An Analysis of Drug Dissolution Rates in the USP 24 Type 2 Apparatus

This paper applies boundary layer theory to the process of drug dissolution in the USP 24, Type 2 Apparatus. The mass transfer rate from the top flat surface of a compact in various positions within the device is evaluated by means of a Pohlhausen integral method. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Homogenization and concentration for a diffusion equation with large convection in a bounded domain

We consider the homogenization of a non-stationary convection–diffusion equation posed in a bounded domain with periodically oscillating coefficients and homogeneous Dirichlet boundary conditions. Assuming that the convection term is large, we give the asymptotic profile of the solution and determine its rate of decay. In particular, it allows us to characterize the “hot spot”, i.e., the precise asymptotic location of the solution maximum which lies close to the domain boundary and is also the point of concentration. Due to the competition between convection and diffusion, the position of the “hot spot” is not always intuitive as exemplified in some numerical tests.     

A consistency check for estimating truncation error due to upstream differencing

A simple method is developed for checking the consistency—i.e., the degree of self-consistent numerical accuracy—of fluid dynamic computations which use upstream differencing for the convection terms. By applying the method to computed results, a quantitative estimate of the size of the first-order truncation error can be made, thus obviating the need for grid-dependence tests based on successive grid refinement. Alternatively, the method can be used to determine the grid size appropriate to an acceptable range of truncation error. In regions of relatively small velocity gradient, a direct consistency check can be achieved by applying a straightforward graphical procedure to computed results. The same graphical construction can be used in the general case to make an adequate first-order consistency check on the convective flux computation. The method is particularly useful in rationalizing empirical turning procedures used to calibrate upstream-difference numerical models in terms of measured results.     

Direct and inverse multichannel scattering problems

We consider small oscillations of a system of pairwise interacting particles in an external field near a stable equilibrium. The system is assumed to consist of finitely many channels, i.e., semi-infinite linear chains of particles, attached to a scatterer, which is a finite system of interacting particles. Direct and inverse scattering problems are considered. In particular, an algorithm finding characteristics of the channels on the basis of scattering data is given.     

Effect of magnetic field dependent viscosity on ferroconvection in the presence of dust particles

This paper deals with the theoretical investigation of the effect of magnetic field dependent (MFD) viscosity on the thermal convection in a ferromagnetic fluid in the presence of dust particles. For a flat ferromagnetic fluid layer contained between two free boundaries, the exact solution is obtained using a linear stability analysis and a normal mode analysis method. For the case of stationary convection, dust particles always have a destabilizing effect, whereas the MFD viscosity has a stabilizing effect on the onset of convection. In the absence of MFD viscosity, the destabilizing effect of magnetization is depicted but in the presence of MFD viscosity, non-buoyancy magnetization may have a destabilizing or a stabilizing effect on the onset of convection. The critical wave number and critical magnetic thermal Rayleigh number for the onset of stationary convection are also determined numerically for sufficiently large values of buoyancy magnetization parameter M ₁. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. It is observed that the critical magnetic thermal Rayleigh number is reduced solely because the heat capacity of clean fluid is supplemented by that of the dust particles. The principle of exchange of stabilities is found to hold true for the ferromagnetic fluid heated from below in the absence of dust particles. The oscillatory modes are introduced due to the presence of the dust particles, which were non-existent in their absence. A sufficient condition for the non-existence of overstability is also obtained.     

Effect of dust particles on a layer of micropolar ferromagnetic fluid heated from below saturating a porous medium

The problem of the effect of dust particles on the thermal convection in micropolar ferromagnetic fluid saturating a porous medium subject to a transverse uniform magnetic field has been investigated theoretically. Linear stability analysis and normal mode analysis methods are used to find an exact solution for a flat micropolar ferromagnetic fluid layer contained between two free boundaries. In case of stationary convection, the effect of various parameters like medium permeability, dust particles, non-buoyancy magnetization, coupling parameter, spin-diffusion parameter and micropolar heat conduction parameter are analyzed. For sufficiently large values of magnetic parameter M₁, the critical magnetic thermal Rayleigh number for the onset of instability is determined numerically and results are depicted graphically. It is also observed that the critical magnetic thermal Rayleigh number is reduced solely because the heat capacity of clean fluid is supplemented by that of the dust particles. The principle of exchange of stabilities is found to hold true for the micropolar ferromagnetic fluid saturating a porous medium heated from below in the absence of micropolar viscous effect, microinertia and dust particles.     

