The development of every new metallurgical method is accompanied by a host of contradictory statements and widely differing opinions, but it is only by the elimination and correlation of parts of recorded observations that a particular process approaches a state of perfection. The theory of flotation has called forth a number of articles, each writer applying a different hypothesis in explaining the puzzling phenomena accompanying the process.

Of the various hypotheses thus far advanced only two are based on principles of sufficiently apparent soundness to warrant serious consideration.

The first of these involves the physical surface phenomena that may produce an inter-facial tension. This has, until recently, been accredited with more importance than all the other explanations combined. The second is called the electrical theory.

The part that surface phenomena may play in linking the particles of ore to the bubble-carriers is ably outlined by O. C. Ralston, whose treatment of this phase of the question includes reference to about all of the theory that has so far been found applicable to flotation. Without doubt a proper application of the laws of physical chemistry will disclose fundamental principles upon which this process may be based, and it may be in the field of colloidal chemistry that most information is to be gained.

With regard to the electrical theory, however, there has been applied a number of laws of electrostatics that, from the general nature of conditions under which flotation is carried out, would seem to be inoperative.

This hypothesis has been tolerated by Mr. Ralston, it is strongly advocated by J. M. Callow, while Thos. M. Bains, Jr., excludes all other theories. These three references contain the gist of all arguments advanced in support of this hypothesis, and the last of them elaborates and definitely formulates the necessary requirements for flotation by electrical means. It is my object to attempt an analysis of the various arguments advanced in support of the electrical theory, and as the only difference between this and any other theory lies in the phenomena that cause the bond between the flotative mineral and the bubble-carrier, it is understood that only this phase of the process is under discussion. It is necessary, however, in order to arrive at practical conclusions, that this question be considered under conditions similar to those encountered in practice.

Before proceeding to a discussion of the electrical theory of flotation it will be necessary to point out briefly a few of the facts of electrostatics upon which it is based.

• A. The production of electricity by friction is a common phenomenon ; almost any two bodies become electrified if they are rubbed together. In the case of several substances, considerable force is then necessary in order to separate them. Attraction or repulsion also occurs when an electrified body is brought near bodies that have been subjected to friction and if these are light enough (as bits of pitch, feathers, wood, paper, etc.) they may be lifted. Bodies may also become electrified by coming in contact with other bodies that already carry a charge. In this case the first body receives electricity of the same sign from the charged body and is then repelled.
• B. Bodies that when electrified at one point are immediately electrified all over are called good conductors; those over which the charge diffuses slowly are poor conductors. All metals, many metallic ores, graphite, ordinary undistilled water, and aqueous solutions of salts are good conductors.
• C. If a piece of metal, or other conducting material held in the hand is rubbed against a non-conductor—say, a piece of dry flannel— only the non-conductor appears afterward to be electrified. The reason is that the electrification produced on the metal spreads over the hand, arm, and body of the experimenter to the floor and walls of the room. If, however, the conductor be insulated, the degree of its electrification cannot be increased or decreased.
• D. By whatever process a body is electrified there is always an equal amount of electricity of the opposite sign, which may reside upon the walls of the enclosing room or upon some other surface insulated from the conductor. Bodies carrying opposite charges, when brought in contact or connected by a conductor, become discharged. If the charges are equal they are neutralized, but if one carries more than the other the system takes on the sign of the excess charge.
• E. If these bodies are strongly electrified, discharge can take place through an appreciable thickness of non-conducting material, such as air, oil, or glass. This discharge is facilitated by the presence of sharp projections upon either body.
• F. (a) The space between two charged bodies is filled with lines of force that tend to move a contained body in the direction of the local lines of force leading to the surface carrying the opposite sign.
  (b) These lines of force do not penetrate the surface of the conductors forming its boundaries and a hollow conductor is electrified on its outside or inside surface only, depending upon whether the opposite charge resides upon one contained without the sphere or upon one contained within and insulated from the shell. In the latter case the entire field is contained within the inner surface of the sphere, and in the former case there is no charge within the hollow conductor.
• G. The force exerted between two small charged bodies is given in the equation F= qq¹/d² in which q and q¹ are the charges in electrostatic units carried by each of the two bodies, and d is the distance between their centres of charge. If the bodies are separated by a medium other than air a factor K, known as its dielectric coefficient, must be used, and the equation becomes F = 1/k • qq¹/d²
• H. Matter itself is not acted upon by an electric force, which acts only between different quantities of electricity. When a conductor is introduced into an electric field it represents a gap or an interruption of the lines of force, resulting in an electrification of its surfaces only, that part becoming positive which is presented toward the negative boundary of the field and the reverse. In other words, the original field is divided into two. This same effect is produced in the case of a poor conductor but to an exceedingly small degree. This explains the attraction of small bodies by another that has been electrified by friction, in which case electrification by influence precedes attraction, and what is really observed is attraction between opposite electric charges.

Before considering these fundamental laws of electrostatics in connection with an explanation of flotation phenomena, it may be well to consider briefly the conditions under which different phases of this process take place.

