Vol. 22, XO. 5
INDUSTRIAL S X D ENGILYEERIXG CHEMISTRY
534
( 5 ) Josse, Z . Ver. d e u t . Ing., 63, 322 (1909). (6) Kerr, Trans. Am. SOC.Mech. Eng., 35, 731 (1913). (7) Lewis, I b i d . , 44, 325 (1922). (8) Nusselt, Z . Vev. d e u l . Ing., 60, 541 (1916).
111-Flow
(9) Nusselt, Z . Ver. d e u t . Ing., 60, 569 (1916). (10) Orrok, Trans. A m . SOC.M e c h . Eng., 34, 713 (1912). (11) Othmer, IND.ENG.CHEX.,21, 576 (1929). (12) Robinson, I b i d . , 12, 644 (1920).
of Fluids at Low Velocities
If heat is added to a fluid flowing at a rate below the critical velocity, the original viscous flow of the fluid is entirely altered by convection currents induced by density differences produced in the fluid stream. For flow of the fluid in a vertical direction at low velocities heattransmission coefficients are not affected by the velocity of the fluid stream but are greatly affected by temperature drop and by the viscosity, density, and coefficient of expansion of the fluid. This type of fluid flow is designated as “thermal turbulent” flow to distinguish it from ordinary viscous flow and from turbulence due to high velocities. The heat-transmission coefficient of water flowing ver. . . . . ..
P
RET’IODS investigations of the rate of heat flow between a solid and a fluid flowing by forced convection have been made almost entirely for fluid velocities well in the turbulent range. For rates of flow near and below the critical velocity (calculated for isothermal conditions) very few data and no satisfactory conclusions have been reported. A common assumption of many experimenters has been that the mechanism of the transmission of heat to fluids in viscous motion is one of simple heat conduction. With this assumption the calculated coefficients are very lorn. Others have suggested the use of natural convection equations which give values higher than those calculated from the turbulent flow formulas. The present investigation was undertaken because of the unsatisfactory state of knowledge of heat transmission a t low rates of liquid flow. This includes an experimental study of the factors controlling the values of the heat-transmission coefficients between a vertical pipe and water flowing inside a t low velocities. The use of a vertical pipe gives the simplest case, since the natural convection currents are parallel to the direction of forced flow. Theoretical equations for the heat-transmission coefficients and the transitional velocity are also shown to be in excellent agreement with these experimental data. The case of horizontal pipes is more complicated, and unfortunately neither an adequate theory nor accurate experimental results are available for this condition, although qualitative agreement will be shown between the data of one investigator and general predictions based on dimensional analysis. Previous Investigations
Only one investigation has been reported in which an attempt was made to determine the controlling factors for heat transmission to fluids a t low velocities. This was a study by Dittus ( 1 ) on “Heat Transfer from Tubes to Liquids in Viscous Motion” for water and several oils flowing through horizontal pipes varying from 0.28 to 1.83 inches i. d., a t velocities below the calculated critical value. Dittus reported the following equation, which he claimed represented his data quite well: h=22 where h
( kat7 96 s) %
(1)
= heat transmission coefficient, in B. t. u. per hour
per square foot per degree Fahrenheit B. t. u. per hour per square foot per degree Fahrenheit At = temperature drop, in degrees Fahrenheit
k
= thermal conductivity, in
tically at velocities less than 0.1 foot per second is given by the empirical equations:
and
ht,
=
0 37 t,
h;d
=
0 44 f
.\”/Ttfor upward flow for downward flow
Dissolved air has no appreciable effect upon this transmission coefficient in vertical pipes even when released by heat. For fluids in general, flowing vertically at low velocities, the more fundamental equation has been developed :
.....
