundary layers in the limit of high stratification parameter.

Electro-Osmotic Flow and Mixing in Heterogeneous Microchannels

Analytical and numerical studies of secondary electro-osmotic flow EOF and its mixing in microchannels with heterogeneous zeta potentials are carried out in the present work. The secondary EOFs are analyzed by solving the Stokes equation with heterogeneous slip velocity boundary conditions. The analytical results obtained are compared with the direct numerical simulation of the Navier-Stokes equations. The secondary EOFs could transport scalar in larger areas and increase the scalar gradients, which significantly improve the mixing rate of scalars. It is shown that the heterogeneous zeta potentials could generate complex flow patterns and be used to enhance scalar mixing.

Dynamics of collapsing fluidized beds and its application in the simulation of pulsed fluidized beds

A new method to study collapsing process of fluidized bed was proposed. The method is based on the analysis of the pressure variation during collapse. A model is proposed to describe the pressure variation on any location of the bed during collapse. Three kind of particles were fluidized by air and the pressure variation after shutting down the gas supply was measured by pressure transducers and simulated by the proposed model. The simulated results were in good agreement with the experimental data. The parameters of the fluidized bed, such as bubble fraction alpha(b), particle fraction in dense phase alpha(p), bubble velocity u(b) and slip velocity of particle u(i), can be estimated from the measured pressure data by using the proposed model. The model was also used to calculate the pressure variation in pulsed fluidized beds with low frequency.

MEASUREMENT OF SOLID SLURRY FLOW VIA CORRELATION OF ELECTROMAGNETIC FLOW METER, ELECTRICAL RESISTANCE TOMOGRAPHY AND MECHANISTIC MODELLING

The study presented here was carried out to obtain the actual solids flow rate by the combination of electrical resistance tomography and electromagnetic flow meter. A new in-situ measurement method based on measurements of the Electromagnetic Flow Meters (EFM) and Electrical Resistance Tomography (ERT) to study the flow rates of individual phases in a vertical flow was proposed. The study was based on laboratory experiments that were carried out with a 50 mm vertical flow rig for a number of sand concentrations and different mixture velocities. A range of sand slurries with median particle size from 212 mu m to 355 mu m was tested. The solid concentration by volume covered was 5% and 15%, and the corresponding density of 5% was 1078 kg/m(3) and of 15% was 1238 kg/m(3). The flow velocity was between 1.5 m/s and 3.0 m/s. A total of 6 experimental tests were conducted. The equivalent liquid model was adopted to validate in-situ volumetric solids fraction and calculate the slip velocity. The results show that the ERT technique can be used in conjunction with an electromagnetic flow meter as a way of measurement of slurry flow rate in a vertical pipe flow. However it should be emphasized that the EFM results must be treated with reservation when the flow pattern at the EFM mounting position is a non-homogenous flow. The flow rate obtained by the EFM should be corrected considering the slip velocity and the flow pattern.

Boundary conditions at the solid-liquid surface over the multiscale channel size from nanometer to micron

The boundary condition at the solid surface is one of the important problems for the microfluidics. In this paper we study the effects of the channel sizes on the boundary conditions (BC), using the hybrid computation scheme adjoining the molecular dynamics (MD) simulations and the continuum fluid mechanics. We could reproduce the three types of boundary conditions (slip, no-slip and locking) over the multiscale channel sizes. The slip lengths are found to be mainly dependent on the interfacial parameters with the fixed apparent shear rate. The channel size has little effects on the slip lengths if the size is above a critical value within a couple of tens of molecular diameters. We explore the liquid particle distributions nearest the solid walls and found that the slip boundary condition always corresponds to the uniform liquid particle distributions parallel to the solid walls, while the no-slip or locking boundary conditions correspond to the ordered liquid structures close to the solid walls. The slip, no-slip and locking interfacial parameters yield the positive, zero and negative slip lengths respectively. The three types of boundary conditions existing in "microscale" still occur in "macroscale". However, the slip lengths weakly dependent on the channel sizes yield the real shear rates and the slip velocity relative to the solid wall traveling speed approaching those with the no-slip boundary condition when the channel size is larger than thousands of liquid molecular diameters for all of the three types of interfacial parameters, leading to the quasi-no-slip boundary conditions.

