Modelling of a single drop impact onto liquid film using particle method

The process of single liquid drop impact on thin liquid surface is numerically simulated with moving particle semi‐implicit method. The mathematical model involves gravity, viscosity and surface tension. The model is validated by the simulation of the experimental cases. It is found that the dynamic processes after impact are sensitive to the liquid pool depth and the initial drop velocity. In the cases that the initial drop velocity is low, the drop will be merged with the liquid pool and no big splash is seen. If the initial drop velocity is high enough, the dynamic process depends on the liquid depth. If the liquid film is very thin, a bowl‐shaped thin crown is formed immediately after the impact. The total crown subsequently expands outward and breaks into many tiny droplets. When the thickness of the liquid film increases, the direction of the liquid crown becomes normal to the surface and the crown propagates outward. It is also found that the radius of the crown is described by a square function of time: r_C = [c(t ? t₀)]^0.5. When the liquid film is thick enough, a crown and a deep cavity inside it are formed shortly after the impact. The bottom of the cavity is initially oblate and then the base grows downward to form a sharp corner and subsequently the corner moves downward. Copyright © 2004 John Wiley & Sons, Ltd.     

A mathematical model of the ring-spinning process

This paper develops a mathematical model of the ring-spinning process that takes into account its non-stationary nature. A complex system of differential equations is obtained, which from a mathematical point of view constitutes a ‘free-boundary’ problem. Its solution involves definition of suitable boundary conditions related to the mechanical characteristics of the process and of the spinning machine itself. The boundary conditions which determine the solution are pointed out. A numerical solution of the system of differential equations can be obtained by the Finite-Segments method, as shown in an example.     

Nuclear spin-lattice relaxation mechanisms in kaolinite confirmed by magic-angle spinning

Spin-lattice relaxation mechanisms in kaolinite have been reinvestigated by magic-angle spinning (MAS) of the sample. MAS is useful to distinguish between relaxation mechanisms: the direct relaxation rate caused by the dipole-dipole interaction with electron spins is not affected by spinning while the spin diffusion-assisted relaxation rate is. Spin diffusion plays a dominant role in ¹H relaxation. MAS causes only a slight change in the relaxation behavior, because the dipolar coupling between ¹H spins is strong. ²⁹Si relaxes directly through the dipole-dipole interaction with electron spins under spinning conditions higher than 2 kHz. A spin diffusion effect has been clearly observed in the ²⁹Si relaxation of relatively pure samples under static and slow-spinning conditions. ²⁷Al relaxes through three mechanisms: phonon-coupled quadrupole interaction, spin diffusion and dipole-dipole interaction with electron spins. The first mechanism is dominant, while the last is negligibly small. Spin diffusion between ²⁷Al spins is suppressed completely at a spinning rate of 2.5 kHz. We have analyzed the relaxation behavior theoretically and discussed quantitatively. Concentrations of paramagnetic impurities, electron spin-lattice relaxation times and spin diffusion rates have been estimated.     

Dynamic Interfacial Tension Behavior of Water/Oil Systems Containing In situ-Formed Surfactants

Time-dependent interfacial tension (IFT) has been investigated for an interfacially reactive immiscible system composed of model-acidified oil and alkaline water. The acidified oil was composed of either lauric acid or linoleic acid dissolved in n-dodecane. Drop volume tensiometry was employed to measure the interfacial tension between the two phases. In the case of lauric acid, the IFT value was found to decrease sharply with increasing alkali concentration, even at low drop formation times. In the case of linoleic acid, the IFT decrease with the drop formation time was more gradual, especially at low alkali concentration. The rate of formation of the interfacial area was also found to be dependent on alkali concentration.     

The effects of the column pressure drop on retention and efficiency in packed and open tubular supercritical fluid chromatography

The effects of the pressure drop across the column on retention and efficiency in SFC have been studied. Numerical methods are described which enable the prediction of hold-up time and pressure drop in both packed and open tubular columns. Predictions of both hold-up time and pressure drop are in good agreement with experimental data. The density gradient along the column can be calculated using the numerical methods and a procedure is described which enables the calculation of the overall capacity factors of the solutes from the density profile in the column. Significant variations of the capacity factor are observed along the column. The effect of the density gradient along the column on local diffusivity and dispersion is studied. The column efficiency in systems with significant pressure drops is affected by changes in: the linear velocity of the mobile phase; the diffusion coefficients; and the capacity factors of the solutes along the column. The overall efficiency of the chromatographic system can be calculated if, as is the case for open tubular columns, adequate plate height equations are available.     