,
D
=
s
= specific gravity of liquid = specific heat a t constant pressure = linear velocity, in feet per second
cp u
p/s =
inside tube diameter, in inches
kinematic viscosity, in square centimeters per second
The apparent agreement between Dittus’ data and his reported equation, however, resulted from a false method of plotting. Closer analysis indicates very poor correlation with but little support for this formula. Dittus plotted values of (h/u s c) ( p / u s D)’/12 against values of ( k At/Du3s)on loglog coordinate paper. The variables included in this plot covered an experimental range of 800 to 1 for velocity, 6 to 1 for pipe diameter, and less than 3 to 1 for the other terms. It is obvious that in such a graph the effect of velocity has masked the effect of the other variables. Since velocity appears as the first power in the ordinates and as the cube in the abscissas (which varies from 512,000,000 to 1 in comparison with the maximum variation of the other variables of less than 6 to I ) , naturally a straight-line plot of experimental data with a slope of 1 / 3 will result on the log-log paper. Such a plot proves that the cube root of the velocity cubed is equal to the velocity, but does not show any correlation of variables. The writers replotted Dittus’ experimental data leaving out the velocity term from both the ordinates and the abscissas (these terms canceled out for the reported equation) and found very little correlation betn-een the data and the reported equation. Dittus derived the dimensionless moduli which he used in plotting by a loose form of dimensional analysis. Such an analysis which is not based on fundamental equations has no support except when it shows agreement with data; when this agreement is lacking the equation loses its significance. I n two investigations of heat transmission to fluids in turbulent flow, a qualitative effect a t low velocities was shown. Nusselt ( 7 ) plotted results on gases in horizontal tubes with values of heat-transmission coefficients as ordinates and a function of mass velocity as abscissas, and found that a t low velocities the slopes of the curves decreased markedly, becoming nearly independent of velocity. The points of departure from the turbulent lines occurred a t higher mass velocities for higher gas pressures, thereby differing from the calculated critical mass velocity, which should be constant for any given diameter and viscosity. Walker, Lewis, and hlcAdams (14) reported values of heat-transmission coefficients considerably higher than were predicted
ILYDL-STRIAL A S D ESGIlYEERISG CHEMIXTRY
May, 1930
from their turbulent-flow equation for oils having low values of the Reynold’s modulus, dpu/p where d
= = = =
p
u I.(
diameter density linear velocity viscosity
They found that an increase in the temperature drop caused an increased value of the heat-transmission coefficient due to induced thermal convection. Because of the similarity of this case with that of natural convection, a brief review of the experimental results in this field will be of value. Apparently the first investigators of the rate of heat flow by natural convection were Dulong and Petit (a),who tested the cooling of a thermometer bulb in a concentric hollow bulb, and found that the rate of heat transmission varied n-ith the 1.223 power of the temperature drop FIG 1 HEATTRANSMISSION COEFFICICNTS OF WATER FILM
h-04Patu t. 50-
40-
(24 1
’“1 O
k
i
1,
-
O
80
100
140
I20
Tcmpeiofvrr of Woler. Deg
r
-
160
I80
and about the 0.5 power of the pressure of the gas. PCclet (11) carried out very careful experiments on the rate of heat dissipation from bodies of various shapes and found that the rate varied with the 1.23 power of temperature drop and with a shape factor. Oberbeck (10) first related the Stokes equation of flow with the differential equation of heat conduction, but he did not reach a practical solution. Lorenz ( 6 ) integrated these equations for the special case of a vertical wall by use of several rough assumptions and arrived a t the equation:
where H = height of the vertical wall T = absolute temperature c p = heat capacity a t constant pressure g = acceleration due t o gravity k = thermal conductivity p = density At = temperature drop p = viscosity
All terms are expressed in consistent units. Nusselt (8) applied a n advanced form of dimensional analysis, which he called “consideration of similarity,” to the fundamental differential equations of fluid flow and heat conduction, and derived for the case of natural convection the following formula:
where a, rn,and TL are to be determined by experiment, and in case of vertical walls the height of the wall is substituted ford. /3 is the coefficient of expansion. Kote that this is a dimensionally homogeneous equation, so that any consistent system of units may be used with it employing the same values of the constants a. m , and n.
535
Griffiths and Davis (4) have conducted the most complete and satisfactory experiments on the cooling of vertical surfaces by natural convection. These investigators determined the heat-transmission coefficients from vertical plane surfaces of various sixes and from vertical cylinders of varied lengths. They found a considerable end effect on the lower part of the hot surface, where the coefficients were much greater than over the rest of the surface. K i t h increasing distance from the bottom the values decreased rapidly to a minimum value and then increased slightly to a constant value for the rest of the surface. Rice (13) has given an equation of the Xusselt type for these results neglecting the end effect: h = 0.115 k P i & ? / )%
(
(4)
where the reciprocal of the absolute temperature is used to replace the coefficient of expansion since such a substitution can be made for gases. At the lower part of the surface the effect of temperature drop seemed to be as the 1 / 4 poiver, indicating that for short lengths the equation for natural convection would be similar to the above but have an exponent of in place of The exponent of was found by Dulong and Petit, PBclet, Rice, and many others, including Nusselt, for the case of small horizontal cylinders, and so would seem to be of application for heat transmission to fluids a t low rates of flow inside horizontal tubes. Nusselt’s equation for this case (9), based on data for gases of Griffiths and Jakeman (6) and Eberle ( 3 ) but predicted to hold for all fluids, is:
Rice (12) derived the following equation from data of many investigators for gases and liquids:
FIG 2 HEATTRANSMISSIGN COCfFlCiENTS OF WATCR FILM h-037At”
f,
.
