Dynamics of a thin film with temperature-dependent viscosity on a rotating disk

Summary The thermal effects on the dynamics of an axisymmetric flow of a non-volatile incompressible viscous thin liquid film on a rotating disk due to viscosity variation depending exponentially on temperature are considered. The nonlinear evolution equation is solved numerically. The numerical results reveal that heating the film from below enhances the rate of thinning. The increase in Biot number increases the film thickness, when the film is heated from below. Further, the relative amount of fluid retained on the substrate decreases as the film is heated from below. The results are reversed for the case of a film which is cooled from below. The rate of thinning of the film is more (less) for the case of temperature dependent viscosity when the film is heated (cooled) from below than for the case of constant viscosity of the fluid.     

A spectral‐element method for modelling cavitation in transient fluid–structure interaction

In an underwater‐shock environment, cavitation (boiling) occurs as a result of reflection of the shock wave from the free surface and/or wetted structure causing the pressure in the water to fall below its vapour pressure. If the explosion is sufficiently distant from the structure, the motion of the fluid surrounding the structure may be assumed small, which allows linearization of the governing fluid equations. In 1984, Felippa and DeRuntz developed the cavitating acoustic finite‐element (CAFE) method for modelling this phenomenon. While their approach is robust, it is too expensive for realistic 3D simulations. In the work reported here, the efficiency and flexibility of the CAFE approach has been substantially improved by: (i) separating the total field into equilibrium, incident, and scattered components, (ii) replacing the bilinear CAFE basis functions with high‐order Legendre‐polynomial basis functions, which produces a cavitating acoustic spectral element (CASE) formulation, (iii) employing a simple, non‐conformal coupling method for the structure and fluid finite‐element models, and (iv) introducing structure–fluid time‐step subcycling. Field separation provides flexibility, as it admits non‐acoustic incident fields that propagate without numerical dispersion. The use of CASE affords a significant reduction in the number of fluid degrees of freedom required to reach a given level of accuracy. The combined use of subcycling and non‐conformal coupling affords order‐of‐magnitude savings in computational effort. These benefits are illustrated with 1D and 3D canonical underwatershock problems. Copyright © 2004 John Wiley & Sons, Ltd.     

Heat and fluid flow in a scraped-surface heat exchanger containing a fluid with temperature-dependent viscosity

Scraped-surface heat exchangers (SSHEs) are extensively used in a wide variety of industrial settings where the continuous processing of fluids and fluid-like materials is involved. The steady non-isothermal flow of a Newtonian fluid with temperature-dependent viscosity in a narrow-gap SSHE when a constant temperature difference is imposed across the gap between the rotor and the stator is investigated. The mathematical model is formulated and the exact analytical solutions for the heat and fluid flow of a fluid with a general dependence of viscosity on temperature for a general blade shape are obtained. These solutions are then presented for the specific case of an exponential dependence of viscosity on temperature. Asymptotic methods are employed to investigate the behaviour of the solutions in several special limiting geometries and in the limits of weak and strong thermoviscosity. In particular, in the limit of strong thermoviscosity (i.e., strong heating or cooling and/or strong dependence of viscosity on temperature) the transverse and axial velocities become uniform in the bulk of the flow with boundary layers forming either just below the blade and just below the stationary upper wall or just above the blade and just above the moving lower wall. Results are presented for the most realistic case of a linear blade which illustrate the effect of varying the thermoviscosity of the fluid and the geometry of the SSHE on the flow.     

Onset of convection in the Rayleigh–Bénard flow under non-Boussinesq conditions: an asymptotic approach

The effect of temperature dependent fluid properties on the onset of convection in a horizontal fluid layer heated from below is investigated. Based on asymptotic expansions of all fluid properties with respect to temperature final results are deduced that are independent of specific property laws. They are general in nature and hold for all Newtonian fluids and all (small) heat transfer rates. A special point of interest is the widely used Boussinesq approximation. Our asymptotic results clearly show how this approximation affects the stability calculations of the flow under investigation.     

Thermal instability in a micropolar fluid layer subject to a magnetic field

In the present paper we have considered thermal instability in a heat conducting micropolar fluid layer under the influence of a transverse magnetic field. Assuming the bounding surfaces to be rigid the eigenvalue problem is solved using finite-difference and Wilkinson's iteration techniques. Here it is seen that the instability sets in not only for adverse temperature gradient but also for positive temperature gradient. Both the microtation and the magnetic field are seen to stabilize the fluid layer. However, the stabilizing effect of microrotation becomes less significant when the strength of the magnetic field is large. In the case of heating from below, the critical wave number is seen to be insensitive to increase in the strength of the magnetic field, while it increases significantly when the fluid is heated from above.     