Of first importance is the fact that all operations are carried out in conducting solutions which in every case are earthed. It is inconceivable that, after any grinding process has been applied in machines such as are commonly used, the individual positively charged particles of ore should not have come in contact with negatively charged bodies and with conducting parts of grinding and mixing machinery, even if oil has been added in a preliminary stage. The ore particles are conductors, the oil is a non-conductor, the bubbles are filled with non-conducting air, and the gangue is composed of non-conducting material.

These conditions being granted, the next step will be to apply the laws of electrostatics to criteria for flotative conditions according to the electrical theory, as summarized by Mr. Bains. These include the main ideas of Mr. Callow’s article and of the theory in general, so that a discussion of these in order will apply to the various other articles advancing a similar hypothesis.

1. “Ores containing valuable minerals or metals that are good conductors are the only ones that are suitable for flotation.”
   This seems in general to be true, but the ratio of flotative tendency to conductivity of the different ore constituents is nothing like a constant. For instance, the conductivity of galena is to the conductivity of chalcocite as 35:1. Their flotative tendencies hardly bear this ratio.
   In entire opposition to this supposed requirement I found that small pieces of diamond attract a grease or oil coating and attach to bubbles quite as readily as does galena.
2. “To buoy these conductors, it is necessary to supply enough electrified bubbles from below to float particles of the conductors that are attracted; hence the smaller the bubble, the better the result, the amount of gas being the same.”

A bubble within a solution of various salts and acids presents a similar condition to that of the air-space within a hollow conducting sphere. It is known (see F (b) above) in this case that in order to have a charge upon this inner surface it is necessary that an opposite charge be maintained within and insulated from it. In the case of the bubble there is nothing inside to carry the charge. In case this space carried water-vapor or ionized gases, a charge could be present, but it would be dissipated quickly by diffusion of these charged particles and resulting contact with the water-surface.

If this sphere did contain charged gases and was lined with oil, there would be present the condition of the hollow conducting spheres, (F (b)) with enclosed charged conductor insulated from it, and carrying an opposite charge. The charges would be equal and the amount governed by the charge on the inside sphere. These charges being balanced, the bubble system could have no influence upon a body— charged or not—without the outer sphere, such as a particle of galena suspended in the water at a distance. There can be no attraction through the intervening conductor, as lines of force will not penetrate a conducting surface.

It appears evident then that, first, unless a bubble contains charged bodies (ionized gas, water-vapor, or solid) within its bounding sphere it can carry no charge; second, that unless it is lined with a dielectric the charge will be rapidly dissipated; and, third, even though a charge is present and insulated from the outer conducting sphere it can have no attraction for any body or charge without the outer sphere, through a thickness of solution.

3. “Some dielectric fluid is necessary to cover the conductor or the bubble, to prevent the dissipation of the electric charge. The thinner the film of dielectric and the greater its dielectric strength the greater the attractive force and the more permanent will be the froth.”

The bubble, both insulated and otherwise, has been considered. The particle of ore, unless insulated, will be immediately discharged by coming in contact with a grounded conductor—the solution. It is immaterial whether the opposite charge is carried by the water or by some other surface, the effect will be the same. Assume, however, that the ore particle is charged, and insulated. Again we have the case of one charged conductor (the ore) being enclosed within another (the surrounding water solution) giving a system which is neutral with regard to any other charge or system without the outer sphere.

Under conditions electro-statically ideal these forces may be pictured as in Fig. 79. Both bodies are charged and insulated, and suspended in an intervening conducting medium. The systems ore- oil-water, and gas-oil-water, are without effect upon each other.

In case the gas is generated from the ore the particle could not be insulated unless by some phenomenon not understood at present. If the gas is air passed mechanically into the pulp it would be forced into contact with ore particles, in which case the charges carried by each would have its effect upon the other. That a mass of air containing charged vapor or gases could be insulated before coming in contact with the conducting solution is not reasonable.

Assuming, however, that both bodies are charged, so that the second part of No. 3 (above) regarding the thickness of insulation may now be considered. It has been proved that the force exerted by a charged sphere acts as if it was concentrated at the centre. Bearing this in mind it is evident that in the case of particles of the size with which flotation deals, a separation of their surfaces by one micron or one millimetre will produce little practical difference in the force exerted between them.

4. “Some material must be added to the water to increase its conductivity, to obtain a clean concentrate; acids in small amounts are now used.”

This factor has been considered under divisions 2 and 3. The working solution is a conductor, parts of which are interposed between the various charged particles, thereby breaking all lines of force between them.

In any attempt to determine experimentally whether or not electrostatic forces play any considerable part in holding the bubble and particles of ore together it is rather difficult to select tests which will give results of value. If these forces act to the exclusion of all others it is evident that they would be represented by charges of easily measurable magnitude. For example, I have separated particles of galena, (uncoated with oil) that have been carried to the top of an acid solution, weighing 60 mg. (52 mg. in water). To hold a particle of this size to the surface of a bubble requires 50.9 dynes—call it 50 in round numbers. The diameter of this particle is about 2 milli metres. The bubble required to buoy this particle must displace at least 52 mg. water or in other words its volume must be 52 mm³. Its diameter would be about 5.2 mm. Using these figures the equation for force becomes 52 (dynes) = QQ¹/12.96 or assuming the charges to be balanced

Q² = 673.92
Q = 25.9 c. g. s. electrostatic units.