Estudos teóricos e numéricos de escoamentos com escorregamento

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Laboratory shearing experiments at low sliding velocities of IODP Hole 343-C0019E

The 2011 Tohoku-Oki earthquake demonstrated that the shallowest reaches of plate boundary subduction megathrusts can host substantial coseismic slip that generates large and destructive tsunamis, contrary to the common assumption that the frictional properties of unconsolidated clay-rich sediments at depths less than View the MathML source should inhibit rupture. We report on laboratory shearing experiments at low sliding velocities (View the MathML source) using borehole samples recovered during IODP Expedition 343 (JFAST), spanning the plate-boundary décollement within the region of large coseismic slip during the Tohoku earthquake. We show that at sub-seismic slip rates the fault is weak (sliding friction µs=0.2-0.26), in contrast to the much stronger wall rocks (µs>~0.5). The fault is weak due to elevated smectite clay content and is frictionally similar to a pelagic clay layer of similar composition. The higher cohesion of intact wall rock samples coupled with their higher amorphous silica content suggests that the wall rock is stronger due to diagenetic cementation and low clay content. Our measurements also show that the strongly developed in-situ fabric in the fault zone does not contribute to its frictional weakness, but does lead to a near-cohesionless fault zone, which may facilitate rupture propagation by reducing shear strength and surface energy at the tip of the rupture front. We suggest that the shallow rupture and large coseismic slip during the 2011 Tohoku earthquake was facilitated by a weak and cohesionless fault combined with strong wall rocks that drive localized deformation within a narrow zone.

A novel methodology for simulating contact-line behavior in capillary-driven flows

Despite the wide swath of applications where multiphase fluid contact lines exist, there is still no consensus on an accurate and general simulation methodology. Most prior numerical work has imposed one of the many dynamic contact-angle theories at solid walls. Such approaches are inherently limited by the theory accuracy. In fact, when inertial effects are important, the contact angle may be history dependent and, thus, any single mathematical function is inappropriate. Given these limitations, the present work has two primary goals: 1) create a numerical framework that allows the contact angle to evolve naturally with appropriate contact-line physics and 2) develop equations and numerical methods such that contact-line simulations may be performed on coarse computational meshes.

Fluid flows affected by contact lines are dominated by capillary stresses and require accurate curvature calculations. The level set method was chosen to track the fluid interfaces because it is easy to calculate interface curvature accurately. Unfortunately, the level set reinitialization suffers from an ill-posed mathematical problem at contact lines: a ``blind spot'' exists. Standard techniques to handle this deficiency are shown to introduce parasitic velocity currents that artificially deform freely floating (non-prescribed) contact angles. As an alternative, a new relaxation equation reinitialization is proposed to remove these spurious velocity currents and its concept is further explored with level-set extension velocities.

To capture contact-line physics, two classical boundary conditions, the Navier-slip velocity boundary condition and a fixed contact angle, are implemented in direct numerical simulations (DNS). DNS are found to converge only if the slip length is well resolved by the computational mesh. Unfortunately, since the slip length is often very small compared to fluid structures, these simulations are not computationally feasible for large systems. To address the second goal, a new methodology is proposed which relies on the volumetric-filtered Navier-Stokes equations. Two unclosed terms, an average curvature and a viscous shear VS, are proposed to represent the missing microscale physics on a coarse mesh.

All of these components are then combined into a single framework and tested for a water droplet impacting a partially-wetting substrate. Very good agreement is found for the evolution of the contact diameter in time between the experimental measurements and the numerical simulation. Such comparison would not be possible with prior methods, since the Reynolds number Re and capillary number Ca are large. Furthermore, the experimentally approximated slip length ratio is well outside of the range currently achievable by DNS. This framework is a promising first step towards simulating complex physics in capillary-dominated flows at a reasonable computational expense.

Measurements of velocity-dependent and slip-dependent frictional strength in laboratory friction experiments on natural samples from IODP Expedition 316 and ODP Hole 190-1174B

Slowslip forms part of the spectrum of fault behaviour between stable creep and destructive earthquakes. Slow slip occurs near the boundaries of large earthquake rupture zones and may sometimes trigger fast earthquakes. It is thought to occur in faults comprised of rocks that strengthen under fast slip rates, preventing rupture as a normal earthquake, or on faults that have elevated pore-fluid pressures. However, the processes that control slow rupture and the relationship between slow and normal earthquakes are enigmatic. Here we use laboratory experiments to simulate faulting in natural rock samples taken from shallow parts of the Nankai subduction zone, Japan, where very low-frequency earthquakes - a form of slow slip - have been observed.We find that the fault rocks exhibit decreasing strength over millimetre-scale slip distances rather than weakening due to increasing velocity. However, the sizes of the slip nucleation patches in our laboratory simulations are similar to those expected for the very lowfrequency earthquakes observed in Nankai. We therefore suggest that this type of fault-weakening behaviour may generate slow earthquakes. Owing to the similarity between the expected behaviour of slow earthquakes based on our data, and that of normal earthquakes during nucleation, we suggest that some types of slow slip may represent prematurely arrested earthquakes.

Entropy generation for microscale forced convection: effects of different thermal boundary conditions, velocity slip, temperature jump, viscous dissipation, and duct geometry

This work presents closed form solutions for fully developed temperature distribution and entropy generation due to forced convection in microelectromechanical systems (MEMS) in the Slip-flow regime, for which the Knudsen number lies within the range 0.001