Tangential Fluid Research Articles

The application of fluid dynamic gauging in characterising cake deposition during the cross-flow microfiltration of a yeast suspension

Abstract Fluid dynamic gauging (FDG) has been used to study cake fouling during cross-flow microfiltration of inactive Saccharomyces cerevisiae yeast suspensions through a 5 μm nominal pore size mixed cellulose ester membrane. Cake thickness was measured in situ and in real-time during fouling, for which an initial growth rate of ca. 0.81 μm s −1 was observed at TMP = 35 mbar and Re duct = 1000. The thickness increased asymptotically to a terminal value of 130 μm, limited by the FDG process. Although it influences the evolution of the cake thickness, FDG can nevertheless be used to perform strength tests on preformed cakes, by imposing controlled shear stresses to the surface and measuring the thickness following deformation. Cake deformation via incremental increases in shear stress demonstrated that the cake's resilience to tangential fluid shear was inversely proportional to its thickness. It was found that preformed cakes over 250 μm thick were deformed by shear stresses −2 , indicating very loose cohesion between cells on the cake's surface. The range and accuracy of thickness measurements is subject to the strength of fouling layers and the operating conditions of the apparatus. Measures to enhance the technique's efficacy have been identified and are currently underway.

Characterization of novel pneumatic mixing for single-use bioreactor application

Background The novel bioreactor system from PBS Biotech is the first with a pneumatic mixing device powered solely by gas buoyancy, eliminating the need for an external mechanical agitator. The patented design of the AirWheel mixing device promotes not only high tangential fluid flow around the wheel but also efficient radial and axial flows. The leverage effect of the Air-Wheel mixing device also allows for lower gassing requirement (v/v) with increasing working volume, making the power utilization from the gas buoyancy more efficient with scale. A series of physical tests were performed to demonstrate that PBS systems can promote uniform, homogenous mixing over a wide range of working volumes and can offer a low-shear environment for cell culture. A series of biological tests were then performed at various evaluation sites to confirm the physical test results.

Bubble Coalescence during Acoustic Cavitation in Aqueous Electrolyte Solutions

Bubble coalescence behavior in aqueous electrolyte (MgSO(4), NaCl, KCl, HCl, H(2)SO(4)) solutions exposed to an ultrasound field (213 kHz) has been examined. The extent of coalescence was found to be dependent on electrolyte type and concentration, and could be directly linked to the amount of solubilized gas (He, Ar, air) in solution for the conditions used. No evidence of specific ion effects in acoustic bubble coalescence was found. The results have been compared with several previous coalescence studies on bubbles in aqueous electrolyte and aliphatic alcohol solutions in the absence of an ultrasound field. It is concluded that the impedance of bubble coalescence by electrolytes observed in a number of studies is the result of dynamic processes involving several key steps. First, ions (or more likely, ion-pairs) are required to adsorb at the gas/solution interface, a process that takes longer than 0.5 ms and probably fractions of a second. At a sufficient interfacial loading (estimated to be less than 1-2% monolayer coverage) of the adsorbed species, the hydrodynamic boundary condition at the bubble/solution interface switches from tangentially mobile (with zero shear stress) to tangentially immobile, commensurate with that of a solid-liquid interface. This condition is the result of spatially nonuniform coverage of the surface by solute molecules and the ensuing generation of surface tension gradients. This change reduces the film drainage rate between interacting bubbles, thereby reducing the relative rate of bubble coalescence. We have identified this point of immobilization of tangential interfacial fluid flow with the "critical transition concentration" that has been widely observed for electrolytes and nonelectrolytes. We also present arguments to support the speculation that in aqueous electrolyte solutions the adsorbed surface species responsible for the immobilization of the interface is an ion-pair complex.

