AICHE Journal

A critical discussion is given of the use of local compositions for representation of excess Gibbs energies of liquid mixtures. A new equation is derived, based on Scott's two‐liquid model and on an assumption of nonrandomness similar to that used by Wilson. For the same activity coefficients at infinite dilution, the Gibbs energy of mixing is calculated with the new equation as well as the equations of van Laar, Wilson, and Heil; these four equations give similar results for mixtures of moderate nonideality but they differ appreciably for strongly nonideal systems, especially for those with limited miscibility. The new equation contains a nonrandomness parameter α₁₂ which makes it applicable to a large variety of mixtures. By proper selection of α₁₂, the new equation gives an excellent representation of many types of liquid mixtures while other local composition equations appear to be limited to specific types. Consideration is given to prediction of ternary vapor‐liquid and ternary liquid‐liquid equilibria based on binary data alone.

To obtain a semi‐theoretical equation for the excess Gibbs energy of a liquid mixture, Guggenheim's quasi‐chemical analysis is generalized through introduction of the local area fraction as the primary concentration variable. The resulting universal quasi‐chemical (UNIQUAC) equation uses only two adjustable parameters per binary. Extension to multicomponent systems requires no ternary (or higher) parameters.

The UNIQUAC equation gives good representation of both vapor‐liquid and liquid‐liquid equilibria for binary and multicomponent mixtures containing a variety of nonelectrolyte components such as hydrocarbons, ketones, esters, amines, alcohols, nitriles, etc., and water. When well‐defined simplifying assumptions are introduced into the generalized quasi‐chemical treatment, the UNIQUAC equation reduces to any one of several well‐known equations for the excess Gibbs energy, including the Wilson, Margules, van Laar, and NRTL equations.

The effects of molecular size and shape are introduced through structural parameters obtained from pure‐component data and through use of Staverman's combinatorial entropy as a boundary condition for athermal mixtures. The UNIQUAC equation, therefore, is applicable also to polymer solutions.

A simple technique is described for calculating the adsorption equilibria for components in a gaseous mixture, using only data for the pure‐component adsorption equilibria at the same temperature and on the same adsorbent. The proposed technique is based on the concept of an ideal adsorbed solution and, using classical surface thermodynamics, an expression analogous to Raoult's law is obtained. The essential idea of the calculation lies in the recognition that in an ideal solution the partial pressure of an adsorbed component is given by the product of its mole fraction in the adsorbed phase and the pressure which it would exert as a pure adsorbed component at the same temperature and spreading pressure as those of the mixture. Predicted isotherms give excellent agreement with experimental data for methane‐ethane and ethylene‐carbon dioxide on activated carbon and for carbon monoxide‐oxygen and propane‐propylene on silica gel. The simplicity of the calculation, which requires no data for the mixture, makes it especially useful for engineering applications.

A group‐contribution method is presented for the prediction of activity coefficients in nonelectrolyte liquid mixtures. The method combines the solution‐of‐functional‐groups concept with a model for activity coefficients based on an extension of the quasi chemical theory of liquid mixtures (UNIQUAC). The resulting UNIFAC model (UNIQUAC Functional‐group Activity Coefficients) contains two adjustable parameters per pair of functional groups.

By using group‐interaction parameters obtained from data reduction, activity coefficients in a large number of binary and multicomponent mixtures may be predicted, often with good accuracy. This is demonstrated for mixtures containing water, hydrocarbons, alcohols, chlorides, nitriles, ketones, amines, and other organic fluids in the temperature range 275° to 400°K.

