Document bwX4qxpv1no0rDLE0RzXgpv0

VAPOR PRESSURE MEASUREMENTS FOR AEROSOL PRODUCTS Reproduced by permission from AEROSOL AGE Vol. II, Nos. 8 & 9, August and September 1966 By Paul Sanders "Freon'' Products Division E. I. du Pont de Nemours & Company Wilmington, Delaware 19898 CM <> CO rH rH o LJ FBEON AND COMBINATIONS OF FREON -- 08 F - WITH NUMERALS ARE DU PONT'3 REGISTERED TRADEMARKS FOR ITS FLUOROCARBON PROPELLENTS The vapor pressures of aerosol prod ucts is a subject that has been of interest to the aerosol industry for many years. Not only is it a factor involved in other aerosol properties, such as spray characteristics, flam mability, and rate of discharge, but it is also an aerosol property which is subject to governmental regulations. It has been recognized for a long time that in order to obtain an accu rate measurement of the pressure of an aerosol product it is usually neces sary to prepressurize the gage with an inert gas, such as air or nitrogen. The reason for this is that practically all aerosol products contain air. The total pressure in these products is equal to the pressure of the aerosol Vapor Pressure Measurements for Aerosol Products By Paul A. Sanders E. I. DU PONT OE NEMOURS Gr COMPANY "FREON" PRODUCTS DIVISION Wilmington, Delaware formulation plus the pressure of the air. Loss of air from the aerosol con tainer during a pressure measurement would result in an erroneous measure ment and this is avoided by prepres surizing the gage to approximately the same pressure as that in the aerosol container. The method of determining the pressure of aerosol products with a prepressurized gage has been described in detail in a previous publication.1 However, in many cases vapor pressure measurements are taken without prepressurizing a gage, either because of a lack of the proper equipment or because of a desire to save time. The significance of vapor pressure measurements taken with a nonprepressurized gage has never been clarified. If the pressure of an aerosol containing air is taken with a gage at a lower pressure than that in the aerosol container, the vapor phase of the aerosol will expand into the gage until the pressure in the gage and the aerosol are equal. The pressure of the propellant in the vapor phase remains essentially con stant during expansion into the gage (neglecting any cooling from expan sion) since bquefied propellant will vaporize to replace that lost by ex pansion into the gage. However, in most cases, the pressure due to air will change during the expansion. The ultimate pressure recorded on the gage, therefore, is not the same as the pressure originally present in the aerosol container. Theoretically, there are two dia metrically different processes that can occur when the vapor phase of an aerosol expands into a gage at a lower pressure. These two processes give different pressures. In the first theoretical process (Process 1), the vapor phase of the aerosol container is assumed to mix completely with the air in the gage during the expan sion, so that the final composition of the vapor phase in the aerosol con tainer is the same as that in the gage. Depending upon the relative volumes and concentrations of air in the vapor phase of the aerosol and the gage, the final pressure could either be higher, lower or the same as that originally present in the aerosol. In the second possible process (Process 2), it is assumed that the expanding vapor phase of the aerosol does not mix with the air in the gage but merely compresses the air. Under these conditions, the air in the gage acts only as a piston for the transmittal of pressure to the gage. The pressure will always decrease if Process 2 takes place, because the air pressure in the vapor phase of the aerosol will decrease as a result of the expansion into the gage. Equations have been developed so that the pressures can be calculated for both Process 1 and Process 2. It is the purpose of this work to com pare the experimentally determined pressures obtained when an aerosol expands into a gage at a lower pres sure with the pressures calculated for the two different processes and thus determine which of the processes actually takes place. Discussion In order to simplify the fol lowing discussion, it is as sumed that the pressure of the air in the vapor phase