Approach for the Determination of Heat Transfer Coefficients for Filling Processes of Pressure Vessels With Compressed Gaseous Media

For fast and effective simulation of filling processes of pressure vessels with compressed gaseous media, the governing equations are derived from a mass balance equation for the gas and from energy balance equations for the gas and the wall of the vessel. The gas is considered as a perfectly mixed phase and two heat transfer coefficients are introduced. The first one is the mean heat transfer coefficient between the gas and the inner surface of the pressure vessel, and the second one is the heat transfer coefficient between outer surface of the vessel and the surroundings. Because of the heat capacity of the wall of the pressure vessel, heat transfer from the compressed gas to the vessel wall strongly influences the temperature field of the gas. Until now no correlations have been available for the heat transfer coefficient between inflowing gas and inner surface of the vessel. To solve this problem, a computational fluid dynamics tool is used to determine the gas velocities at the vicinity of the inner surface of the vessel for a number of discrete surface elements. The results of a large amount of numerical experiments show that there exists a unique relationship between the gas velocity at the inlet and the tangential fluid velocities at the vicinity of the inner surface of the vessel for each vessel geometry. Once this unique relationship is known, the complete velocity distribution at the vicinity of the inner surface can be easily calculated from the inlet gas velocity. The near-wall velocities at the outer limit of the boundary layer are substituted into the heat transfer correlation for external flow over flat plates. The final heat transfer coefficient is the area-weighted mean of all local heat transfer coefficients. The method is applied to the special case of filling with hydrogen a 70-MPa composite vessel for fuel cell vehicles.

Boundary integral equation approach for stokes slip flow in rotating mixers

In order to employ continuum models in the analysis of the flow behaviour of a viscous Newtonian fluid at micro scale devices, it is necessary to consider at the wall surfaces appropriate slip boundary conditions instead of the classical non-slip condition. To account for the slip condition at the nano-scale, we used the Navier's type boundary condition that relates the tangential fluid velocity at the boundaries to the tangential shear rate. In this work a boundary integral equation formulation for Stokes slip flow, based on the normal and tangential projection of the Green's integral representational formulae for the Stokes velocity field, which directly incorporates into the integral equations the local tangential shear rate at the wall surfaces, is presented. This formulation is used to numerically simulate concentric and eccentric rotating Couette mixers and a Single rotor mixer, including the effect of thermal creep in cases of rarefied gases. The numerical results obtained for the Couette mixers, concentric and eccentric, are validated again the corresponding analytical solutions, showing excellent agreements.

Effect of Process Conditions on the Growth of Three-Dimensional Dermal-Equivalent Tissue Obtained by Microtissue Precursor Assembly

Bottom-up approach is an appealing strategy to build complex three-dimensional (3D) viable tissues in vitro starting from microtissue precursors (μTP). In this work we biofabricated a thick dermal-like tissue by sequentially combining two steps: a μTPs production and assembly followed by tissue maturation in a purpose-built bioreactor. The μTPs were produced by first seeding bovine primary fibroblasts on gelatine microparticles and then cultivating them in stirring conditions until a thick layer of ~80 μm of de novo synthesized extracellular matrix uniformly covered the microparticle surface. The μTPs were then loaded into a cylindrical chamber (2 mm in depth and 35 mm in diameter) and let to maturate and assemble into a 3D viable biohybrid tissue under specific fluid flow conditions. Several combinations of perfusion and/or tangential fluid flow were applied and their effect on the tissue formation and maturation was assessed. Results show that structural composition and mechanical features of the final 3D bioengineered tissue are strongly affected by the hydrodynamic environment and demonstrate that by optimizing culture conditions a 3D viable tissue with properties similar to that of native derma could be produced.

