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(civil engineering)
A new alignment to correct a deviation of a stream channel or bank.
The process of converting an alternating current to a unidirectional current.
The simplification and straightening of the outline of an initially irregular and crenulate shoreline through the cutting back of headlands and offshore islands by marine erosion, and through deposition of waste from erosion or of sediment brought down by neighboring rivers.
(graphic arts)
The transformation of a photograph onto a horizontal plane so as to remove or correct displacements (distortions in perspective) by tilt.


(religion, spiritualism, and occult)

Rectification is the process of adjusting the birth chart to the precise birth time in cases where the birthday is known but the birth moment is inexact or completely unknown. Rectification is accomplished by working backward from the native’s personality traits and from important events in the person’s life. In other words, an astrologer rectifying a natal chart asks the question, Given certain traits and events, what should this person’s birth chart look like?

For example, suppose someone the astrologer knows was born around sunrise. Further assume that before 7:15 a.m. on the day of birth the planet Uranus would have been in the native’s eighth house and after 7:15 it would have been in the seventh house. Uranus represents, among other things, sudden, unexpected changes. The eighth house indicates inheritance, other people’s money, and the like. The seventh house is partnership and marriage. Thus, if the individual had experienced many sudden beginnings and endings of relationships, the astrologer would infer that the person was born when Uranus was in the seventh house; if, by contrast, the individual had regularly received money from other people in sudden, unexpected ways, the astrologer would infer that the person was born when Uranus was in the eighth house. Through a reasoning process like this, applied to as many different factors as possible, the astrologer could eventually determine precisely when the native was born.


Foreman, Patricia. Computers and Astrology: A Universal User’s Guide and Reference. Burlington, VT: Good Earth Publications, 1992.
Gettings, Fred. Dictionary of Astrology. London: Routledge & Kegan Paul, 1985.



a method for separating liquid mixtures based on the division of the components of the mixture into liquid and vapor phases. In rectification, vapor and liquid are passed countercurrent to one another through a special apparatus, known as a rectification column, in which there are multiple points of contact between the two phases. Part of the liquid and vapor leaving the column is recovered after condensation, in the case of the vapor, and evaporation, in the case of the liquid. This countercurrent movement of phases is accompanied by heat and mass exchanges, which proceed at each contact stage until the phases are in equilibrium. Thus, the ascending flow of vapor is continuously enriched with the more volatile components, while the descending liquid flow is enriched with the less volatile components. With the expenditure of the same amount of heat as in distillation, rectification permits a greater extraction and enrichment in the required component or group of components. Rectification is widely used in industry and in laboratory work, often in conjunction with other separation methods, such as absorption, extraction, and crystallization.

According to Dalton’s law and the laws of Raoult, the concentration of any component i in a vapor under conditions of thermodynamic equilibrium differs from that component’s concentration in the liquid by a factor of Ki, the distribution coefficient; Ki = pi*, where pi* is the saturated vapor pressure of component i and ρ is the total pressure. The ratio of the distribution coefficients Ki and Kj of any two components is called the relative volatility and is indicated by αij. The more αij departs from unity, the easier is the separation of the components through rectification. In many cases, αij can be increased by introducing a new component, called a selective entraining agent, which will form an azeotropic mixture with certain components of the system. To this end, a solvent is added with a significantly higher boiling point than the boiling points of the components of the original mixture. The corresponding rectification processes are then called azeotropic or extractive processes. The value of αij depends on the pressure, and, as a rule, αij increases as the pressure decreases. Rectification at reduced pressures, called vacuum rectification, is especially suitable for the separation of substances that are thermally unstable.

Apparatus for rectification. The apparatus used in carrying out rectification are called rectification columns. They consist of a column in which countercurrent contact of the vapor and liquid occurs and devices in which evaporation of the liquid and condensation of the vapor occur, namely, a still and a de-phlegmator. The column is a hollow vertical cylinder, within which there are either contact devices of various design, called plates, or irregularly shaped materials, known collectively as packing. The still and dephlegmator are usually shell-and-tube heat exchangers, although tube stills and rotary evaporators also find use.

Figure 1. Diagram of plates with downcomers: (a) bubble-cap plate, (b) plate with S-shaped caps, (c) plate with flat grating; (1) base with a layer of liquid, (2) slots for the passage of vapor, (3) caps, (4) and (5) downcomers, and (6) S-shaped caps

Plates and packing are used to enlarge the vapor-liquid interface and promote contact between the liquid and vapor. As a rule, the plates are equipped with downcomers, which permit the downward passage of liquid. Three types of plates are shown in Figure 1. Rings with outer diameters equal to their height are usually used as the packing of rectification columns. The Raschig ring, together with its modifications, is the most widely used (Figure 2).