of the aerosol container is greater than that in the gage, and that the volume of the gage is less than the volume of the vapor phase of the aerosol container. EID11363 The two alternative processes (Process 1 and Process 2) can be more easily understood if the proc esses are considered to take place stepwise as follows: Pbocess 1 Process 1 assumes that the expand ing vapor phase of the aerosol con tainer mixes completely with the air in the gage. The final composition of the vapor phase of the container is the same as that in the gage. Step 1 When the valve between the container and the gage is opened, the vapor phase of the aerosol expands into the gage until the pressure in the aerosol and the gage are about equal. During this expansion, the vapor phase of the aerosol and the air in the gage are assumed to mix completely. Step 2 Sufficient liquid vaporizes from the surface of the liquefied pro pellant to maintain the pressure exerted by the propellant at a rela tively constant value. The volume of the vapor phase of the aerosol can now be considered to consist of the original vapor phase in the container plus the volume of the gage. On the basis of the original assumption that the air concentra tion in the aerosol container ini tially was greater than that in the gage and that the volume of the gage was less than that of the vapor phase, the final concentration oi air in the combined volumes of the vapor phase of the initial aerosol and the gage will be less than that originally present in the aerosol container. Therefore, after expan sion into the gage, the pressure due to air will be less than that originally present in the container and the pressure recorded on the gage will be less by this factor than the original pressure in the aerosol container. Step 3 The container and gage are now shaken to reestablish equilibrium between the air in the liquid phase and that in the vapor phase. When this occurs, the pressure will rise for the following reason: the dis tribution of air between the liquid and vapor phases of an aerosol is a function of the volume ratio of the liquid phase to the vapor phase (Kef. 2). Since the vapor phase of the aerosol after expansion into the gage can now be considered to be increased by that of the gage, the distribution ratio will change and air will leave the liquid phase in order to establish equilibrium at the new liquid phase/vapor phase ratio. The increased concentration of air in the vapor phase will cause the pressure to rise. Therefore, if Process 1 takes place, the pressure will first de crease as a result of expansion into the gage and this will be followed by an increase in pressure after the container and gage are shaken. Process 2 The vapor phase of the aerosol during expansion does not mix with the air in the gage. The air in the gage, therefore, merely acts as a pis ton for transmittal of pressure to the gage. If this process takes place, the following steps can be considered to take place during the pressure meas urement: Step 1 When the valve between the can and the gage is opened, the vapor phase of the aerosol expands into the gage until the pressure of the expanded vapor phase and the pres sure in the gage are equal. Step 2 Sufficient liquid vaporizes from the liquefied propellant to main tain a constant propellant pressure in the vapor phase. Step 3 The container is now shaken. Some of the air originally present in the aerosol was lost by expan sion into the gage. Therefore, some air will have to leave the liquid phase and enter the vapor phase in order to maintain the original distribution ratio of air between the two phases. In this case, the ratio of the volume of the liquid phase and the vapor phase is the same as that initially present in the container, since the redistribution of air occurs only in the aerosol container. Step 4 The redistribution of air in the vapor phase that results from shaking increases the concentration of air in the vapor phase and con sequently the pressure increases. - Since the pressure in the aerosol is now higher than that in the gage, the vapor phase of the aerosol will again expand into the gage until the pressures in the system equalize. The second expansion of the vapor phase of the aerosol into the gage causes a further loss of air from the aerosol