Tromp curve

Definitions. The performance of a hydrocyclone is generally characterised by means of a grade efficiency or Tromp-curve which is the fractional mass recovery expressed as a function of particle size. 

The Tromp-curve for the removal of coarse particles with the underflow is defined by ... 

Probable error (Ecart probable moyen) Measure of separating efficiency of a separator (jig, cyclone, etc.). Calculated from a Tromp curve. 

Tromp curve (partition curve, distribution curve) Most widely used method of determining graphically the value of as a measure of separation efficiency. Synonyms partition curve, distribution curve. 

The best known means of investigating and predicting theoreticalbeneficiationresnlts are the so-called washabil-ity cnrves, which represent graphically the experimental separation data obtained nnder ideal conditions in so-called float-sink tests. Float-and-sink analysis is also used to determine the Tromp curve, which measures the practical results of a density separation. The practical results of separation can then be compared with the ideal and a measure of efficiency calculated. 

The curves are plotted according to European convention and represent the percent of feed reporting to reject. In American practice, Tromp curves usually give the percent of feed reporting to washed coal. 

The Tromp curve from the mathematical point of view is a cumulative distribution curve and as such can be linearized on probability graph paper. Such anamorphosis is produced by plotting the partition coefficients on a probability scale versus specific gravity on a linear scale (Fig. 22b) for dense-media separation, and versus log 8 - 1) for jigs. 

Gravity sedimentation equipment, hydrocyclones, sedimenting centrifuges or flotation cells have also been extensively used in mineral processing for separation of minerals according to density or affinity to water. In such separations, the efficiency is expressed by the Tromp curve which, similar to the grade efficiency curve, shows probability of separation as a function of material density or mineral composition. The steepness of the curve is a measure of the sharpness of the separation. 

For any separator with a size-dependent performance, such as a hydrocyclone, a sedimenting centrifuge or a settling vessel, the grade efficiency varies with particle size, and a graphical representation of this is called the grade efficiency curve (see section 3.2.2). As the value of the grade efficiency has the character of probability, it is sometimes referred to as the partition probability the curve then becomes the partition probability curve or Tromp curve. 

The selectivity (separation efficiency) is characterized by what percentage of a given particle size in the classifier feed is discharged in the tailings. Plotted against particle size, it appears as a curve (separation curve, Tromp curve) representing the so-called classifier selectivity function (Fig. 32a). 

Fig. 3. Castle Cement (Ribblesdale) Cement Mills 9 and 10, SD 120 elassifier Tromp Curves for O.P.C. (3600 Blaine)...

Typical tromp curves as achieved by the separator are given in Figure 3. 

Figure 5.3. The basic steps for generating a Tromp s curve to evaluate the efficiency of an elutriator. a) Size distribution of the (xjwder sample, b) Size distributions of the undersize and oversize from the elutriator. c) Tromps curve for the elutriator spans the size range between the lower limit of the oversize fraction and the upper limit of the undersize fraction. The Index of Fractionation Efficiency is the ratio of the values x25nt75.

In practical terms the cut size fractionation of an elutriator is never a clean cut fractionation and the oversize fraction often contains some of the particles smaller than the cut size and vice-versa. In industrial situations the efficiency of an elutriative fractionation is measured by what is known as a coarse grade-efficiency curve. This curve is often referred to as Tromp s curve after its originator [3]. To be able to calcu-... 

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