/
’“t / Theoretical Discussion
For the case of a vertical plane surface theoretical equations have been derived by Lorenz and Kusselt. Lorenz’ equation, derived with several inaccurate assumptions as to velocity and temperature distribution in the fluid near the surface, does not agree with the data of Griffiths and Davis for long surfaces, since it includes a height factor and since the exponent is instead of Ija. Susselt’s equation is not rigorous and does not predict what value the exponent should have. A new conception in the mechanism of heat transmission by natural convection has been introduced by one of the writers (article in preparation) in deriving the following theoretical equation for the case of a vertical surface:
I-VDUSTRIAL A X D E.VGI.VEERl,\rG
536 F, = 0,104k
(m)” fi2
(7)
where the variables are expressed in consistent units. This conception assumes that there is a boundary layer next to the surface, flowing upward when the liquid is being heated, ON.-
B W0J.-
T H E R M A ~COEFFICIENT OF EXPANSION
CHEMISTRY
Vol. 22, No. 5
For the case of horizontal pipes the problem is much more complicated, since the film thickness is no longer definite. Furthermore, the “thermal flow” in horizontal pipes is directed a t right angles to the main fluid flow, so that there will probably not be two definite ranges covered by independent equations, as with vertical pipes. It will be expected that there will be a wide intermediate range where the two velocity effects will simultaneously affect the rate of heat flow. Furthermore, the heat-transmission coefficients a t even very low velocities might not be independent of the forced-flow velocity. Since no theoretical solution has been made for this case, preliminary correlation might be made by use of the general Kusselt equation for natural convection. Experimental Procedure
40
60
100 / t o 140 /60 t-Tempemlura of Watrr -De$ f
80
/EO
ZbO
dJ
A general description of the experimental equipment and procedure used in this investigation is given in Part 11. The rate of heat flow was determined from an air-steam mixture flowing through an annular space 7 feet long surrounding a vertical 3-inch i. d. pipe to cooling water passing through the pipe at low velocities. The rate of flow of the water was determined by direct weighing, and was maintained constant by use of a constant-head tank. Temperatures of the pipe surface and water were measured at distance intervals along the pipe (Figure 1, Part 11). Multiple-junction thermocouples described in Part I were used to determine the average temperatures of the pipe and of the liquid a t various cross sections. The rate of heat flow across any 6-inch section was calculated from the increase in temperature of the water in flowing through the section and the rate of flow of the water. Heattransmission coefficients were calculated for six typical positions in the condenser. Since the individual values were apparently not affected by an entrance effect when the first
due to a density difference between the fluid in the layer and that in the main body, and that this flow follows the laws of viscous motion having a velocity of zero a t the surface and increasing with the distance from the surface out to a certain critical thickness. Beyond this critical thickness the flow will be turbulent. The relationship between critical thickness and velocity is found from viscous- and turbulent-flow equations for a plane surface. The flow of heat from a solid surface to a fluid is by simple conduction across this viscous layer, after which the heat is distributed by turbulent mixing in the main body of the fluid. Because of the relatively great rate of heat flow by turbulent convection, all the resistance to heat flow, and hence the entire temperature drop, is assumed to reside in the viscous film. The amount of heat picked up by the film itself is small compared with the amount flowing across because of the very small thickness of the film. The end effects.found by Griffiths and Davis can be 400 explained by the fact that the very high temperature 300 gradient just a t the bottom of the surface will cause high coefficients there. As the film becomes heated it begins to flow upward and the temperature gradient decreases. The viscous layer becomes thicker and extends beyond (&+) the critical thickness in a metastable state before it breaks into turbulence a t its outer boundary. This ab80 normal thickness of the viscous film causes the minimum value of heat-transmission coefficient just before the conSO stant value is reached. 50 In applying this new conception to the case of fluid flow A,At in a vertical pipe a t low velocities, it is suggested that as long as the velocity of the fluid by forced flow is less than the foot of tube was not included, the six values were averaged for value a t the critical film boundary, the equation for natural each run to give better agreement, and were correlated with an convection will hold and the heat-transmission coefficients will average of the corresponding liquid temperatures and of the be independent of the forced-flow velocity. When the forced- cube roots of the corresponding values of temperature drops flow velocity is greater than the value that would be obtained across the liquid film. By preliminary correlation these facfor natural convection a t the film boundary, the thickness of tors had been found to be the controlling variables. the film will be dependent entirely on the