and a second re distribution of air between the liquid and vapor phases occurs upon shaking. This causes another increase in pressure in the aerosol and another expansion into the gage. Therefore, the cycle contin ues until equilibrium is eventually established. The overall result if Process 2 takes place is an initial decrease in pressure as the vapor phase ex pands into the gage, followed by a higher pressure when the con tainer and gage are shaken. The pressure continues to increase gradually until equilibrium is es tablished. These results are similar to the results of Process 1, but the magnitude of the changes is con siderably different than those from Process 1. {' V A comparison of the pressures calculated for Process 1 and Process 2 with the experimentally measured pressures in Table I indicates that Process 2 is the predominant process that occurs when the vapor phase of an aerosol expands into the gage. In most cases, the calculated pressures of Process 2 are fairly close to the experimentally measured pressures. There is a slight tendency for the measured pressures to fall in between the pressures calculated for Process 1 and those calculated for Process 2. This probably indicates that there is a slight mixing of the expanding vapor phase of the aerosol with the air in the gage at the aerosol vapor phase-air boundary. Although the air in the gage acts as a piston for trans mittal of pressure, the interface be tween the air in the gage and the expanding vapor phase of the aero sol is somewhat diffuse, as would be expected. In general, however, there is very little mixing of the expanding vapor phase of the aerosol with the air in the gage. The fact that the expanding vapor phase of the aerosol did not mix sig nificantly with the air in the gage confirms previous evidence for this behavior reported bv H. M. Parmelee EID11364 TABLE I Comparison of Experimental Pressures With Calculated Pressures fpsi at 70*5] Calculated Pressures-Process t Mixing Experimental Pressures P; * 60 Calculated Pressures-Process 2 No Mixing________ (Initial] Expansion Expansion Expansion P2 * 56. Shaking P3 - 58.1 Expansion P2 - 54.0 Shaking 1 P-t - S7.0 Expansion ?2 * 52.2 I Sh aking vl/ Pj - 56.9 Expansion 55.0 I Shaking P5 - 55.7 Expansion ?6 - S3. Shaking l P7 - 53.1 51.0 Shaking <1- 54.0 P4 - 50.2 Shaking l P5 - 54.4 Expansion P6 - 48.5 Shaking 1 Expansion Pft - 48.5 Shaking i P7 - 52.0 (Reference 4). Parmelee noted that when air was pumped into a cylinder of "Freon-12", the air acted initially as a piston and compressed the "Freon-12", vapor. Under static con ditions, three hours were required for the air to mix with the "Freon-12" vapor. Since Process 2 is the predominant process that occurs, the pressure will always decrease when the vapor phase of the aerosol expands into the gage if air is present in the vapor phase. The decrease in pressure will result from the change in air pressure in the aerosol as the air pressure drops during the expansion into the gage. It is interesting to speculate what would happen to the pressures if Process 1 occurred with an aerosol product containing no air in the vapor phase when pressures were taken with a gage filled with air at atmos pheric pressure. In this case, if the expanding vapor phase of the aerosol mixed with the air in the gage, the final vapor phase, which would con sist of that of the aerosol and the gage, would contain more air than was initially present in the vapor phase of the aerosol alone. The pres sure after expansion into the gage would be higher than the initial pres sure in the aerosol as a result of the added pressure of the air. Upon shaking, some air would dissolve in the liquid phase of the aerosol in order to establish equilibrium and this would decrease the concentra tion of air in the vapor phase. There fore, the pressure would decrease upon - shaking, but still would lx higher than the original pressure in the aerosol. Experimental As previously mentioned, the pres sures from both Process 1 and Process 2 were calculated. The equations that were developed for the calculations and examples of the calculations are covered in the appendix. A compari son of the experimentally determined pressures with the calculated pres sures indicated that Process 2 was the predominant process occurring