Electrokinetic framework of dielectrophoretic deposition devices

Numerical modeling and experiments are performed investigating the properties of a dielectrophoresis-based deposition device, in order to establish the electrokinetic framework required to understand the effects of applied inhomogeneous electric fields while moving particles to desired locations. By capacitively coupling electrodes to a conductive substrate, the controlled large-scale parallel dielectrophoretic assembly of nanostructures in individually accessible devices at a high integration density is accomplished. Thermal gradients in the solution, which give rise to local permittivity and conductivity changes, and velocity fields are solved by coupling electric, thermal, and fluid-mechanical equations. The induced electrothermal flow (ETF) causes vortices above the electrode gap, attracting particles, such as single-walled carbon nanotubes (SWNTs), before they are trapped by the dielectrophoretic force and deposit across the electrodes. Long-range carbon nanotube transport is governed by hydrodynamic effects, while local trapping is dominated by dielectrophoretic forces in low concentration SWNT dispersions. Results show that by decreasing the ac frequency ac electroosmosis on the metallic electrodes occurs due to the emergence of an electric double layer, disturbing the initial flow pattern of the system. By superimposing a dc potential offset, a generated tangential electroosmotic fluid flow in the dielectric electrode gap also disrupts the ETF. Capacitive coupling is most efficient in the high frequency regime where it is the dominating impedance contribution. Understanding the occurrence and interaction of these different effects, including a self-limiting integration mechanism for individual nanostructures, allows an increased deposition yield at overall lower electric field strengths through a prudent choice of electric field parameters. The findings provide important avenues toward gentler particle handling, without direct current throughput, a relevant aspect for limiting process effects during device fabrication, all while increasing dielectrophoretic deposition efficiency in nanostructured networks.

The compressional and compositional stratifications in Maxwell earth models: the gravitational overturning and the long-period tangential flux

SUMMARY We analyse self-gravitating compressible Maxwell earth models with compressional and compositional stratifications by taking into account the continuous variations of the initial density and of the bulk modulus. We derive the analytical solution in the Laplace domain of an earth model composed of a homogeneous inviscid core and a viscoelastic mantle characterized by a specific Darwin-law density profile. This makes us discover a new class of relaxation modes, the compositional C-modes, of which the previously discussed RT-modes are a subclass. Compositional stratifications present a denumerable set of C-modes situated on the positive and negative real axis depending on the sign of the square of the Brunt–Vaisala frequency ω and converging to the origin of the Laplace domain, while compressional stratifications do not present such modes. If ω2 0 the C-modes are stable, but they affect the tangential perturbation in such a way that the tangential fluid limit diverge. We interpret this perturbation as a long-period tangential flux of material. By analysing the tangential velocities, we show that this flux fades in the fluid limit controlled by the viscosity. Our findings shed new light on the isostatic criterion, which we reformulate in a new way. Successively, by means of a numerical algorithm, we consider earth models including also the continuous variations of the bulk modulus. In this case, the differential system describing the conservation of the momentum and the self-gravitation is not uniformly Lipschitzian in the region of the Laplace domain associated with the inverse compressional relaxations times. This implies a continuous spectrum in the transient region that the normal mode approach cannot deal with. Nevertheless, the buoyancy mode regions is not characterized by a continuous spectrum and the C-modes are still present for the compositional stratifications.

On three simple experiments to determine slip lengths

It is now well established that for fluid flow at the micro- and nano-scales the standard no-slip boundary condition of fluid mechanics at fluid–solid interfaces is not applicable and must be replaced by a boundary condition that allows some degree of tangential fluid slip. Although molecular dynamics studies support this notion, an experimental verification of a slip boundary condition remains lacking, primarily due to the difficulty of performing accurate experimental observations at small scales. In this article, three simple fluid problems are studied in detail, namely a fluid near a solid wall that is suddenly set in motion (Stokes’ first problem), the long-time behavior of a fluid near an oscillating solid wall (Stokes’ second problem), and the long-time behavior of a fluid between two parallel walls one of which is oscillating (oscillatory Couette flow). The no-slip boundary condition is replaced with the Navier boundary condition, which allows a certain degree of tangential fluid slip via a constant slip length. The aim is to obtain analytical expressions, which may be used in an experimental determination of the constant slip length for any fluid–solid combination.

