Second-order Stokes solutions for internal waves in three-layer density-stratified fluid

In this paper, internal waves in three-layer stratified fluid are investigated by using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory. As expected, the first-order solutions are consistent with ordinary linear theoretical results, and the second-order solutions describe the second-order modification on the linear theory and the interactions between the two interfacial waves. Both the first-order and second-order solutions derived depend on the depths and densities of the three-layer fluid. It is also noted that the solutions obtained from the present work include the theoretical results derived by Umeyama as special cases.

Second-order solutions for random interfacial waves under steady uniform currents

In the present research, the study of Song (2004) for random interfacial waves in two-layer fluid is extended to the case of fluids moving at different steady uniform speeds. The equations describing the random displacements of the density interface and the associated velocity potentials in two-layer fluid are solved to the second order, and the wave-wave interactions of the wave components and the interactions between the waves and currents are described. As expected, the extended solutions include those obtained by Song (2004) as one special case where the steady uniform currents of the two fluids are taken as zero, and the solutions reduce to those derived by Sharma and Dean (1979) for random surface waves if the density of the upper fluid and the current of the lower fluid are both taken as zero.

Second-order solutions for random interfacial waves in N-layer density-stratified fluid with steady uniform currents

In the present paper, the random inter facial waves in N-layer density-stratified fluids moving at different steady uniform speeds are researched by using an expansion technique, and the second-order a symptotic solutions of the random displacements of the density interfaces and the associated velocity potentials in N-layer fluid are presented based on the small amplitude wave theory. The obtained results indicate that the wave-wave second-order nonlinear interactions of the wave components and the second-order nonlinear interactions between the waves and currents are described. As expected, the solutions include those derived by Chen (2006) as a special case where the steady uniform currents of the N-layer fluids are taken as zero, and the solutions also reduce to those obtained by Song (2005) for second-order solutions for random interfacial waves with steady uniform currents if N=2.

Second-order Stokes wave solutions for intefacial waves in three-layer stratified fluid with background current

In this paper, interfacial waves in three-layer stratified fluid with background current are investigated using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory, and the Kelvin-Helmholtz instability of interfacial waves is studied. As expected, for three-layer stratified fluid with background current, the first-order asymptotic solutions (linear wave solutions), dispersion relation and the second-order asymptotic solutions derived depend on not only the depths and densities of the three-layer fluid but also the background current of the fluids, and the second-order Stokes wave solutions of the associated elevations of the interfacial waves describe not only the second-order nonlinear wave-wave interactions between the interfacial waves but also the second-order nonlinear interactions between the interfacial waves and currents. It is also noted that the solutions obtained from the present work include the theoretical results derived by Chen et al (2005) as a special case. It also shows that with the given wave number k (real number) the interfacial waves may show Kelvin-Helmholtz instability.

A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system

This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters: the nonlinearity ratio epsilon, represented by the ratio of amplitude to depth, and the dispersion ratio mu, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin et al in the study of the surface waves when considering the order up to O(mu(2)). As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin et al for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.

Biosorption of Cr(VI) from aqueous solutions by nonliving green algae Cladophora albida

Biosorption of Cr(VI) from aqueous solutions by nonliving green algae Cladophora albida was investigated in batch experiments. The influence of pH, algal dosage, initial Cr(VI) concentration, temperature and coexisting anions on removal efficiencies of C. albida was studied. Cr(VI) removal process was influenced significantly by the variation of pH, and the optimum pH was chosen at a range of 1.0-3.0. The optimum algal dosage 2 g/L was used in the experiment. The removal rate of Cr(VI) was relatively rapid in the first 60 min, but then the rate decreased gradually. Removal mechanism was studied by analyzing Cr(VI) and total Cr in the solution. Biosorption and bioreduction were involved in the Cr(VI) removal. Biosorption of Cr(VI) was the first step. followed by Cr(VI) bioreduction and Cr(III) biosorption on the algal biomass. Actual industrial wastewater was used to evaluate the practicality of the biomass C. albida. From a practical viewpoint, the abundant and economic biomass C. albida could be used for removal of Cr(VI) from wastewater by the reduction of toxic Cr(VI) to less toxic Cr(III). (C) 2008 Elsevier Ltd. All rights reserved.