Influence of natural convection on the crystallization of pseudobinary compounds

The solution of the problem concerning the influence of intrinsic convection on the crystallization rate of pseudobinary compounds in an ampul by the method of vertical-directed crystallization is considered. A mathematical model of the physical processes occurring in the apparatus for the growth of semiconducting structures is outlined. An algorithm for numerical realization of the proposed model is constructed. The significant influence of natural convection in the melt/solution on the rate of crystal growth is shown.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 94–98, 1988.     

Thermocapillary motion of deformable fluid particles in tubes

The boundary integral technique is used to study the effect of deformation on the steady, creeping, thermocapillary migration of a fluid particle under conditions of axisymmetry, negligible thermal convection and an insulated tube wall. The spherical radius of the fluid particle (i.e. the radius as if the particle were a sphere, a ′= (3V _p ^′ /4π)^1/3, V _p ^′ is the particle volume) and that of the tube are denoted, respectively, by a′and b′. For small capillary numberCa = 0.05, only for a large fluid particle (a′/b′ = 0.8) is deformation significant. Fora′/b′= 0.8, hydrodynamic stresses squeeze the particle, reduce the interaction of the particle with the wall and thereby increase the terminal velocity. For small particles a′/b′< 0.8 and Ca = 0.05 the fluid particles translate as spheres, due to the fact that the fluid particle is too far away from the wall to be subject to distending hydrodynamic stresses. The deformable particle moves faster than a spherical one in the thermocapillary migration. The increase in velocity with capillary number is larger for thermocapillary motion than for buoyancy.     

On dispersion of settling particles from an elevated source in an open-channel flow

Longitudinal dispersion of suspended particles with settling velocity in a turbulent shear flow over a rough-bed surface is investigated numerically when the settling particles are released from an elevated continuous line-source. A combined scheme of central and four-point upwind differences is used to solve the steady turbulent convection–diffusion equation and the alternating direction implicit (ADI) method is adopted for the unsteady equation. It is shown how the mixing of settling particles is influenced by the ‘log-wake law’ velocity and the corresponding eddy diffusivity when the initial distribution of concentration is regarded as a line-source. The concentration profiles for the steady-state conditions agree well with the existing experimental data and some other numerical results when the settling velocity is zero. The behaviours of iso-concentration lines in the vertical plane for different releasing heights are studied in terms of the relative importance of convection, eddy diffusion and settling velocity.     

Lexicographical dynamic goal programming approach to a robust design optimization within the pharmaceutical environment

The primary objective of this paper is to develop a new robust design (RD) optimization procedure based on a lexicographical dynamic goal programming (LDGP) approach for implementing time-series based multi-responses, while the conventional experimental design formats and frameworks may implement static responses. First, a parameter estimation method for time-dependent pharmaceutical responses (i.e., drug release and gelation kinetics) is proposed using the dual response estimation concept that separately estimates the response functions of the mean and variance, as a part of response surface method. Second, a multi-objective RD optimization model using the estimated response functions of both the process mean and variance is proposed by incorporating a time-series components within a dynamic modeling environment. Finally, a pharmaceutical case study associated with a generic drug development process is conducted for verification purposes. Based on the case study results, we conclude that the proposed LDGP approach effectively provides the optimal drug formulations with significantly small biases and MSE values, compared to other models.     