during expansion of the vapor phase of the aerosol into a gage at a lower pressure. The experimental tests were car ried out as follows-, an empty 6-ounce aerosol container was capped with a valve without a dip tube and thus was filled with air at atmospheric pressure. The container was pressure loaded to 84.5% volume fill with an accurately prepared mixture of "Freon-12"/"Freon-11" (50/50). The vapor phase in the aerosol after the addition of the propellant was 35 Pressures were determined using a calibrated Ashcroft gage with 2-lb. scale division. Pressures were esti mated to the nearest 0.5 psi. The gage was connected to the aerosol container by means of a can punctur ing device equipped with valves for prepressuring the gage and allowing the gage to return to atmospheric pressure. The total volume of the gage and connections was 24 cc. The aero sol container was tbermostated at a temperature of 70"F. The initial pressure in the aerosol container (Pt) was determined with a prepressurized gage and found to be 60.0 psig at 70F. The pressure of the propellant at 70F. was 37.5 psig (Reference 3) and the pressure due to air therefore was 22.5 psi. After the pressure had been meas ured, the valve between the gage and the aerosol container was closed and the gage was vented and returned to atmospheric pressure. The valve be tween the gage and the aerosol con tainer was then opened and the vapor phase of the aerosol was allowed to expand into the gage. Care was taken not to shake the aerosol con tainer during the expansion into the gage. The pressure after expansion was 54.0 psig (P2). The aerosol con tainer was then shaken to reestablish EID11365 equilibrium for the air between the liquid phase and vapor phase. The pressure rose to 57.0 psig (P,) and then remained essentially constant. The valve between the gage and the aerosol container was closed and the gage was again vented and returned to atmospheric pressure. The cycle of allowing the aerosol to expand into the gage at atmospheric pressure without shaking, followed by shaking to establish equilibrium, was repeated two more times. The experimentally determined pressures for the three cycles are given in Table I along with the pres sures that were calculated for both Process 1 and Process 2. For both processes, the pressures after expan sion into the gage were calculated from the experimentally determined pressures Pu P3 and P5. However, the pressures for Process 1 and Process 2 after shaking were calculated from the previously calculated pressures after expansion. This is illustrated diagrammatically in Table I. I. Calculations of Pressures Assuming Complete Mixing of the Vapor Phase of the Aerosol with the Air in the Cage A. Pressure After Expansion into the Cage The initial pressure in the aerosol (P,) was 60.0 psig at 70F. The pressure of the propellant, "Freon12/"Freon-11" (50/50) was 37.5 psig, as reported in Reference 3. Subtraction of the propellant pres sure from the total pressure gave the initial air pressure of 22.5 psi. The rnols of air in the vapor phase of the aerosol were calculated using the relationship n (mols air) ~ --P--V-- = RT 22.5 ------ x 35 14.7 0.00222-------------------------------------------- 82.06 X 294.1 The total mols of air in the aerosol container were calculated from the distribution ratio of air in the aerosol and the number of mols of air in the vapor phase. The distribution ratio of air at 84.5% volume fill is 74% in the liquid phase and 26% in the vapor phase (Reference 2). The total mols of air in the aerosol container therefore were 0.00222 ------------- = 0.00853 0.26 The mols of air in the gage were calculated from the volume of the gage, 24 cc, assuming the air in the gage at atmospheric pressure, n (mols air in gage) = 1 x 24 . ----------------------- = 0.00098 82.06 x 294.1 After expansion into the gage and mixing, the total volume of the vapor phase is 35 -- 24 -- 59 cc. The total number of mols of air in the new vapor phase is equal to 0.00222 -j0.00098 = 0.0032. The pressure of the air in the expanded vapor phase is 0.0032 x 82.06 x 294.1 P (air) = --------------------------------------- = 59 1.31 atm = 19.3 psi The total pressure in the aerosol and gage therefore is 37.5 -f- 19.3 -- 56.8 psig. B Pressure After Shaking Considering that the gage