turbulent-flow equaThe liquid temperature a t each position was measured by tion, and the heat-transmission coefficients will be independent two three-junction couples located so as t o determine an of any of the factors controlling natural convection alone, such average d u e for a giren cross section. These couples were as temperature drop. The value for this boundary velocity located on a movable support so that the same two couples could be used a t all positions. The outer couples in the secin terms of the fluid properties and temperature drop is: tion were distributed inch from the pipe surface, so the film Vt= 15 ( p p 2 g At /A)% (*) temperature was not included in the average. Thus the where T‘t is the transitional mass velocity and all terms are in entrance effect could not be determined from the heat-input consistent units. It is suggested that the type of flow caused measurements. I n fact, for cases of quite low velocities of by temperature gradient be called “thermal flow” t o dis- water flow, no heat input into the main body of cooling water tinguish it from forced turbulent flow and also from purely was indicated for distances of from 6 inches to 2 feet above the viscous flow (m-hich apparently cannot exist in cases of heat entrance of the water t o the heat exchanger (a typical example transmission), and that the value of the boundary velocity be is shown in Figure 1, Part 11). Measurements of the decalled “transitional velocity” to distinguish it from the creasing temperature along the gas-vapor stream and main“critical velocity,” the term used to designate the change tenance of usual values of temperature drops across the gas from turbulent to viscous flow under isothermal conditione. and cooling-water films indicated that th’e rate of heat flow
ILVDCSTRIdLA S D ELVGI.VEERI.2'G CHEMISTRY
May, 1930
into this abnormal region was of the same order of magnitude as into the adjoining sections. This is the condition previously describecl-namely, storage of heat in the boundary film a t the bottom of a vertical hot surface. It was noticed, in taking experimental data, that a t the position where the inain body of water firqt showed a definjte temperature increase the thermocouples fluctuated considerably and the increase was abnormally large in this section. To measure the relative-velocity profile a t any cross section of the liquid, a velocitv thermocouple was used. This consisted of -a fine copperrconstantan therniocouple having the junction coated with qhellac and having a short heating coil
537
could be drawn through points of the same temperature drop, Values of heat-transmission coefficients divided by temperature were plotted logarithmically against temperature drop. This plot indicated that the coefficients varied with the cube root of the temperature drop. To show the degree of agreement of the data, the heat-transmission coefficients divided by the cube roots of their respective temperature drops were plotted against water temperatures and also against the film temperatures (Figures 1 and 2) with the following resulting empirical equations, for upward flow: h, = 0 4 2 At% tw h, = 0 3 7 At% t j
(9) (10)
where h , = B. t. u. per hour per square foot per degree Fahrenheit, Af and t = " F. For downward flow the average numerical constants of the equations were calculated from experimental data, giving the following equations: h , = 0 4 9 At% trr hw = 0 4 4 At% tf
'
40$,,o,
2
J
4
5
6
8
l0
io
30
2T
so do /oo
x,o'
A, A i
of fine constantan n i l e Jipped o ~ e the r junction. The junction n a s faitened to a iwir-el which permitted it to be m u n g to any po-ition 111 the crobq section. The temperature of the liquid a t a certain point could be read, and then a m a l l current pas-ed through the wrrounding coil would cause an iiicrea-e in temperature. The magnitude of this increase wa. a function of the velocity of the liquid at that point. Since accurate thermocouple. e. in. f readings could bc> made by Like of a type K potentiometer, only a small temperature intreace n a y u.ed, 30 that difficulty caused by induced comettion currents n a i a niininluni. This instrument qhowed that a t lox ~elocitieiof nater flowing in an upnard diiection the T elocity near thf. pipe iurface n a s greater than in the main fluid itreani. Thi. is farther proof that xiscous flow doe- not e1i.t in a fluid stream n h i c h 1 4 being heated or cooled. Experiments with gla5.i apparatus illowed that a t high *urface teniperaturei ga- bubble> were continuously r e l e a d on the wrface To test the effect of relea.ed air bubbles on the rate of heat flow,separate te.ts were m a d e w i t h thcx cooling water deaerated by spraying through a vacuum and also completely aerated by spraying through air. The range of other variable5 in1 estigated were as follow. ( a ) water velocity from OOWI 4 0.5 to 11 pounds per square foot per second (note that the i - o t h e r m a l critical velocitv for theqe conditions is about 4 pounds per square foot per second); ( b ) temperature from 40" to 180" F., (c) temperature drop across water film from 7 " to 70" F.; and finally ( d ) tests were made with water flowing in both upward and downward direction.. The results of theqe tests were plotted againqt the properties of the main fluid stream and of the film itself. Dittus' data mere replotted according to the general S t w e l t equation for convection to see if an approximate equation could be obtained for horizontal pipes.