Modernization of standard and rapid pressure-reducing and cooling units with injection of high pressure water

Operating experience with different standard (ROU) and rapid (BROU) pressure-reducing and cooling units is examined. A scheme for updating standard ROU and BROU steam desuperheaters is proposed which avoids formation of stress concentrations and erosion washout of the parts by eliminating the rigid connection between the feeder element and the injector device: modernization of commercial steam inlet nozzles and injector regulator valves with multistep throttling of the working medium which ensures reliable, long duration operation with water feed from an electrical feed pump. For the modernized version it is proposed that the worm swirler be replaced by a bushing with a tangential fluid feed. Modernization can be done in the repair shops of operating power plants, as well as at the manufacturers' plants.

A Numerical Analysis of Rotordynamic Fluid Forces on an Artificial Heart Pump Impeller in Whirling Motion

In centrifugal pumps for artificial hearts, a magnetic drive and lightly loaded journal bearing system are often used to avoid leakage and to minimize the damage on blood cells. In such system, the rigidity of the bearing is small and the impeller usually rotates over the critical speed. For such cases, rotordynamic fluid forces play an important role for the stability of operation. Authors reported an experimental investigation of characteristics of the rotordynamic fluid forces. In the present study, a numerical study has been conducted. The comparison of fluid forces between the experimental and the numerical results has showed good agreement. Discussions are made on the mechanisms of flows producing the tangential fluid force which may cause self excited shaft vibrations.

Midplane-symmetry breaking in the flow between two counter-rotating disks

This paper considers the axisymmetric steady flow driven by exact counter rotation of two co-axial disks of finite radius. At the edges of the rotating disks one of three conditions is (typically) imposed: (i) zero velocity, corresponding to a stationary, impermeable, cylindrical shroud (ii) zero normal velocity and zero tangential fluid traction, corresponding to a (confined) free surface and (iii) an edge constraint that is consistent with a similarity solution of von Kármán form. The similarity solution is valid in an infinite geometry and possesses a pitchfork bifurcation that breaks the midplane symmetry at a critical Reynolds number. In this paper, similar bifurcations of the global (finite-domain) flow are sought and comparisons are made between the resulting bifurcation structure and that found for the similarity solution. The aim is to assess the validity of the nonlinear similarity solutions in finite domains and to explore the sensitivity of the solution structure to edge conditions that are implicitly neglected when assuming a self-similar flow. It is found that, whilst the symmetric similarity solution can be quantitatively useful for a range of boundary conditions, the bifurcated structure of the finite-domain flow is rather different for each boundary condition and bears little resemblance to the self-similar flow.

Deposition of foulant particles during tangential flow filtration

The fraction of foulant particles deposited on Anopore aluminum oxide microfiltration membranes during tangential flow filtration was measured by direct visual observation (DVO). Yeast cells and 4.5 μm, 10 μm, and 20 μm latex particles were used as model foulants. The fractional particle deposition was found to increase with increasing permeate flux and decrease with increasing wall shear rate. At a fixed permeate flux and wall shear rate, the fractional deposition decreased with increasing particle size, allowing for particle segregation by size. For feed suspensions at the isoelectric point of the membrane (pH 8), individual particles and cells were frequently observed rolling over the membrane surface. To better understand the observed fractional deposition and foulant rolling speed, a mathematical model of a sphere rolling over a rough, permeable surface due to viscous shear flow was developed. The primary parameter in the model is the dimensionless permeate flux, defined as the ratio of permeate flux (velocity of fluid flowing normal to the surface) to the characteristic shear velocity (velocity of fluid flowing tangentially over the surface at one particle radius above the surface). For a given permeate flux, a sphere will stick to the surface only when it encounters a roughness element taller than a critical height. The time-averaged translational velocities of particles rolling over the membrane surface were also calculated using the model and are in good agreement with experimental results, with values reduced by interactions with the membrane to typically 20–50% of the undisturbed tangential fluid velocity at one radius above the membrane.