Stability of a micropolar fluid layer heated from below

The stability of a layer of micropolar fluid heated from below is studied employing a linear theory as well as an energy method. It is proved that the principle of exchange of stability holds and the critical Rayleigh number is obtained. It is observed that the micropolar fluid layer heated from below is more stable as compared with the classical viscous fluid. The energy method is then used to study the stability under finite disturbances. A variational method is applied to obtain the sharp stability limit. It is found that no subcritical instability region exists and the critical Rayleigh number as derived from the energy method is identical to that of the linear limit.     

Collective drag and sedimentation: comparison of simulation and experiment in two and three dimensions

We simulate systems of particles immersed in fluid at Reynolds numbers on the particle scale of 0.1 to 20. Our simulation method is based on a finite differencing multi-grid Navier-Stokes solver for the fluid and a molecular dynamics technique for the particle motion. The mismatch between the fixed rectangular grid and the spherical particle shape is taken into account by considering analytical series expansions of the pressure and velocity of the fluid in the vicinity of the particle surface. We give an expression for the force on a particle in terms of the expansion coefficients. At each time step these coefficients are determined from pressure and velocity values on the fluid grid. We demonstrate the validity of our approach by performing numerical simulations of flow through porous solid beds and of bulk sedimentation in two and three spatial dimensions. We compare our results to experimental data and analytical results. Quantitative agreement is found in situations where the volume fraction remains below approximately 0.25 both in two and three dimensions, provided that at the same time the Reynolds number remains below about 10. In contrast, e.g., to finite-element techniques the method remains fast enough to allow dynamical simulations of particle-fluid systems with several hundred spheres on workstations taking all inertial effects into account.     

Axisymmetric Flow in an Oil Reservoir of Finite Depth Caused by a Point sink above an Oil-Water Interface

The flow of a stratified fluid (e.g., oil/water) withdrawn from a vertically confined porous medium through a point sink is considered. The withdrawal tends to cause the oil-water interface to move upwards. So long as the interface is below the well, the less dense fluid (oil) is pumped into the well without the denser fluid (water) until a critical flow rate is reached. The flow is considered to be axisymmetric, and involves a nonlinear boundary condition along the free surface. A boundary-integral equation method (BIEM) is used to find the interface position for different pumping rates. For small flow rates, a small-parameter expansion is derived and the results are compared with numerical solutions to the problem. There exists a critical withdrawal rate beneath which the water does not break through into the sink, this rate depending on the sink location and bottom geometry.     

Effects of suction-injection-combination (SIC) on the onset of Rayleigh-Benard magnetoconvection in a micropolar fluid

The effects of suction-injection-combination (SIC) and magnetic field on the linear stability analysis of Rayleigh-Benard convection in a horizontal layer of an Boussinesq micropolar fluid is studied using a Rayleigh-Ritz techinque. The eigenvalues are obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations with isothermal and adiabatic temperature conditions on the spin-vanishing boundaries. The eigenvalues are also obtained for lower rigid isothermal and upper free adiabatic boundaries with vanishing spin. The influence of various micropolar fluid parameters on the onset of convection has been analysed. It is found that the effect of Prandtl number on the stability of the system is dependent on the SIC being pro-gravity or anti-gravity. A similar Pe-sensitivity is found in respect of the critical wave number. It is observed that the micropolar fluid layer heated from below is more stable compared to the classical fluid layer.     

Efficient DG‐like formulation equipped with curved boundary edges for solving elasto‐acoustic scattering problems

A Discontinuous Galerkin (DG)‐based approach is proposed for computing the scattered field from an elastic bounded object immersed in an infinite homogeneous fluid medium. The proposed method possesses two distinctive features. First, it employs higher‐order polynomial‐shape functions needed to address the high‐frequency propagation regime. Second, it is equipped with curved boundary edges to provide an accurate representation of the fluid–structure interface. The most salient benefits resulting from the latter feature, as demonstrated by the numerical investigation, are the following: (i) an improvement by—at least—two orders of magnitude on the relative error and (ii) the disappearance of spurious resonance frequencies in the surrounding fluid medium. In addition, the reported numerical results reveal that when using cubic polynomials with less than three elements per wavelength, the proposed DG method computes the scattered field with a relative error below 1% for an elastic scatterer of about 30 wavelengths. This observation highlights the potential of the proposed solution methodology for efficiently solving mid‐frequency to high‐frequency elasto‐acoustic scattering problems. Copyright © 2014 John Wiley & Sons, Ltd.     

