Nonlinear Liquid Research Articles

Comparison between experimental and theoretical band profiles in nonlinear liquid chromatography with a pure mobile phase

The experimental profiles obtained for large size samples in normal- and reversed-phase liquid chromatography are compared to the profiles predicted by the theory of nonlinear chromatography. When the sorption isotherms of the analytes are determined accurately, the agreement between the experimental and the theoretical profiles is quantitative in all cases. When the solvent is a mixture of a strong and a weak solvent, and if a nonselective detector is used, both the competitive adsorption isotherms of the analyte and the strong solvent should be taken into account. Then a two-component model of nonlinear chromatography must be used, and the system peaks are predicted. If a nonselective detector is used, however, which gives no response for the solvent (i.e., no system peak is detected), and the strong solvent is less strongly adsorbed than the solute studied, the elution profile of a large concentration band can be predicted with a one-compound model, knowing the adsorption isotherm of the solute from the solution. The conditions under which a single-component model can be used to predict with good or excellent agreement the profiles of large concentration bands of analyte eluted with a binary mobile phase are investigated.

Comparison between experimental and theoretical band profiles in nonlinear liquid chromatography with a binary mobile phase

Comparison between experimental and theoretical band profiles in nonlinear liquid chromatography with a binary mobile phase

Analysis of the information in a preparative chromatogram for further optimization of the operating conditions

It was demonstrated how the most salient theoretical aspects of linear and non-linear elution liquid chromatography can be used, without the aid of sophisticated optimization software, to analyse the information in a preparative chromatogram. It is important. First, to be able to recognize whether a given preparative chromatogram was obtained under volume- or mass-overload conditions or both. This permits further optimization of the injection conditions (size, volume and concentration of the sample), depending on the preparative objectives, and improvement of the stationary phase particle size and of the mobile phase flow-rate. This approach can also provide insight into the performance characteristics of the injection device, the efficiency of the column packing and the stationary phase capacity. Some examples taken from the recent literature are discussed.

Computer simulation of the separation of a two-component mixture in preparative-scale liquid chromatography

A model describing the propagation of a binary mixture at finite concentration in nonlinear liquid chromatography is discussed. This model consists of two mass balance equations, one for each solute. A finite difference method is used to derive numerical solutions of this set of nonlinear partial differential equation with boundary conditions corresponding to the elution of large concentration bands. These solutions describe the shape of the elution profiles of partially resolved compounds. Although the model used corresponds to ideal chromatography (constant equilibrium between the mobile and stationary phase, i.e., infinite column efficiency), it is possible to simulate the smoothing effect of a finite column efficiency by properly selecting the differential space element in the numerical integration. The numerical solutions appear to converge satisfactorily toward a stable solution of the system of equations provided the Courant-Friedrichs-Lewy (CFL) criterion is met in the choice of the integration parameters. The profiles obtained are very realistic and fare quite well with experimental results retrieved from the literature. Some of the results obtained are discussed in detail.

Laser-induced optical effects in a liquid suspension

A theoretical study of laser-induced optical inhomogeneity in suspensions of nonlinear (linear) particles in a linear (nonlinear) liquid is presented. Multiple scattering theory is used to determine the transmission loss and the external self-action arising from the nonlinear scattering process.

Variations of polarization of an intense optical wave in absorbing liquids in the presence of a dc electric field

For an optical wave propagating within a nonlinear liquid in which an anisotropy is induced by an external dc electric field, the influence of linear absorption on the state of polarization was studied. The distribution of the intensities of the optical field components and their phase shifts were determined by numerical methods. It was found that even a relatively weak absorption (~10−2 cm−1) drastically changes the features of a light-polarization ellipse. The absorption reduces the effect of light self-action, whereas it has no influence on the effects due to birefringence. As a consequence, the light-polarization ellipse changes its orientation in a way that does not occur in systems considered previously. For arbitrary initial conditions the rotary movement of the ellipse develops into an oscillatory one. The role of dichroism is immaterial in the systems considered.

Nonisothermal flow of a polymeric liquid under a pulsating pressure gradient

A study has been made of the effects of pressure-gradient pulsations on the nonisothermal flow of a nonlinear liquid with memory in an annular channel.

Study of peak profiles in nonlinear liquid chromatography

Un modele a quatre parametres decrit bien le profil d'elution, c'est-a-dire compte-tenu de la taille de l'echantillon, la dispersion axiale, la pente a l'origine de l'isotherme, le coefficient de tassement du pic

Non-linear parametric liquid sloshing under wide band random excitation

The stationary response of a liquid free surface, in a partially filled cylindrical container, to a wide band random parametric excitation is investigated. Two analytical approaches are employed. These are the Gaussian closure scheme to truncate the infinite hierarchy moment equations, and the Stratonovich stochastic averaging method. The validity of the two solutions is examined by comparing the two predicted probability densities with the one measured experimentally. The comparison reveals poor agreement with the Gaussian closure results in contrast to those obtained by the stochastic averaging method, which gives a good description for the random surface motion. In general, the results compare well for surface amplitudes greater than the most probable amplitude, but below the most probable amplitude there is a remarkable deviation. This deviation is found to increase as the excitation level decreases. It is concluded that the uncertainty of the experimental measurements and the inaccuracy of the experimental fitting curves are the main source of the resulting difference.