相互碰撞的圆粒子在竖直通道中沉降的数值研究

采用格子Boltzmann方法,数值模拟了考虑相互碰撞的两圆粒子的沉降,分析了Re数、初始相对位移及通道宽度对粒子沉降的影响．结果表明,在0.1＜Re＜20范围内, 粒子沉降具有周期性．Re数越大,两圆粒子的相互作用越强,粒子横向位移的幅度也越大．在大Re数时,沉降的过程是两个粒子交替领先;在较小Re数时,当后面的粒子接近的时候,领先的粒子被向右侧推了一段后仍会继续领先;对中等Re数,原先在后面的粒子在第一次加速后将取得领先位置并一直保持下去．粒子的初始分布位置对沉降的形态影响不大．管道宽度变化时,粒子总的沉降特性不变,而周期改变,管道越宽,周期越长．     

一个抛物型方程侧边值问题的正则逼近解在一类Sobolev空间中的最优误差界

逆热传导问题(IHCP)是严重不适定问题,即问题的解(如果存在)不连续依赖于数据．但目前关于逆热传导问题的已有结果主要是针对标准逆热传导问题．文中给出了出现在实际问题中的一个抛物型方程侧边值问题,即一个含有对流项的非标准型逆热传导问题的正则逼近解一类Sobolev空间中的最优误差界．     

Determination of the characteristics of viscoelastic media from the data of quasi-static tests

By representing memory-influence functions in the form of generators of the Dirac -function in order to describe the relaxation processes on a small initial interval [3], formulas are constructed for determining the true characteristics of viscoelastic media from the data of quasi-static creep tests and relaxation tests by means of the irreversibility effect [2], i.e., the dependence of the relaxation processes on the initial loading conditions.Mekhanika Polimerov, Vol. 3, No. 5, pp. 803–811, 1967     

Comparison between experimental data and theoretical calculations of free convection in water near its density maximum

Experimental data on free convection of water in the region of maximum density are interpreted by a theoretical model. The agreement between our theory and experimental data is excellent.Typical arrests in the temperature versus time curves and loops in warming-cooling cycles indicate large effects on convection generated by small changes in the space-time density profiles. These observations are fully explained by an extended theoretical approach which takes into account complex phenomena occurring in the boundary layer region. The comparison between theory and experiments indicates how the convective motion propagates from the boundary layer to the internal region of the fluid (central nucleus). Thanks to the extreme sensitivity of the temperature behaviour to relatively small density variations, a complete information about density profile around 4°C can be obtained by a quite simple experimental apparatus. Experimental data at temperature ranges between 0°C and 8°C can “feel” the asymmetry in the density curve around 4°C which is of about 8 parts per million. Our results can bring some light on the experiments performed by Azouni about the water hysteresis loop around 4°C.     

A linear stability analysis of a mixed convection plume from a line source: higher order effects

Aiding mixed convection flow resulting from the vertical flow of a uniform stream past a horizontal line source of heat is of importance in many practical situations such as hot-wire anemometry, etc. In this paper, the stability of such a flow to small disturbances is analyzed in terms of the linear stability theory. The analysis treats the presence of the free stream as a perturbation of a natural convection plume generated by the line source of heat. The base flow as well as the disturbance field are determined by means of a systematic perturbation expansion.The results presented here extend the results of an earlier investigation [1], by considering second-order mixed convection effects. The results reveal that the free stream has a stabilizing effect. As expected, consideration of second-order mixed convection effects further enhances the stability of the flow. The reported results are valid at a large distance from the source where the flow field is dominated by buoyancy effects.

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Résumé Aidant la convection mixte d'un écoulement résultant d'un écoulement uniforme vertical, à l'arrière d'une source rectiligne horizontale de chaleur, est important en plusieurs situations pratiques, comme celui de l'anémomètre à fil chaud, etc. Dans cet article, la stabilité de ce genre d'écoulement aux pertubations est analysée par la théorie de la stabilité linéaire. L'analyse traits la présence de l'écoulement libre comme perturbation d'une convection naturelle du panache crée par la source rectiligne de chaleur. L'écoulement de base ainsi que le champ exposé aux perturbations sont déterminés au moyen d'une série de perturbations systématiques. L'analyse prend en considération la nature non-parallèle de l'écoulement de base.Les résultats présentés ici, élargissent les résultats d'une étude précédente [1], en considérant le second ordre des effets de la convection mixte. La consideration du second ordre des effets de la convection mixte augmente la stabilité de l'écoulement. De même, l'effet de la convection mixte sur la courbe neutre semble différent de celle-ci pour une paroi limitée des écoulements.