Quenches of formvar - coated NbTi/Cu caused by step input in power

We have investigated the stability of the composite Nb48Ti/Cu coated with a formvar layer (30 μm thick). Starting from thermal equilibrium in the superfluid liquid He II range below the lambda temperature (T = Tλ), the composite temperature is found to rise first monotonically with time t, upon onset of energy dissipation. However, restricted stability is visible as a relative temperature maximum (Tmax) of the composite at the time tmax, followed by a relative minimum in T at tmin. These coated composite phenomena are similar to stability conditions of bare composites in the same "conductor-in-box " geometry employed. However at a specified power the times tmaxand tminare shifted in comparison to the bare composite. Diagnosis is based on power-time functions whose tangents are characterized by power law exponents (m) . The m-values found are re - presentative of strong, localized solid - coolant interaction, of a caloric condition, or of locally turbulent fluid motion. In the range covered by the present transients, stability is available by creation of entropy - rich buffer domains of fluid, below the superconducting transition temperature, between He II and the heated composite. The latter is quench - protected in an intermediate power range.     

A critical study of the Bingham model in squeeze-flow mode

Electrorheological (ER) fluids offer the user the option of changing the performance of a damping device quickly and without much effort. Many authors agree on the validity of the Bingham model for describing the fluid. In this paper, the authors have studied this model in squeeze-flow mode. Calculations were compared with experimental results. Material data for the model were estimated from tests both in shear-flow mode and in squeeze-flow mode. The investigation shows that estimates from squeeze-flow mode give the closest fit. Cyclic loading at frequencies below 50 Hz was studied. Amplitude and frequency dependence is not well predicted by the model, so the material data are valid for one amplitude and one frequency only.     

Convective instability of a micropolar fluid layer by the method of energy

The convective instability of a micropolar incompressible fluid layer heated from below is treated within the framework of Serrin-Joseph's energy method. In presence of coupling between temperature and micro-rotations, a region of subcritical instability is displayed. The influence of the various micropolar parameters on the onset of convection is also analyzed.     

Evaluation and comparison of a moist granulation technique to conventional methods

In the moist granulation technique (MGT), a minimum amount of liquid is used to activate a binder in a planetary mixer. Then, any excess moisture is absorbed by the addition of a moisture-absorbing substance. In the experiments described below, acetaminophen (APAP) was the model drug; polyvinylpyrrolidone (PVP) and microcrystalline cellulose (MCC) served as the binder and moisture-absorbing material, respectively. Water was used as the granulating fluid. Comparison of the MGT with direct compression (DC) and wet granulation (WG) methods was accomplished by sieve analysis (particle size) and density measurements. Moist granulation yielded an increase in particle size compared to direct compression; these results are comparable to those from the traditional wet granulation after drying and screening. Based only on the particle size, moist granulation appears comparable to conventional wet granulation for this formula. The moist granulation technique appears to have potential for the development of controlled-release formulations.     

The effect of microstructure on the thermal convection in a rectangular box of fluid heated from below

The effect of microstructure on the thermal convection in a rectangular box of fluid heated from below has been investigated by applying the micropolar fluid theory. The influence of lateral walls on the convection process in a rectangular box has been determined. The Galerkin method has been employed to get an approximate solution for the eigenvalue problem. The beam functions which satisfy two boundary conditions on each rigid surface have been used to construct the finite roll (cells with two nonzero velocity components depend on all three spatial variables) trial functions for the Galerkin method. The effect of variations of material parameters at the onset of convection has been presented graphically. It is observed that as the distance between the lateral walls increases the effect of one of the material parameters, characterizing the spin-gradient viscosity, at the onset of stability diminishes. A comparison has been made with the corresponding results for a Newtonian fluid.     

Thermal relaxation effect on magnetohydrodynamic instability in a rotating micropolar fluid layer heated from below

Summary. The effect of a vertical magnetic field on the onset of convective instability in a conducting micropolar fluid (Oldroyd fluid) layer heated from below confined between two horizontal planes under the simultaneous action of the rotation of the system and a vertical temperature gradient is considered. Linear stability theory and normal mode analysis are used to derive an eigenvalue system of order twelve, and an exact eigenvalue equation for natural instability is obtained. Under somewhat artificial boundary conditions, this equation can be solved exactly to yield the required eigenvalue relationship from which various critical values are determined in detail. The effects of magnetic field, the relaxation time and micropolar parameters on the critical Rayleigh number and critical wave number are discussed and presented graphically. The analysis presented in this paper is more general than any previous investigation.     