Motion of an elastoviscous liquid within a tube after removal of a pressure differential

The nonisothermal flow of a nonlinear hereditary liquid within a ring-shaped channel after instantaneous removal of a pressure differential is studied.

Non-Stationary Random Responses of Non-Linear Liquid Motion in a Cylindrical Tank

Non-Stationary Random Responses of Non-Linear Liquid Motion in a Cylindrical Tank

Application of the recursion method in the numerical solution of multidiagonal nonlinear systems

The recursion method of solving banded matrix equations is presented. End conditions are shown to be automatically incorporated in the recursion formulae thus simplifying computer programming. Application of the method to the numerical solution of the nonlinear liquid jet equations by finite differences is given as an example.

Optical-thermal induced total internal reflection-to-transmission switching at a glass-liquid crystal interface

An intensity dependent change from a state of total internal reflection to transmission of an optical beam at a nonlinear glass-nematic liquid crystal interface is observed. The effect is attributed to optically induced molecular reorientation and thermal indexing, depending on the liquid crystal used.

A system of equations of motion of a nonlinear viscoelastic liquid suitable for describing the flow of linear polymers and filled systems based on linear polymers

On the basis of the available experimental facts for simple cases of flow it is proposed that the equations of motion of linear polymers can be extended to describe the flow of filled systems. The equations of motion (1) to (4) describe in the simplest manner the nonlinear effects which are observed during the flow of a large and practically important class of nonlinear viscoelastic liquids based on linear polymers. The system of equations includes the two material constants ηo and τo and function f(ϕ, D) which must be determined experimentally. In order to refine the form of function f (ϕ, D), systematic experimental investigations into the flow of filled systems containing different amounts of the filler are required. The material constants ηo and τo and the form of the function f (ϕ, D) are determined by the structure of the system. In order to gain an understanding of the mechanism of flow and the formation of the consistency of these materials, particularly at high filler concentrations, it is necessary to investigate the dynamics and relaxation behavior of the macromolecules on a free surface and in a restricted volume.

Two-way chromatography: Flow reversal in non-linear preparative liquid chromatography

A liquid chromatographic process is described in which the mixture to be separates and the eluant are introduced alternately at either end of the colum The products are also withdrawn alternately at either end or in side-streams. Difrerent operating schemes are shown to be possible, according as the el is more, or less strongly retained by the adsorbent than the components to be separated. Experiments are presented on the ion-exchange chromatography of Na + = K + mixtures with H + as eluant. A theoretical analysis is given using the non-linear multicomponent equilibrium theory and performance criteria are determined. Both experiments and theory lead to the following salient fea of the process, which permit to distinguish it from existing, analytical or preparative chromatographic processes: the process is preparative: it treats large injections of highly concentrated components; the process is separative: it does not merely remove solutes from a solvant, it separates solutes from each other; the process is a binary split: it gives two products; thus multicomponent mixtures require several steps if complete separation is desired; the process is non-linear, as a result of the high concentrations used; the tailing of the peaks induced by the non-linearity is counteracted by recompression due to flow-reversal; the process reduces dilution and saves eluant: one of the components may be collected highly concentrated, even pure, avoiding thus secondary separation; the process requires slightly more adsorbent capacity than conven chromatography, for the same production; the process works best when the eluant is more, or less strongly retained than the components to be separated, but not intermediately; the process uses intermediate storage of part of the effluents, and their “reflux” in subsequent steps.

Nonlinear and Nonconventional Liquid Level Controllers

Nonlinear and Nonconventional Liquid Level Controllers

Motion of a nonlinear viscous liquid in a cylindrical channel under conditions of slip

Motion of a nonlinear viscous liquid in a cylindrical channel under conditions of slip

Constraints, dissipation functions and cholesteric liquid crystals

Our recently introduced dissipation function theory of molecular liquids and solids is extended to include constrained motions. Lagrangian multipliers are used in the reversible parts of the field equations of motion. Conservation laws of mass, momentum, energy and angular momentum are derived (in both the material and spatial frames) and shown to hold under the same general conditions as in the unconstrained case. Our theory is then applied to liquid crystals. Within our formalism, constitutive relations characterizing linear and nonlinear liquid crystals are given. In the linear regime, for cholesterics, depending on whether the heat flux or the temperature gradient is used in the dissipation function we show that different reciprocal relations follow. Our results for incompressible nematics and cholesterics are compared with the Ericksen-Leslie theory and others.

Motion of a nonlinear viscoelastic liquid in cylindrical channels of triangular cross section

The problem of the nonrectilinear steady-state flow of a nonlinear viscoelastic liquid in cylindrical channels is considered. It is established that in channels whose cross sections form an equilateral triangle or an isosceles right-angled triangle there are six transverse currents (eddies) in a plane perpendicular to the main longitudinal flow. In cylinders with cross sections in the form of an arbitrary triangle there may be four or six eddies, depending on the shape of the triangle.

Flow of a nonlinear viscoelastic liquid in cylindrical channels

The problem of nonrectilinear steady-state flow of a nonlinear viscoelastic liquid in an arbitrary cylindrical channel is examined. On the assumption that the cross flows are insignificant as compared with the longitudinal flows an equation of state is derived for the flow regime in question. A variational principle established for steady-state flows of the investigated media is proposed as the basis of a method of solving problems of the flow of polymer materials in arbitrary cylindrical channels. The flow of a polymer solution in rectangular channels is investigated.