Li
Results
A preliminary plot of heat-transmission coefficients against water temperature showed that approximately straight lines
(11) (12)
Velocity was found to have no effect on the heat-transiiiission coefficient. over the range invehtigated, which included values up to two and one-half times the critical velocity as calculated for iyothermal f l o ~ . This checked the result. of the dehumidification experiment> reported 20; in Part 11, in which velocity was found to have no effect below the transitional value. The magnitude of the transitional velocity was apparently not reached in the n-ater-film experiment.. According to Equation 6 the transitional velocity i- a function of physical properties varying with the temperature and of temperature drop. For water having an average temperature of 110" F. and an average teniperature drop of 30" F., thii wlocity will be about 11 pounds per square foot per qecond. To determine the extent of correlation of the data with the theoretical Equation 5 derived for the ca5e of a vertical surface, the thermal properties of n ater mere first collected and plotted in convenient form. In securing value5 of the coefficient of expanqion of water, use was made of the relation: where p is the coefficient of espaniion,
'
'OdOI
b
'
i
'
p
the den-it\-, and T
'
0.01
0.)
(D'S'at C J B )
the absolute temperature. written: p = - - = 6- 1nc - P 6 T
This equation may also br 6 Ine s 6 t
(14)
where s is the specific gravity of the liquid and 1 is temperature in O F. From data given in the Smithsonian tables, Ine s was plotted against temperature, and the value of the coefficient of expansion at any temperature was found from the slope of the resulting curve a t that temperature. These values for the coefficient of expansion were replotted against temperature. (Figure 3) Since the properties of viscosity, density, thermal conductivity, and coefficient of expansion of a given liquid
Vol. 22, No. 5
INDUSTRIAL AND ENGINEERING CHEMISTRY
538
depend only on temperature, the moduli containing these terms will be functions of temperature. Two such moduli, zlso used in the theoretical equations, were accordingly plotted. These moduli are:
Values of h/k B” were plotted against values of (A At) using values of m = ’/a and m = ‘/4. (Figures 4 and 5 ) The values of IC, A , and B were taken a t the arithmetic mean temperature of the film. The resulting equations are:
film, tending to cause greater film velocities and therefore a smaller viscous film thickness. KO quantitative determinations were made of the heattransmission coefficients near the entrance to the heat-exchange space, but the qualitative effects previously mentioned are a further support of the theory of thermal flow. The data of Dittus for oils flowing through horizontal pipes a t low velocities are shown replotted against the variables predicted by the Nusselt Equation 3, assuming m and n to be equal. (Figure 6) Although the correlation is very poor, the following equation was determined by the curve drawn: h = 0.64
h = 0.145 kf
The agreement of the data seems to be good for both exponents of B. Equation 15, however, shows better agreement with Rice’s Equation 4 for gases a t vertical surfaces if the constant value of 0.74 for diatomic gases is substituted for B , giving:
The agreement between Equations 17 and 4 is quite remarkable and shows that heat-transmission coefficients for forced flow in a vertical direction a t low velocities are the same as for natural convection with no forced flow. For downward flow according to the above empirical equations (7 to lo), the constant in the equation will be about 18 per cent greater. If the properties are taken a t the fluid temperature, the constant in the equations will be about 12 per cent greater for downward flow. The fine agreement of the experimental results with the theoretical Equation 5 is an excellent substantiation of the theory of thermal flow a t vertical surfaces. Unfortunately, no data mere taken for water velocities higher than the theoretical transitional