Biosorption of copper(II) from aqueous solutions by green alga Cladophora fascicularis

Biosorption is an effective means of removal of heavy metals from wastewater. In this work the biosorption behavior of Cladophora fascicularis was investigated as a function of pH, amount of biosorbent, initial Cu2+ concentration, temperature, and co-existing ions. Adsorption equilibria were well described by Langmuir isotherm models. The enthalpy change for the biosorption process was found to be 6.86 kJ mol(-1) by use of the Langmuir constant b. The biosorption process was found to be rapid in the first 30 min. The presence of co-existing cations such as Na+, K+, Mg2+, and Ca2+ and anions such as chloride, nitrate, sulfate, and acetate did not significantly affect uptake of Cu2+ whereas EDTA substantially affected adsorption of the metal. When experiments were performed with different desorbents the results indicated that EDTA was an efficient desorbent for the recovery of Cu2+ from biomass. IR spectral analysis suggested amido or hydroxy, C=O, and C-O could combine strongly with Cu2+.

Biosorption of copper (II) and lead (II) from aqueous solutions by nonliving green algae Cladophora fascicularis: Equilibrium, kinetics and environmental effects

Biosorption of Cu2+ and Pb2+ by Cladophora fascicularis was investigated as a function of initial pH, initial heavy metal concentrations, temperature and other co-existing ions. Adsorption equilibriums were well described by Langmuir and Freundlich isotherm models. The maximum adsorption capacities were 1.61 mmol/ g for Cu2+ and 0.96 mmol/ g for Pb2+ at 298K and pH 5.0. The adsorption processes were endothermic and biosorption heats calculated by the Langmuir constant b were 39.0 and 29.6 kJ/ mol for Cu2+ and Pb2+, respectively. The biosorption kinetics followed the pseudo- second order model. No significant effect on the uptake of Cu2+ and Pb2+ by co-existing cations and anions was observed, except EDTA. Desorption experiments indicated that Na(2)EDTA was an efficient desorbent for the recovery of Cu2+ and Pb2+ from biomass. The results showed that Cladophora fascicularis was an effective and economical biosorbent material for the removal and recovery of heavy metal ions from wastewater.

The inhibition of mild steel corrosion in 1 M hydrochloric acid solutions by triazole derivative

The title compound 1-(4,5-dihydro-3-phenylpyridine-1-yl)-2-(1H-1,2,4-triazole-1-yl)ethyl ketone (DTE) was synthesized and its inhibiting action on the corrosion of mild steel in 1 M hydrochloric acid solutions was investigated by means of weight loss, potentiodynamic polarization, electrochemical impedance spectroscopy (EIS) and scanning electronic microscope (SEM). Results obtained revealed that DIE performed excellently as a corrosion inhibitor for mild steel in 1 M hydrochloric acid media and its efficiency attains more than 90.9% at 1.0 x 10(-3) M at 298 K. Polarization curves indicated that the inhibitor behave mainly as mixed-type inhibitor. EIS showed that the charge transfer controls the corrosion process in the uninhibited and inhibited solutions. Adsorption of the inhibitor on the mild steel surface followed Langmuir adsorption isotherm. And the values of the free energy of adsorption Delta G(ads) indicated that the adsorption of DTE molecule was a spontaneous process and was typical of chemisorption. (c) 2008 Elsevier B.V. All rights reserved.

Removal of endotoxin from human serum albumin solutions by hydrophobic and cationic charged membrane

A novel matrix of macropore cellulose membrane was prepared by chemical graft, and immobilized the cationic charged groups as affinity ligands. The prepared membrane Fan be used for the removal of endotoxin from human serum albumin (HSA) solutions. With a cartridge of 20 sheets affinity membrane of 47 mm diameter, the endotoxin level in HSA solution can be reduced ro 0.027 eu/mL. Recovery of HSA was over 95%.