A Home-made Simple Set-up for Measurement of Electrochemical Surface Tension Spectrum on a Mercury Drop Electrode

A setup for recording surface tension curves at a mercury drop during potential scanning is designed based on photo-sensitive detection system. Surface tension spectrum at Hg drop can be recorded by voltammetric study. A Yb(III)-NO2- catalytic reduction system was used for characterization. The simple, sensitive technique can be expected to provide fresh information on molecular interactions at electrode surfaces.     

稳态双曲流场中液/液混合的粘性液滴哑铃分散模型

通过对稳态双曲流场中液／液混合体系分散相液滴所受分散作用力的分析，建立了粘性液滴的哑铃分散模型．趋于将两粘性液滴分开的分散作用力与粘度比、流场类型和强度、液滴半径、哑铃取向和尺寸有关．该模型解释了流场类型与分散作用的关系．流场类型对液滴的分散具有很大影响，在纯应变拉伸流场中分散作用力是简单剪切流场中的两倍，因而对于液滴的分散，拉伸流场较简单剪切流场更有效，这与以前的实验结论符合．当体系粘度比趋于无穷大时本模型转化为刚性哑铃分散模型     

The melt hollow fiber spinning process: steady-state behavior,sensitivity and stability

The rheology of the melt hollow fiber spinning process is examined in the thin filament limit. The resulting thin filament equations are also applicable to single-phase and two-phase extensional flows. Using a novel numerical solution procedure, the sensitivity of the fiber spinning equations to material property and process variations is investigated. Fiber geometry is directly controlled by the mass flowrates of the core and clad fluids while the spinline tension is most strongly influenced by clad viscosity. A maximum can occur in the clad stress profile if a core liquid is used and the ratio of core to clad viscosity increases greatly with temperature. Isothermal spinning of high viscosity clad liquids with either a core gas or liquid is unstable for draw ratios greater than 20.2 as found for solid fibers.     

Voltammetric Behavior of Arsenic(III) in the Presence of Sodium Diethyl Dithiocarbamate and Its Determination in Water and Highly Saline Samples by Adsorptive Stripping Voltammetry

This paper describes the voltammetric behavior of As(III) at the hanging mercury drop electrode (HMDE) in the presence of sodium diethyl dithiocarbamate (SDDC) and a new voltammetric method for the determination of As(III) at trace levels. The method is based on the adsorptive deposition of a As(III) complex with SDDC at ?0.45 V (vs. Ag/AgCl) on the HMDE in acidic medium of 0.01 mol L^?1 HCl (pH 2.0) and its cathodic stripping during the potential scan (100 mV s^?1). The linear range for the determination of As(III) in the presence of SDDC (4 μmol L^?1) in water samples was between 1 and 10 μg L^?1 for a deposition time of 300 s (r=0.994) and between 10 and 100 μg L^?1 for a deposition time of 60 s (r=0.999). For the determination of As(III) in dialysis concentrate samples, the linear range was between 5 and 25 μg L^?1 for a deposition time of 180 s (r=0.992) and between 10 and 100 μg L^?1 for a deposition time of 60 s (r=0.996). Detection limits of 0.3 and 2.2 μg L^?1 in water and dialysis concentrate samples were calculated for the method using a deposition time of 300 and 180 s, respectively. Recovery values between 93.0 and 110.0% for As(III) added to deionized, mineral, seawater (synthetic and real) and dialysis concentrate samples prove the satisfactory accuracy and applicability of the procedure.     

Erosion of efficiency in non-uniform linear chromatography

In linear chromatography (i.e. chromatography performed in the absence of sample overloading), when the plate height of a column is roughly uniform along its length, variations in the velocities of solutes are the only possible causes of erosion of efficiency. The sources of these variations (variations in capacity ratio and in the density of the mobile phase, etc.) play no direct role in the erosion of efficiency except through their effect on solute velocities. In other words, what eventually causes the erosion of efficiency is merely variation in the time required for solutes to traverse equally small segments of a column. Significant erosion can only arise from abrupt and deep deceleration of solutes in one or several relatively small segments of a column. If erosion of efficiency caused by pressure gradients in linear SFC is to be large, the depth and the sharpness of the deceleration of a solute must go beyond that hitherto confirmed experimentally. Many relevant examples are analyzed graphically.