Incompressible Finite Elements via Hybridization. Part I: The Stokes System in Two Space Dimensions

In this paper, we introduce a new and efficient way to compute exactly divergence-free velocity approximations for the Stokes equations in two space dimensions. We begin by considering a mixed method that provides an exactly divergence-free approximation of the velocity and a continuous approximation of the vorticity. We then rewrite this method solely in terms of the tangential fluid velocity and the pressure on mesh edges by means of a new hybridization technique. This novel formulation bypasses the difficult task of constructing an exactly divergence-free basis for velocity approximations. Moreover, the discrete system resulting from our method has fewer degrees of freedom than the original mixed method since the pressure and the tangential velocity variables are defined just on the mesh edges. Once these variables are computed, the velocity approximation satisfying the incompressibility condition exactly, as well as the continuous numerical approximation of the vorticity, can at once be obtained locally. Moreover, a discontinuous numerical approximation of the pressure within elements can also be obtained locally. We show how to compute the matrix system for our tangential velocity-pressure formulation on general meshes and present in full detail such computations for the lowest-order case of our method.

The effect of roughness on biophysical stimuli at the bone–cartilage interface

Numerical simulations are often used to investigate the effect of mechanical environment on fracture healing. Although these models exhibit biologically relevant mechanical parameters at the bone–callus interface, this interface is modelled as perfectly smooth when in fact it is rough. In this study, a macro–micro-two-scale finite element model was used to determine if roughness significantly alters calculated local mechanical parameters. An idealized fracture healing poroelastic model with a small micro-modelled sub-domain of cartilaginous callus adjacent to rough bone was subjected to cyclic loading. The shear stress, tangential fluid velocity, and pore pressure were investigated. With roughness similar to that at the growth plate, solid matrix shear stress differed substantially with interface roughness, whereas interstitial fluid velocity and pore pressure were only slightly affected. Hence, when modelling local micro-mechanical environments near hard–soft tissue interfaces, interface roughness should be considered.

改良型液体サイクロンによる微粒子の分級

Classification performance of hydro-cyclone with adjustable guide plate as well as blow-up and blow-down method has been investigated both experimentally and theoretically. The cyclone has the adjustable inlet guide plate at the inlet, and 50% cut size is controlled from 8.8 to 12.4μm by changing the inlet width ratio of the guide plate from 0.1 to 1. The 50% cut size is successfully controlled from 18.6 to 40μm by the use of guide plate, along with blow-up and blow-down method. In the case of constant liquid flow rate condition, the 50% cut size is reduced by decreasing the inlet width ratio of the guide plate. The experimental results qualitatively agreed with the numerical calculation results based on the direct simulation method. In the case of small inlet width ratio under constant liquid flow rate, the 50% cut size is decreased because the tangential and axial fluid velocity near conical wall increase and a part of fluid entering the dust box rapidly changes its direction to side wall of the dust box.

Hydrodynamic problems related to the electrodeposition of AuCu/B 4C composites

Hydrodynamic actions leading to the electrodeposition of AuCu/B 4C composites have been investigated experimentally and theoretically. Translation and rotation of cylindrical cathodes have been studied. Embedding of particles into disk electrodes rotating at various speeds has been analysed. The dependence of volume fraction of embedded particles on fluidisation conditions has been investigated. Higher volume fractions correlate with higher mass transport rate to the cathode and are found in points on which flow lines are closer to normal to the cathode surface (stagnation points), irrespectively of the overall flow sign. Hydrodynamic classification of particles diameters has also been observed: lower fluidisation velocities and tangential (to cathode surface) fluid flow components correlate with larger particles whilst higher fluidisation velocities and normal fluid flow components correlate with smaller particles. These effects have been modelled analytically on the basis of a hydrodynamic treatment of interactions among fluid flow, electrode surface and particles. Effects of the cathode roughness — and related local flow conditions — on particle embedding have also been disclosed and explained with the above-mentioned hydrodynamic model.