It is not likely that a particle of ore or a bubble of the nature given can have a charge of this magnitude, for the reason that a potential of this intensity would discharge through a very strong dielectric. Experiments have been carried out that give ratios for electro-static units, potentials, and distance through which discharge will take place in air, using brass knobs of one centimetre diameter.

According to these figures the charge necessary to exert a force of 50 dynes in lifting a particle of galena would be so intense that it would discharge through a dielectric as strong as air at the distance by which the centres of charges are separated. Not satisfied, however, with this apparent theoretical disproval of the electric theory I undertook a series of experiments that should serve to check the various points in the above theoretical discussion.

• No. 1. Galena ore was ground in an agate mortar and poured from an agate spoon (to prevent discharge of positive electricity, if present, from ore) between two plates of an electro-static machine. The material was deflected as shown. Plates were electrified almost to discharge point. This shows that galena ground under insulating conditions carries a charge and that a particle of this nature, suspended in a non-conductor in an electro-static field, is attracted.
• No. 2. Ore was ground in conducting earthed mortar and poured from earthed spoon. Deflection of only a very few particles was shown. Perhaps the deflected particles were insulated with oil or did not come in contact with earthed surface.
• No. 3. Ore treated as in No. 1 and poured between glass sides of a cell. Glass was 1 mm. thick and separated by 2 cm. Potential between plates of machine was 8500 volts. Deflection as shown. The interposition of glass had very little effect.
• No. 4. As in No. 3. but the cell was full of water. Used conductivity, tap, and acid water. No deflection. This indicates that particles charged, or otherwise, suspended in a conducting solution (i. e., enclosed within our hypothetical conducting sphere) is not affected by electro-static forces without.
• No. 5. Cell contained ore and nitric acid solution to generate gas. Neither bubble rising or ore particles dropping showed deflection. Potential, 10,000 volts. The conditions here duplicate those of No. 4.
• No. 6. Bubbles blown through canvas into water or acid solution were not deflected. A charge of bubbles flowing in one direction would produce an electric current, and even if they were charged they could not be attracted, as here again the charges are enclosed in a conducting material.

• No. 7. Ore poured into cell containing gasoline. There seemed to be a slight deflection. 10,000 volts between plates. Conditions here should not differ greatly from those of No. 3. Solution may not have been sufficiently non-conducting.
• No. 8. Solution placed in electrolytic cell, arranged as shown, gave no deflection of ore or bubble with conducting or non-conducting solution. Both ions and charged colloids are susceptible to this treatment, and no doubt they would move easier than the larger body and so lessen the potential on the larger masses.
• No. 9. The water itself was electrolyzed to furnish gas. A two¬way switch gave either hydrogen or oxygen at the bottom pole, which was covered with a layer of ore. Both gases carried apparently equal amounts of ore and with equal readiness. Bubbles in either case, upon striking the upper plate, did not discharge their burden of ore, no matter what the sign of electrode.
• No. 10. Set up as in No. 9, except that gas was furnished by action of nitric acid on ore. Changing of sign produced no discernible effect upon bubble or ore or upon bubbles with load when coming in contact with upper electrode plate.

I wish to point out the fact that this discussion and these results are to be considered only in connection with the bond between a bubble and ore particles. The conditions chosen have been ideal, in order to isolate this particular phase of the problem. Particles of appreciable mass (+ 200-mesh) have been used, but this permits of an electro-static consideration without interference from exaggerated surface conditions due to smaller bodies. It is possible that an ionized solution does not behave like a solid metallic conductor toward an electro-static charge, but I know of no evidence to the contrary. Very little is known regarding contacts between solid-liquid-gas phases, but it is doubtful whether charges such as accompany phases of a colloidal solution are of much influence in the case of bodies of the size herein considered. It may be found that the oil-water emulsion or the oil- films introduce the colloidal element, and no doubt many of the slimes contain colloids, in which the electric charges are of great importance. It is known that masses of sulphides, such as galena, are positive, but

these same sulphides in colloidal form are negative. Metals in mass and as atoms are positive but these also as colloids are negative. This complicates considerably the electrical theory in the case of pulp containing both sand and slime. It may be interesting to call attention to the enormous increase of surface produced by subdivision, in which case phenomena that are purely superficial are greatly enhanced.

When it is considered that these small particles contain the energy necessary to subdivide them, whether electrical or otherwise, it is apparent that phenomena encountered throughout a range in size of particle body will not bear a direct ratio to its mass or constituent material. A consideration of this phase of the subject is, however, without the scope of this paper, which is only given to point out a few of what would appear to be misapplications of the laws of electrostatics.