118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. THE PROPERTIES OF POWDERS. PART VIII. THE INFLUENCE OF THE VELOCITY OF COMPRESSION ON THE APPARENT COMPRESSIBILITY OF POWDERS. BY E. E. WALKER, D.Sc. (A Paper read before THE FARADAY SOCIETY, Monday, November 1 2 t / t , 1923, SIR ROBERT ROBERTSON, K.B.E., F.R.S., PRESIDENT, i f 2 t& Chair.) Received October 3 4 I 9 2 3.Th Creeping of Powders Under Pressure. When a powder is compressed in a cylinder by a constant load, the velocity of compression is very high to begin with and then rapidly falls off, but no case has been observed up to the present in which it falls off to zero before the powder is completely compressed. TABLE I. Time in Seconds. Volume Ratio. K'. 5 10 20 40 80 160 320 640 1280 2560 5120 10,240 20,480 81,920 40,960 1.329 1.316) 1.295 1.257 1.236) 1-214 1-18,) 1.158 1.030 1-007 1'000 J -019 '0185 '021 '0195 .orgo '015 '012 '0035 This phenomenon has been investigated, using the apparatus described in Part VI. of these studies. The general method of procedure, including the preparation of the powders, was the same as described in that com- munication, but, instead of varying the load, observations were made on the height of the plunger after various intervals of time, the load being kept constant.As a rule the load was applied by means of a small Tangye press, and kept constant by manipulation of the hand-operated oil pump- but in certain cases where it was necessary to keep the load constant for several hours a dead load was employed. The load was applied as rapidly and gently as possible, and zero time taken from the moment at which the 614THE PROPERTIES OF POWDERS-PART VIIL 615 ,789 '759 ,736 '653 full load was applied. On account of errors arising from the estimation of zero time, observations made in less than 2 0 seconds were liable to consider- able error. One series of observations made on ammonium nitrate is recorded in Table I.The relationship between the volume ratio' (V) and the load (t) is given by the empirical equation :- V, - V2 = IOK' (t2h - t,is) . * ( I ) -032 '034 '03 I -03 I TABLE 11. - Potassium Nitrate. Load ~ o r j kiloelsq. cm. Ammonium Nitrate. Load 101*5 kilos/sq. cm. K' K - K' K K' K V t V 1.548 1.532 1'516 1'497 1.477 1.455 1'409 K' '040 '03 7 '037 '03 7 -032 *028 -026 - K '518 '501 '478 '469 '449 '421 ,386 - *076 '074 '077 '079 -071 '47 '067 - - 10 20 40 80 160 320 640 1280 2560 "339 1.303 1-267 1,229 1.188 1.150 1.114 =.q9 - -0165 '0155 *or7 -017 *018 ,016 '506 '5 15 322 '531 '536 '033 -030 '03 3 '03 2 '03 4 '547 ,029 Mean = '0318 Potassium Chloride. Load 203 kiloslsq. cm. Ammonium Chloride. Load 183 kilos/sq. cm. V K I K' K' '0021 'OOIg -0017 t 40 320 2560 54820 t I0 40 160 640 2560 1.478 1.431 1.374 1.318 1'260 '425 -418 ,411 '025 '026 ,023 '020 - Mean = -0044 - Values of the velocity coefficient K' are recorded in Table I., and it is seen that they vary within very narrow limits until compression is practically complete, when its value falls rapidly to zero.In the diagram experimental 1 The volume ratio is apparent Of powder actual volume of solid particles.616 INFLUENCE OF VELOCITY OF COMPRESSION volume-ratios are plotted as ordinates and logarithms of the time as abscissz. V = 1.5665 - -1985tih A curve calculated from the equation :- is drawn for comparison and is seen to be in good agreement with the results of the experiment. It is found that equation I is capable of representing the relationship between V and t for all the powders hitherto investigated over that range of volume ratios for which the logarithmic law V = C - K l o g R TABLE 111.Class I . *Ammonium nitrate. . . . . . Sample A2 {Trinitrotoluene 20 per cent. } Sample B2 Trinitrotoluene . . . . . . "Sodium chloride . . . . . . *Potassium chloride . . . . . . Potassium nitrate . . . . . . Ammonium nitrate 80 per cent. class I I . Class III. *Ammonium chloride (pure) . . . . 9 , .. (commercial) . . . Tetranitromethylaniline . . . . . "Barium nitrate . . . . . . Calcium carbonate (precipitated) . . . K' K - . '0731 '0552 . '0299 . '0272 . -0128 . s0320 . '0318 . -0032 . '0044 . -0176 . '0039 . '0094 holds as a first approximation ; but where K in this expression is variable K' is found to vary also.In fact it is the ratio - which is constant for a K' K See Part. VI. of this series, Vol. XIX., p. 79. 