Boundary Effects on Diffusiophoresis of Cylindrical Particles in Nonelectrolyte Gradients

The diffusiophoretic motion of a long circular cylinder in a transversely imposed gradient of a nonionic solute near a large plane wall parallel to its axis is analyzed. The range of the interaction between the solute and the solid surfaces is assumed to be small relative to the particle radius and to the gap width between the particle and the wall, but the polarization effect of the mobile solute in the thin diffuse layers adjacent to the solid surfaces caused by the strong adsorption of the solute is incorporated. A normal flux of the solute and a slip velocity of the fluid at the outer edge of the diffuse layers are used as the boundary conditions for the fluid domain outside the diffuse layers. Through the use of cylindrical bipolar coordinates along with these boundary conditions, a set of transport equations governing this problem is solved in the quasisteady situation and the wall effects on the diffusiophoresis of the cylinder are computed for various cases. For the diffusiophoretic motion of a cylinder normal to a plane, the particle mobility decreases monotonically with the decrease of the distance of the particle axis from the wall. The stronger the polarization effect in the diffuse layer, the weaker the wall effect on the diffusiophoresis. The effect of the normal plane on the diffusiophoresis of a cylinder is much more significant than that for a sphere at the same separation. For the diffusiophoresis of a cylinder parallel to a plane, the boundary effect is a complicated function of the relevant parameters (not necessarily varies monotonically with the extent of separation) mainly due to the existence of a diffusio-osmotic flow caused by the tangential fluid velocity at the plane wall.

A numerical model for prediction of the air-core shape of hydrocyclone flow

Hydrocyclones are used extensively for solid particles separation and classification in the minerals processing industry. By means of the tangential fluid feeding and solid particle, a strong rotational movement takes place inside the equipment, that charged a centrifugal field. Because of this field, the solid particles are suspended in the fluid and tend to move towards the walls. As well, by the high tangential velocity of the fluid in the central part of the device, the pressure decreases until a values smaller than atmospheric pressure. A low pressure region is starting, causing the formation of an air-core in the central line. In spite of the simple geometry and operation, explaining the detailed mechanisms of the work is extremely complicated. One difficulty in finding the actual flow of the hydrocyclones is the necessity of specifying the form and location of the air-core surface. In the usual models applied to an hydrocyclone, the interface that bounds the air-core is modeled as a fixed cylindrical surface, that greatly simplifies the problem. This simplification avoids the necessity of the calculation of an unknowing boundary that modifies the domain, where the field equations must be solved. Nevertheless, such a simplification can produce bad results. Many research works have studied theoretical models to approximate the air-core radius. In this work, it is considered the air-liquid interface being a Young-Laplace type. With an iterating process the air-core radius is updated, in order to minimize the error in the Young-Laplace jump condition. The results obtained for velocity field are compared with those obtained expemerimentally in a previous paper, where it is possible to get satisfactory answers.

In situ and real-time observation of the formation and dynamics of a cellular interface in a succinonitrile-0.5 wt% acetone alloy directionally solidified in a cylinder

In situ and real-time observation of the solid-liquid interface during upward Bridgman growth of succinonitrile-0.5 wt% acetone in a cylinder was carried out. This first article concentrates on the study of the emergence and building of nonplanar patterns. By observation under white light in the solidification direction, bright field images and video records of the interface microstructure were obtained, which allowed dynamical phenomena such as the ripening and arrangement of cellular arrays with time. All results show a significant influence of natural convection in the melt. In particular, a microstructure gradient was observed at the interface. From a phenomenological model based on a boundary layer approach, its origin can be attributed to a ramp in solute concentration along the growth front created by tangential fluid flow. Statistical analyses of the evolution of primary spacing and array disorder show that the stable arrangement can still be described as a honeycomb disturbed by Gaussian noise. Convection was also found to be responsible for primary spacings smaller than that given by theoretical diffusive models and experiments on thin samples.