velocity, owing to less experimental accuracy a t high velocities and since a t the time of the investigation it was thought by the writers that rates double and treble the calculated isothermal critical velocity would surely be in the range covered by the heat-transmission equations for turbulent flow. However, the agreement of the theoretical transitional velocity with the experimental values reported in Part I1 is an excellent support of the theory of thermal flow. For all velocities below the transitional velocity the coefficients were found to be higher than predicted by the equations of turbulent flow, but agreed excellently with values calculated from the theoretical equations assuming thermal flow. I n the theoretical derivation of the equations of heat flow for vertical surfaces a plane surface was assumed, whereas experiments were made with vertical cylinders by Griffiths and Davis, and with the inside of a vertical pipe in the present investigation. I n these investigations the effect of surface curvature was negligible because of the large diameters of the cylinder and pipe in comparison with film thickness. For cylinders and pipes of small diameter, however, there may be some complication due to the changing area of the film, and possibly different critical thicknesses will result for different interfacial velocities. Furthermore, the isothermal critical velocity will increase with decreasing diameters, while the transitional velocity as given by Equation 9 is independent of diameter, so that for very small diameters different effects may occur in the critical range. The presence of air in the cooling water was found to have no noticeable effect on the heat-transmission coefficients. Possibly the effect on insulation of the heating surface by liberated air was offset by the added density drop across the
( $ ) (y)” ( d3 6 P2
P2
g)>”
(18)
As predicted for the case of horizontal pipes, the runs with high velocities resulted in points lying above the curve. The data did not seem sufficiently accurate to permit determining the exact velocity effect, although Dittus determined it roughly as the power. Dittus’ data for water were not included in the plot since they showed wide deviations. A comparison of Equation 18 for fluids flowing inside horizontal tubes a t low velocities with Equations 5 and 6 for natural convection on the outside of cylinders of small diameter shows considerable similarity. Summary of E q u a t i o n s
(Heat transmission coefficients for water flowing in vertical pipes a t low velocities below the transitional velocity.) When heat is flowing into a stream of liquid flowing a t low velocities, convection currents are established owing to temperature differences. Under such conditions the water is defined as moving in thermal flow. As the velocity of flow increases as a result of forced convection, turbulent flow results. The velocity a t which the flow of liquid changes from thermal to turbulent flow is termed the “transitional” velocity. The transitional velocity is much higher than the so-called critical velocity for large pipes. The term “critical velocity” does not apply strictly to liquids being heated or cooled, for under such conditions viscous flow does not exist. EMPIRICAL
EQUATIONS FOR
~ ~ A T E R
For upward flow in vertical pipes: hw 0.42 At% tw hw = 0.37 At%’ tf
For downward flow: hw = 0.49 At% t, hw = 0.44 At% if where hw = B. t. u. per hour per square foot per degree Fahrenheit At = temperature drop across water film, degrees Fahrenheit tw = temperature of main water stream, degrees Fahrenheit tf = average temperature of water film, degrees Fahrenheit
GENERALEQUATIONS (ALLLIQUIDS) For upward flow in vertical pipes: 1, = 0.128 kf
(v)” ( ’’ p2
“
P2/
where
kj
pf
(19)
= thermal conductivity of film
= = pi = At = g = cp = pf
)”
density of film coefficient of expansion of film viscosity of film temperature drop across film acceleration due to gravity specific heat of film
Equation 19 is dimensionally homogeneous and so can be used with any system of consistent units.