is now' part of the aerosol, the new volume of the aerosol is 225 cc -|- 24 cc = 249 cc. The percent liquid fill there fore has changed from 84.5% to 76.4%. The distribution ratio of air therefore changes from 74% in the liquid phase and 26% in the vapor phase to 64% in the liquid phase and 36%. in the vapor phase. The total mols of air in both the aerosol container and gage is 0.00853 -a 0.00098 =: 0.00951. The number of mols of air in the vapor phase, after shaking and redistribution of the air, is 0.36 X 0.00951 = 0.00342. The pressure of the air after shaking therefore is: 0.00342 82.06 X 294.1 P (air) = ------------------------------------ = 59 1.40 atm or 20.6 psi The total pressure in the aerosol and gage is 37.5 -j- 20.6 = 58.1 psig. The pressures for the two following cycles of expansion and shaking were calculated in a similar manner. II. Calculations of Pressures Assum ing no Mixing of the Vapor Phase of the Aerosol with the Air in the Cage In this case it is assumed that the expanding vapor phase of the aerosol merely compresses the air in the gage and does not mix with it. The decrease in pressure results from the change in air pressure dur ing the expansion. In order to calcu late the pressures for Process 2, it was necessary to derive an equation"" which gives the increase in volume1 of the vapor phase after expansion. The following assumptions were made m the derivation: 1. The expansion of the vapor phase is isothermal; 2. The pressure of the formula tion due to propellant remains constant as a result of further vaporization of the liquid phase during the expansion; 3. No mixing of the expanding vapor phase with the air in the gage occurs. Actually, two equations were de rived. The first equation is cumber some and vvas not used in the present calculations. The terms used in the derivation and their meanings are as follows. Pi = Initial pressure in the container P = Final pressure in either container or gage x` Pp = Pressure of propellant *' : P ~ Initial pressure of air in container Pip -= Final pressure of air in container V -- Volume of vapor phase in container Vi = Volume of gage Pi = Initial pressure in gage Pti = Final pressure in gage X = Increase in volume of vapor phase of aerosol during expansion The derivation of the first equation vvas as follows: (1) P = Pp + Pfa = pfg (2) paV = Pfa (v + x> (3) Pfa =_PaV_ V+X (4) pgvg= pf? tv9 " x) (5) Pfq PgVa (6) p = P,, + ?aV = PPV9- V -r X Vg - - (7) Pp + PaV ^ pgvg V+X X EID11366 Solving the equation for X leads to the following quadratic equation. The intermediate steps in the solu tion are available if desired. X = - [vg (Pg - Pp) + Pjvj + / [vc (Pc - Pp) + P1vD 2 - 4Pc (v Vq (Pq - P-, )] 2 Pp Equation 8 is obviously cumber some to use. Therefore, a new equa tion was developed in which a trial value for X is improved by iteration. This is a standard procedure used in mathematics. The new equation was developed from equation 7 by substituting Xfor X on the left hand side of the equation as follows: (9) P.V p.v, P, + ------------- = ------------- V + X. V, - X Solving equation 9 for X leads to the final equation as follows: (10) vg 1 - Pg Pp + Pa/ V \ \V + Xo ` In using equation 10. values of X are assumed and substituted for X-. The equation is then solved for X. The value of X thus obtained is then substituted for X and the equation again solved for X. After X has been obtained, the final pressure in the vapor phase due to air is obtained from the equation. P.V Pu = ------------- V+X A. Pressure After Expansion into the Cage In order to calculate the pressure after expansion, it was first necessary to determine X, the increase in vol ume, using equation 10. The follow ing values were used for equation 10: P := 52.2 psia at 70F P = 14.7 psia P* = 22.5 psia V -- 35 cc V, -- 24 cc A trial value of 18 cc was first assumed for X and substituted in equation 10 for X. as follows: Solving the equation for X gave a value of IS.7 cc. This value was then substituted for X. and the equa tion again solved for X. The value of X remained at 18.7 cc and further substitution was not necessary. The air pressure after expansion was then calculated as follows: 35 Pt. = ----------------- X 22.5 = 14.7 psi 35 + 18.7 The total pressure in the aerosol then is 37.5 -j- 14.7 = 52.2 psig at 