Phân tích thành phần chính phi tuyến (NLPCA) là một kỹ thuật mới cho phân tích dữ liệu đa biến, tương tự như phương pháp phân tích thành phần chính (PCA) nổi tiếng. NLPCA, giống như PCA, được sử dụng để xác định và loại bỏ các mối tương quan giữa các biến vấn đề nhằm hỗ trợ giảm chiều, trực quan hóa và phân tích dữ liệu khám phá. Trong khi PCA chỉ xác định các mối tương quan tuyến tính giữa các biến, NLPCA phát hiện cả các mối tương quan tuyến tính và phi tuyến, không bị giới hạn bởi đặc điểm của các phi tuyến trong dữ liệu. NLPCA hoạt động bằng cách huấn luyện một mạng nơ-ron feedforward để thực hiện ánh xạ đồng nhất, trong đó đầu vào của mạng được tái hiện ở lớp đầu ra. Mạng này chứa một lớp “nút thắt” nội bộ (chứa ít nút hơn so với các lớp đầu vào hoặc đầu ra), buộc mạng phải phát triển một biểu diễn gọn gàng của dữ liệu đầu vào và hai lớp ẩn bổ sung. Phương pháp NLPCA được trình bày qua dữ liệu phản ứng lô mô phỏng theo thời gian. Kết quả cho thấy NLPCA thành công trong việc giảm chiều và tạo ra bản đồ không gian đặc trưng tương tự như phân bố thực tế của các tham số hệ thống tiềm ẩn.

Models are presented for determining flow regime transitions in two‐phase gas‐liquid flow. The mechanisms for transition are based on physical concepts and are fully predictive in that no flow regime transitions are used in their development. A generalized flow regime map based on this theory is presented.

The splitting of globules is an important phenomenon during the final stages of disintegration processes. Three basic types of deformation of globules and six types of flow patterns causing them are distinguished.

The forces controlling deformation and breakup comprise two dimensionless groups: a Weber group N_We and a viscosity group N_Vi. Breakup occurs when N_We exceeds a critical value (N_We)_crit. Three cases are studied in greater detail: (a) Taylor's experiments on the breakup of a drop in simple types of viscous flow, (b) breakup of a drop in an air stream, (c) emulsification in a turbulent flow.

It is shown that (N_We)_crit depends on the type of deformation and on the flow pattern around the globule. For case (a) (N_We)_crit shows a minimum value ∼ 0.5 at a certain value of (N_Vi) and seems to increase indefinitely with either decreasing or increasing ratio between the viscosites of the two phases. For case (b) (N_We)_crit varies between 13 and ∞, depending on N_Vi and on the way in which the relative air velocity varies with time, the lowest value refers to the true shock case and N_vi→0. For case (c) (N_We)_crit, which determines the maximum drop size in the emulsion, amounts to ∼1, and the corresponding values of N_Vi appear to be small. A formula is derived for the maximum drop size.

Most models for fixed bed adsorbers have used either the homogeneoussolid or pore diffusion model for the pellets. When the adsorption isotherm is linear, the two models can lead to identical breakthrough curves. The conditions for this equivalence are presented here. It is shown that one of the bulk flow factors that was included in the formulation of one pore diffusion model will be significant only for feedstreams containing a relatively high concentration of adsorbate. The prosity factor of the pore model is shown to be very important, especially as the porosity decreases. The importance of the two diffusional models with respect to the predicted breakthrough curves is demonstrated. For comparable beds, it is shown that the breakthrough curve based on the homogeneous model is delayed with respect to that based on the pore model at early times, regardless of the shape of the isotherm. Finally, the various possible solutions for an irreverisble isotherm are reviewed for each of the models, and a solution is presented for the general case of a pore model with an outside film resistance.

This study deals with boundary‐layer flow on continuous solid surfaces. Flow of this type represents a new class of boundary‐layer problems, with solutions substantially different from those for boundary‐layer flow on surfaces of finite length. In this paper the boundary‐layer behavior on continuous surfaces is examined, and the basic differential and integral momentum equations of boundary‐layer theory are derived for such surfaces. In subsequent papers these equations will be solved for the boundary layer on a moving continuous flat surface and a moving continuous cylindrical surface, for both laminar and turbulent flow in the boundary layer.