A new measuring method to detect the emissions of metal working fluid mist

During metal machining the rotating machine tool or grinding wheel is generating fine droplets and vapor which can cause occupational health problems. A new continuous measuring method was developed to detect both droplets and vapor of metalworking fluid mist and to provide information about the droplet size distribution. According to this method, an air sample of the metalworking fluid mist is segregated by impactors of different cut sizes, carried out in several successive passes. In each pass the droplets that are not collected in the impactor are fed into an evaporator that immediately evaporates all droplets, and subsequently the sample is analyzed in-line by a Flame Ionization Detector (FID). By subtraction of the value measured at the respectively next smaller fraction, the oil amount of the metalworking fluid mist found in a certain droplet size range is obtained. The metalworking fluid mist is thus segregated according to the droplet size, and a definite cut size between droplet and vapor can be defined, below which we can say "vapor". This method was calibrated with Di-2-Ethylhexyl-Sebacat (DEHS) as equivalence substance for further measurements applied on various metalworking fluids.     

Observation of the morphology of thin films of solid helium deposited from the fluid onto sapphire

Thin layers of solid helium were grown on sapphire single-crystal substrates at pressures from about 500 bar to 9 kbar. Grain boundaries can be observed in these layer crystals. The morphology of the grains depends on the crystal modification. In the hcp phase (below about 1.13 kbar) a system of parallel bands is observed, probably due to slip and twinning. In the fcc phase (above 1.13 kbar) a polygonal structure similar to a helium froth is found. Melting of this froth in the fcc phase shows grain boundary melting; fluid helium is wetting the fcc grains. Grain boundaries in the hcp phase are, in contrast, not wetted by fluid helium. Near the triple point at 1.13 kbar and 15.0 K one can deposit both crystalline phases side by side. In such structures, the transition fcc hcp⁴He can be observed during isothermal holding. The transition proceeds by the parallel motion of low-energy grain boundaries.     

Fluid and Particle Laser Doppler Velocity Measurements and Mass Transfer Predictions for the Usp Paddle Method Dissolution Apparatus

This research was motivated by the lack of experimental data concerning the complex flow fields produced by the USP Paddle Method Dissolution Test Apparatus, which influence the reproducibility and sensitivity of the resulting dissolution data.

A one-component He-Ne fiber optics laser Doppler anemometer and a conditional sampling computer data acquisition provided unique three-dimensional fluid velocity measurements in most regions of the fluid inside the vessel. Tangential velocities which are predominant in magnitude decrease as a function of distance from the paddle to the liquid surface. Low magnitude circulation patterns in the axial direction exist with little Interaction between the fluid above and below the paddle. The radial velocity component also exhibits a low magnitude. In the vicinity of the paddle, a periodic fluid motion produced by the wake formed behind the paddle exists. Close to the bottom of the vessel, tangential fluid velocities were approximately equal to solid body rotation created by the paddle, and make possible predictions of mass transfer rates from a non-disintegrating calibrator resting at the bottom of the vessel.

The motion of drug particles from a dissolving tablet was simulated by using 216 /im diameter polystyrene latex spheres. They provided the Stokes number matching an average drug particle diameter of 190 /im. Tangential particle velocity measurements taken at selected locations using two different paddle speeds (50 and 60 RPM) revealed that the particles closely followed the fluid. A comparison between the fluid and the particle tangential velocities at 50 and 60 RPM showed that for 60 RPM the particle to fluid relative velocity above the paddle increased by about 100%, with the mass transfer rate in that region predicted to be enhanced by 37%.     

Microfluidic sorting with a moving array of optical traps

Optical sorting was demonstrated by selective trapping of a set of microspheres (having specific size or composition) from a flowing mixture and guiding these in the desired direction by a moving array of optical traps. The approach exploits the fact that whereas the fluid drag force varies linearly with particle size, the optical gradient force has a more complex dependence on the particle size and also on its optical properties. Therefore, the ratio of these two forces is unique for different types of flowing particles. Selective trapping of a particular type of particles can thus be achieved by ensuring that the ratio between fluid drag and optical gradient force on these is below unity whereas for others it exceeds unity. Thereafter, the trapped particles can be sorted using a motion of the trapping sites towards the output. Because in this method the trapping force seen by the selected fraction of particles can be suitably higher than the fluid drag force, the particles can be captured and sorted from a fast fluid flow (about 150 μm/s). Therefore, even when using a dilute particle suspension, where the colloidal trafficking issues are naturally minimized, due to high flow rate a good throughput (about 30 particles/s) can be obtained. Experiments were performed to demonstrate sorting between silica spheres of different sizes (2, 3, and 5 μm) and between 3 μm size silica and polystyrene spheres.