70F. B. Pressure After Shaking Before expansion into the gage, there were 0.00222 mols air vapor phase, and 0.00631 mols air liquid phase, for a total of 0.00853 mols air in the aerosol container. After expansion, the number of mols air remaining in the vapor phase of the aerosol container was 35/53.7 x 0.00222 = 0.00145 mols. The total mols of air in the aerosol container after expansion therefore was 0.006314- 0.00145 = 0.00776. The distribution ratio of air in the aerosol container is 74% liquid phase and 26% vapor phase. Therefore, assuming that the redistribution of air occurs only in the aerosol con tainer upon shaking, the number of mols of air in the vapor phase afteT shaking is 0.26 x 0.00776 = 0.00202. The pressure of air in the vapor phase then is: 0.00202 X 82.06 x 294.1 P (air) = --------------------------------------- = 35 1.39 atm = 20.4 psi The total pressure in the aerosol is 37.5 psig 4- 20.4 psi -- 57.9 psig at 70"F. However, the pressure in the aerosol is now higher than that in the gage, so a second expansion into the gage occurs and it is neces sary to obtain a second value for X. Assuming an initial value of 6 cc for X and substituting for X- in equation 10 gives a value of 1 cc. After several more trial substitutions, a final value of 1.7 cc for X was obtained. The final pressure of the air after the ex pansion therefore is 20.4 x 35/36.7 ~ 19.4 psi. The total pressure in the aerosol after shaking therefore is: P = 37.5 + 19.4 -- 56.9 psig at 70 F. The pressures after expansion into the gage and subsequent shaking for the next two cycles were calculated similarly. Summary The expansion of the vapor phase of an aerosol product containing air into a gage at a lower pressure can occur by two different processes. Either the vapor phase of the aerosol can mix completely with the air in the gage or the air in the gage can act merely as a piston for transmittal of pressure to the gage. In the latter case the vapor phase of the aerosol does not mix with the air in the gage. Comparison of pressures calculated for the two different processes with experimentally determined values shows that essentially no mixing of the vapor phase of the aerosol with the air in the gage occurs. The derivation of equations used to calculate the pressures, assuming no mixing of the vapor phase of the aerosol with the air in the gage, is shown. References 1. "Freon" Aerosol Report. FA-11, "A Method for Measuring the Vapor Pressure of Aerosol Products." 2. "Freon" Aerosol Report, FA-15, "The Effect of Air on Pressure In Aerosol Containers." 3. "Freon" Aerosol Report, FA-22. "Vapor Pressure and Liquid Density of `Freon' Propellants." 4. Parmelee, H. M., `Solubility of Air in `Freon-12' and `Freon-22'," Refrig erating Engineering, June 1951. Acknowledgement The author would like to express his appreciation to Fred Chromev, Carneys Point Development Laboratory, Explo sives Department, who developed the mathematical equations used for the cal culations of pressures by Process 2 m tins paper. EID11367 FOR FURTHER INFORMATION Please contact one of the following district offices: 60 Glenwood Avenue East Orange, New Jersey 07018 Phone: 676-1112 (Area Code 201) 7 South Dearborn Street Chicago, Illinois 60603 Phone: 222-5000 (Area Code 312) 701 Welch Road Palo Alto, California 94304 Phone: 326-2840 (Area Code 415) 712 Main Street Suite 324 Gulf Building Houston, Texas 77002 Phone: 222-2468 (Area Code 713) 3503 North Hoyt Street El Monte, California 91734 Phone: 2S3-0548 (Area Code 213) or: Wilmington, Delaware 19898 Phone: 999-3620 (Area Code 302) The information contained herein is based on technical data and tests which we believe I to be reliable and is intended for use by persons having technical skill, at their own discretion j and risk. Since conditions of use are outside of Du Pont's control, we can assume no liability , for results obtained or damages incurred through the application of the data presented. Publication of the information in this bulletin should not be understood as permission or j recommendation for the use of the "Freon' compounds in violation of any patents. EID11368 Better Things for Better Living ... through Chemistry 1-67 3M E. 1. DU PONT DE NEMOURS & COMPANY INCORPORATED "Freon" Products Division Wilmington, Delaware 19898 PRINTED U. S.