2 Sample A was prepared by mixing the two powders under heavy rollers in edge runner mills. Sample B was prepared by mixing the hot ammonium nitrate powder with molten trinitrotoluene so that every particle was coated. It is interesting to note that K' whereas sample A has the value of -, which might be expected from its composition, K the value for sample B is almost the same as that found for pure trinitrotoluene.ON COMPRESSIBILITY OF POWDERS 61 7 Load, *pproxirnate Idean Kilos per Sq. Cm. Volume Ratio. 81 1.25 I 62 1-14 324 1-06 given powder rather than K' itself; as the following observations on a mixture of ammonium nitrate and trinitrotoluene show :- K' ir K Mean Value.K' Mean Value. '339 '0209 '0615 '296 '0177 '060 '227 '0135 '0595 K' K been found that - is very nearly constant in the case of all the substances, the compressibility of which was measured in Part VI. of these studies ; but in some cases the value of K' is so small that the experimental error in determining it is very high. Examples of the application of equation I to observations on various substances are given in Table 11. Collected values of 5' are given for a variety of substances in Table 111. Those marked with a star refer to samples of powder, the compressibilities of which are recorded in Part VI. K Inzuzme 01 t h VeZocity of Compression. The relationship between the length of time for which the load has been applied and the velocity with which compression takes place can be calculated simply from equation I as follows :- dv Velocity of compression = - - dt = K't - 0'9 .* ( 2 ) When a powder is compressed by blows in the manner described in Part VI. of this series the impact velocity is known and, if equation I is applicable to very small time intervals, as it is for time intervals ranging from 5 to 20,000 seconds, it should be possible to calculate the relationship between the resistance which a powder offers to compression by impact of known velocity (RJ and its resistance to a static load of known duration (Rp). Taking the mean velocity of compression as half the velocity of impact, we get dv v x A - = velocity of compression = ~ dt 2 4 v 3 impact velocity of falling weight in cm./sec.A = cross sectional area of cylinder Q = quantity of powder (in cubic centimetres) hence for a container having a cross sectional area of 10 sq. cm. where (3) ' (4) K't- 0'9 = K5 Q and since :- &2 V, - Vz = K log - R. a we get by equations I, 2, 3 and 4 log,o iy- Ri = I - from which 5 may be calculated. The results are recorded in Table IV., RP618 INFLUENCE OF VELOCITY OF COMPRESSION '0399 -0xg8 '0122 '00487 and the observed values are given for comparison. I n classes I. and 111. the average observed value of -* is given for all volume ratios (excluding those below I '2, since these values are rather abnormal, see Part VI., p. 80). The value of -- is not even approximately constant for substances in Class 11. and the limits are therefore given instead of the mean value.I n the case of substances in Class I. the calculated and observed values are in fair agreement, but there is no agreement in the other two classes. This lack of agreement is quite consistent with the hypothesis put forward in Part VI. to explain the behaviour of these substances towards slow and rapid compression. Substances in Class I. are regarded as normal substances, which are com- pressed by deformation of the particles both when static loads are employed and when compression is brought about by the impact of falling weights. Accordingly the calculated and observed values of - are in fair agreement. Substances in Class 11. are regarded as behaving normally when they are compressed slowly by static loads, but when the compression is brought about suddenly by blows the particles are broken down into fragments which fall together into closer order, so that the resistance to compression is much less than the calculated value to begin with.As compression proceeds further disintegration takes place causing an increase of resistance analogous to the hardening of metals by cold working. Accordingly the ratio -' rises and finally reaches or exceeds the calculated value. In Class 111. conditions are exceedingly complex since disintegration is caused both by slow and by rapid compression (impact), and accordingly there is no connection between the calculated and observed values of R. RP Ri RP Ri R, R. RP 14'53 Ammonium nitrate 5'6 4-16 14'68 Mixture