Figure 2. Various types of packing: (1) Raschig ring, (2) spiral ring, (3) Lessing ring, and (4) Pall ring

In both columns with packing and columns with plates, the kinetic energy of the vapor is used to overcome the hydraulic resistance of the contact devices and to create a dynamically dispersed vapor-liquid system with a large vapor-liquid interface. Rectification columns also exist in which mechanical energy is used to create a dispersed system through the rotation of a rotor mounted on the column’s axis. These rotor apparatus have a reduced pressure drop over height, which makes them well suited for vacuum columns.

A distinction is made between continuous and batchwise rectification based on the means of carrying out the operation. In continuous rectification, the mixture is continuously fed into the rectification column and two or more fractions, enriched in some components and depleted in others, are continuously withdrawn. A typical apparatus for continuous rectification is shown in Figure 3,a. The complete column comprises a rectifying section and a stripping section. The original mixture, usually at its boiling point, is fed into the column, where it mixes with the stripped liquid. The mixture then descends through the contact devices (plates or packing) of the stripping section countercurrent to the ascending stream of vapor. Upon reaching the bottom of the column, the liquid, which is now enriched in the least volatile components, is fed into the still. Here, the liquid partially evaporates as a result of the introduction of heat energy, and the vapor rises into the stripping section. Leaving this section, the distilled vapor then rises into the rectifying section, after which the vapor, now enriched in the most volatile components, enters the dephlegmator and is usually fully condensed by suitable cooling agents. The condensed liquid is separated into two streams: the distillate and the reflux. The distillate forms the product stream, and the reflux returns to the rectifying section and descends through the contact devices. A portion of the liquid is withdrawn from the still to form the residual liquid product stream.

Figure 3. Diagram of the streams in a rectification column: (a) continuous rectification, (b) batchwise rectification; (1) rectifying section, (2) stripping section, (3) still, and (4) dephlegmator

The ratio of the mass of reflux to that of the distillate is designated R and called the operating reflux ratio. This number is an important characteristic of rectification; the higher the number, the greater the cost of operation. The minimal expenditure required for the heating and cooling related to a particular separation can be computed with the concept of the minimum ratio, which is found by assuming that the number of contact devices or the total height of the packing approaches infinity.

If the original mixture must be separated by the continuous method into more than two fractions, a series of parallel-series connection of columns is used.

In batchwise rectification (Figure 3,b), the original liquid mixture is loaded in one batch into the still, the volume of which corresponds to the desired output. Vapors from the still enter the column and rise to the dephlegmator, where they undergo condensation. In the initial period, the entire condensate returns to the column, which corresponds to an operating mode of complete reflux. Eventually, however, the condensate is divided into reflux and distillate. As the distillate is removed, under either a constant or changing reflux ratio, the most volatile components are extracted first, followed by the components with moderate volatility, and so on. The required fraction or fractions are withdrawn into a suitable accumulator, and the operation is continued until the entire original mixture is separated.

Basis of calculations for rectification columns. From a physico-chemical viewpoint, rectification is a complex process of countercurrent heat and mass exchange between liquid and vapor phases under complicated hydrodynamic circumstances. An approach toward a mathematical description of this process has developed only with the application of digital computers.

Nevertheless, in quantitative considerations of the operation of rectification columns, the concept of the theoretical plate is usually used. A theoretical plate is understood as a hypothetical contact device in which thermodynamic equilibrium is established between the vapor and liquid phases leaving the device; that is, the concentrations of the components of these streams are related by the distribution coefficient. Any real rectification column can be represented as a column with a certain number of theoretical plates so long as the inlet and outlet streams of the theoretical column correspond in both quantity and concentration to the streams of the real column. It may be said, for example, that a given real apparatus is equivalent in efficiency to a column with, say, five or six theoretical plates. The column efficiency can be expressed on this basis as the ratio of the number of theoretical plates corresponding to this column to the actual number of plates. For packed columns, the value of the height equivalent of a theoretical plate (HETP) can be determined through the ratio of the height of the layer of packing to the number of theoretical plates to which the layer is equivalent in separating action.