     

A robust and parallel relaxation method based on algebraic splittings

We propose and analyze a new relaxation scheme for the iterative solution of the linear system arising from the finite difference discretization of convection–diffusion problems. For problems that are convection dominated, the (nondimensionalized) diffusion parameter ϵ is usually several orders of magnitude smaller than computationally feasible mesh widths. Thus, it is of practical importance that approximation methods not degrade for small ϵ. We give a relaxation procedure that is proven to converge uniformly in ϵ to the solution of the linear algebraic system (i.e., “robustly”). The procedure requires, at each step, the solution of one 4 × 4 linear system per mesh cell. Each 4 × 4 system can be independently solved, and the result communicated to the neighboring mesh cells. Thus, on a mesh connected processor array, the communication requirements are four local communications per iteration per mesh cell. An example is given, which illustrates the robustness of the new relaxation scheme. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 91–110, 1999     

Network modeling of chromatography by stochastic phenomena of adsorption,diffusion and convection

The limitation of macroscopic models to represent structural parameters, such as topology and morphology, as well as population effects, i.e. multi-molecules movement, in the modeling of chromatography systems has implications on the understanding of the phenomenological aspects that contribute to the separation mechanisms in porous media. The representation of the porous structure of chromatographic columns by a three-dimensional cubic network of interconnected sites allows a better analysis of the structural characteristics of the porous column and its connection with the phenomena of adsorption, diffusion and convection. In the present work the application of an interconnected cubic network model associated with a stochastic modeling of the adsorption, diffusion and convection phenomena leads to the proper representation of the dynamic aspects of the breakthrough curves related to separation processes in chromatographic columns. Therefore, it is possible to study the dynamics of solute retention from the molecules distribution in the separation processes throughout the column. Among the mass transfer mechanisms investigated, the convection showed to be closely related to the separation dynamics of chromatography, with the diffusion having little effects. The adsorption influenced both the separation dynamics and solute retention.     

On the stability of mixed convective motions in a vertical layer with wave-like boundaries

The stability of the stationary and oscillatory convective motions which develop in a vertical layer with periodically curved boundaries is studied for the case of longitudinal fluid injection. The amplitude of the boundary undulations and the flow of fluid along the layer are both assumed to be small, and methods of perturbation theory are used. The characteristic properties of the incremental spectrum of the spatially periodic motions are studied and the most dangerous types of perturbations as well as the forms of the stability regions are determined.

Theoretical investigations of the effect of spatial inhomogeneity of the boundary conditions on the stability of convection were sparse, and they deal mainly with horizontal layers of fluid /1–3/. Stationary, spatially periodic motions in a vertical layer with curved boundaries were investigated in /4/ for the case of free convection (when the flow was closed), and their stability was investigated in /5/. It was established that the presence of a small but finite flow of fluid along the layer leads to an increase in the number of different modes of flow, and to the appearance of non-stationary convective motions in the region near the threshold.     

Quasi-stationary solution of a problem of electrochemical copying of a cogged surface

We solve a problem of non-stationary electrochemical machining by an electrode-tool with a cogged form. For simulation of the process of anode dissolution we use a step-function for the current efficiency. We find an exact (i.e., expressed in quadratures) solution to the problem and obtain numerical results allowing to define the shape of the processed surface in various moments of time.     

Lattice-Boltzmann model for dissolution phenomena

We briefly review the modelling of complex dissolution phenomena using a lattice Boltzmann formulation. The model can describe both diffusion- and reaction-controlled dissolution of arbitrarily shaped solid phases, possibly giving rise to thermosolutal natural convection. Applications of the model are discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)