sample B 1.92 I -86 15-23 Trinitrotoluene I'&9 1-62 14-68 Mixture sample A 3-14 3'32 - Ri.Calcium carbonate is quoted in Table IV. as an example of this total Rb '0079 '02 I5 '0175 lack of agreement. TABLE IV. _ _ ~ ~- 1 Ri I 11-48 Sodium chloride 1-30 I 1:13 - 2.78 1 5 12-53 Potassium chloride 2-01 I 04 - 2-06 6 Potassium nitrate 1'97 I '875 - 2-18 7 1°'00 I I i I l- ___- ___ I '0040 1 4-97 1 Calcium carbonate 1'26 I 2'91 , 8 1 : 1 3 For 2, 3 and 4 v = 173 and t = 20. The remaining data required tor these calcu- lations are in Table 111. of this paper, and in Table 11. Part VI. of these studies.ON COMPRESSIBILITY OF POWDERS 619 Th Shrinkage of Powdered Ammomkn Nifra fe. If ammonium nitrate is finely ground in a mortar or some form of mill, and is then pressed into pellets, the pellets will often shrink consider- ably.The rate at which this shrinkage takes place depends largely on the fineness of the grinding and on the quantity of moisture present ; 0.2 per cent. of moisture is quite sufficient to promote shrinkage. The rate of shrinkage also depends on the extent to which the pellets are compressed, and decreases with increasing compression. The following experiments were carried out on 50 gram blocks of powder which had been milled in edge runner mills. The volumes of the blocks were measured in mercury. Original volume ratios 1.270 1.181 1.103 Percentage reduction in volume after 12 hours 2.05 1-80 1-22 It is seen that the rate of shrinkage falls off with increasing compression. Professor Lowry and the present author described a case of expansion and shrinkage of potassium carbonate in Part V.of these studies, but this referred to the uncompressed salt, which is much more liable to shrink. The author believes that ammonium nitrate is quite exceptional in the readiness with which highly compressed pellets will shrink under the influ- ence of minute traces of water. I t is hoped that further light may be thrown on this question during the discussion. Although the capillary forces which tend to produce shrinkage are present in all powders containing moisture, it can be shown by means of the following calculations that in the case of ammonium nitrate a small force of this kind is particularly likely to cause a large contraction. From equations I, 2, and 4, we get for the velocity of compression under any load P when the volume ratio = Vl where P, is the load required to compress the powder to a volume ratio of V, in t, seconds.dv df From the data given in Part VI. it is possible to calculate - for any load at any given volume ratio from this expression. For example :- if P = 30 kilos./sq. cm. and V, = 1.3 then the following values of fl are obtained :- df dV dt I_ ammonium nitrate potassium nitrate sodium chloride ammonium chloride 8.5 x I O - ~ = 1.8 per cent. per hour. 3.0 x I O - ~ = 7.3 per cent. per year. 4.6 x 1 0 - l ~ = 1.1 x I O - ~ per cent. per year. 4-9 x 1 0 - l ~ = 1-2 x I O - ~ per cent. per year. These figures demonstrate that ammonium nitrate is quite specially liable to shrink under the influence of prolonged external pressure, and this fact explains why powdered ammonium nitrate is particularly liable to shrink when acted upon by capillary forces.620 COMPRESSIBILITY OF POWDERS Summary. compressed powder has been investigated. (a) The influence of the duration of the load on the volume ratio of (b) The isobaric curve has been correlated with the value of the ratio resistance to impact resistance to static load’ and further evidence for the validity of the classifi- cation of powders suggested in Part VI. of these studies has been obtained. (t) The exceptional readiness with which powdered ammonium nitrate shrinks has been shown to be dependent chiefly on the high value of its velocity coefficient. The author desires to thank Professor Lowry for suggesting that this work on powders, which was originally undertaken to settle certain practi- cal problems, should be extended to a variety of substances with the object of publishing it in its present form. (Parts VI., VII., and VIII. of these studies.) The author is also indebted to the Department of Scientific and Industrial Research for a grant which made this work possible, and to the Chief Superintendent, Research Department, Woolwich, for permission to use the Fairbanks compression testing machine and the Tangye press mentioned in these communications.