The useful idea of separating the structural and hydraulic parameters from such technological parameters as the flux ratio and distribution coefficient is related to the concept of the theoretical plate. The comprehensive problem of designing a rectification column is thus separated into two simpler independent problems. The first problem involves the technological considerations for establishing the composition obtained with a fixed number of theoretical plates or finding the number of theoretical plates required to obtain the desired composition of the outlet streams. The second problem arises when it is necessary to establish the number of real plates or the height of the packing to be used in matching the desired number of theoretical plates. From a mathematical viewpoint, the first problem permits a clear formulation and reduces to the solution of an extended system of nonlinear algebraic equations (for continuous operation) or to the integration of a system of ordinary differential equations (for batchwise operation). In the case of rectification of a mixture with many components, solution is possible only with the use of a digital computer. Computers also permit calculations for complex columns, the use of which was previously hampered to some extent by the lack of precise methods of calculation. In the second, hydraulic, problem mentioned above, direct empirical correlations can be used between the values of HETP and efficiency, on the one hand, and the structure of the plate, type of packing, and hydraulic parameters (unit loads for the vapor and liquid), on the other. It is also possible to use ratios of HETP and efficiency to kinetic and diffusion parameters, such as the mass-transfer coefficient and the coefficient of effective diffusion.

The major areas for the industrial use of rectification are the production of separate fractions and individual hydrocarbons from crude petroleum in the petroleum refining and petrochemical industries and the production of ethylene oxide, acryloni-trile, caprolactam, and alkylchlorosilanes in the chemical industry. Rectification is also widely used in other areas of the national economy, for example, in nonferrous metallurgy, in the by-product coke industry, and in the timber chemistry, food-processing, and pharmaceutical industries.


Kasatkin, A. G. Osnovnye protsessy i apparaty khimicheskoi tekhnologii, 8th ed. Moscow, 1971.
Aleksandrov, I. A. Rektifikatsionnye i absorbtsionnye apparaty, 2nd ed. Moscow, 1971.
Kogan, V. B. Azeotropnaia i ekstraktivnaia rektifikatsiia, 2nd ed. Moscow, 1971.
Olevskii, V. M., and V. R. Ruchinskii. Rektifikatsiia termicheski nestoikikh produktov. Moscow, 1972.
Platonov, V. M., and B. G. Bergo. Razdelenie mnogokomponentnykh smesei: Raschet i issledovanie rektifikatsii na vychislitel’nykh mashinakh. Moscow, 1965.
Holland, C. Mnogokomponentnaia rektifikatsiia. Moscow, 1969. (Translated from English.)
Krell, E. Rukovodstvo po laboratornoi rektifikatsii. Moscow, 1960. (Translated from German.)



Vertical photograph.
Tilted photograph.
Rectified print.
i. The process of rephotographing an aerial photograph so that the effects of tilt are eliminated. The rectification of a tilted photograph taken from a given exposure station in space transforms the photograph into an equivalent vertical photograph taken from the same exposure station. Often the equivalent vertical photograph is enlarged or reduced as a part of this process.
ii. In aircraft maintenance, setting right any fault or shortfall in an aircraft or equipment.
References in periodicals archive ?
For the rectification of distorted stereo images, Son and Moon proposed accumulation-based rectification with radial distortion correction [19].
The proposed rectification method uses the inverse mapping scheme to map rectified image coordinates ( [x.sub.r] , [y.sub.r] ) onto input image coordinates (x, y).
According to the pixel-processing sequence for rectification, shown in Fig.
Thus, we propose a rectification method that uses multi-level accumulations defined as
In addition, during rectification within one row, because g([y.sub.r]) and h([y.sub.r]) are uniquely determined as constants, all of the coefficients, [b.sub.x]([y.sub.r]), [c.sub.x]([y.sub.r]), [d.sub.x]([y.sub.r]), [e.sub.x]([y.sub.r]), [f.sub.x] ([y.sub.r]) , [b.sub.y] ([y.sub.r]), [C.sub.y]([y.sub.r]), [d.sub.y] ([y.sub.r]), [e.sub.y] ([y.sub.r]), and [f.sub.y] ([y.sub.r]), are also fixed as constants according to (17) and (18).
As a result, using only simple multi-level accumulations, the proposed method produces the same rectified image with rectification using (5), (10), (11), (14), and (15).
This section presents a hardware circuit of the proposed rectification method based on multi-level accumulations explained in Section 2.
The bilinear interpolator generates the value of rectified image pixel ([x.sub.r], [y.sub.r] ), as the final output of the proposed rectification circuit.
To evaluate the proposed rectification method, we used MATLAB to model five rectification methods, described in Table 6.
Zhang et al., "Nanofluidic diode based on branched alumina nanochannels with tunable ionic rectification, " ACS Applied Materials & Interfaces, vol.
Wu et al., "Solution-pH-modulated rectification of ionic current in highly ordered nanochannel arrays patterned with chemical functional groups at designed positions, " Advanced Functional Materials, vol.
Majumdar, "Rectification of ionic current in a nanofluidic diode, " Nano Letters, vol.