INDUSTRIAL A.VD ENGIhTEERINGCHEMISTRY
May, 1930
Literature Cited Dittus, University of California, Bull. 2, No. 11 (1929). Dulong and Petit, A n n . chim. p h y s . , 7, 113, 225 (1817). Eberle, 2. T'er. deut. Ing., Sa, 481 (1908). Griffiths and Davis, Food Investigation Board, Dept, Scientific and Industrial Research, S p . Rep!., 9 (1922). ( 5 ) Griffithsand Jakeman, Engineering, 123, 1 (1927). ( 6 ) Lorenz, W i e d . Ann., 13, 682 (1881). (7) Kusselt, Miit. Forsck.-.47b., Heft 89 (1909). (1) (2) (3) (4)
539
Nusselt. Gesundh. I n a . . 38. 477, 490 (1915). . . Nusselt, 2. Ve7. deut. Ing., 73, 1475 (19291. Oberbeck, Wied. Ann., 7 , 271 (1870). Peclet, "Traite de la chaleur," Paris, 1860. Rice, Trans. Am. Inst. Elect. En&, 43, 131 (1924); International Critical Tables, Vol. V, p. 236 (1929). (13) Rice, International Critical Tables, Vol. V, p. 234 (1929). (14) Walker, Lewis, and McAdams, "Principles of Chemical Engineering," p. 141 (1927). (8) (9) (10) (11) (12)
Study of the Fibroin from Silk in the Isoelectric Region' Milton Harris* and Treat B. Johnson DEPARTMEKT OF C H E Y I S T R Y ,
Y A L E UNIVERSITY,
NEW
HAX'EX,
C06N.
Stable colloidal solutions of fibroin may be prepared The work of von Weimarn (6),n-hereby it has become physical as well as the by dissolving the degummed silk in concentrated possible to disiolve fibroin of chemical properties of aqueous solutions of neutral salts and subsequent natural silk have proved very dialysis to remove t h e salts. silk in strong aqueous solution Determinations i n t h e isoelectric region gave t h e of neutral salts, has given us valuable in the testile industry. Since hydrogen-io11 confollowing results for t h e isoelectric point: solubility a nem method of attack. H e trol plays an important role measurements, pH 2.1; viscosity, pH 2.3; electrohas pointed out that fibroin in such processes as degumphoresis method, 2.2; precipitation of dyed fibroin, can be obtained in colloidal ming, dyeing, soaking, and tin PH 2. dispersion in concentrations as great as 30 to 35 per cent x-eighting, it is necessary to know not only a t what p H we get the best procws, but also by heating 10 to 20 minutes a t the boiling point of concenat what point the silk itself is most stable. This is readily trated solutions of very soluble salts. These include the shown by isoelectric determinations. chlorides, bromides, iodides, nitrates, thiocyanates, and Investigation of the action of salts on silk is of twofold chlorates of calcium, strontium, barium, or lithium; also importance. Certain salts have a definite weakening effect sodium iodide or sodium thiocyanate. In some cases, as on the fibers, which makes it necessary to keep them from lithium thiocyanate, dispersion can be obtained a t 25" C. a n y prolonged contact with the textile material. Other in a few minutes. B y combining von Weimarn's discoveries with methods salts are capable of acting as solvents in neutral solutions and these are proving very interesting as a possible method of which they have worked out for preparation and purification dissolving and precipitating silk similar to rayon manu- of the protein solutions, the present writers have been able to determine many properties of fibroin in the isoelectric facture. It is the purpose of this and subsequent papers to contrib- region which were previously unobtainable owing t o their Ute data which will be of commercial a s well as scientific inability to prepare solutions sufficiently concentrated for making a more accurate chemical study. For these deimportance in the silk industry. I n studying the properties of fibroin the greatest difficulty terminations a large number of methods are available. has been the extreme insolubility of this protein in ordinary They are based on the fact that at the isoelectric point the solvents. That strong acids and alkalies will dissolve it osmotic pressure, viscosity, amount of alcohol required has long been known, but their action is so drastic that few for precipitation, migration of particles in a n electric of the original properties of the fibroin are retained in the field, conductivity, and swelling, are all a minimum. The resulting solutions. In order t o study the physical properties methods which the authors found to be most satisfactory in the isoelectric region, we must not only dissolve the employ electrophoresis, viscosity, and solubility measurefibroin, but in effecting solution it is necessary that we ments. utilize methods which 6ill cause as little change as possible Preparation a n d Purification of Solutions in the original substance. I n previous studies on the isoelectric point of fibroin I n the preparation of the fibroin solutions a highly purified carried out in this laboratory, Hawley and Johnson ( 2 ) silk was used which had been carefully boiled off to remove succeeded in preparing solutions of fibroin by dry grinding sericin. This mas dissolved in either a 50 per cent lithium of the material in a ball mill and subsequent suspension bromide or a 70 per cent calcium thiocyanate solution by in water to form a fairly stable colloidal solution. Although warming to 80" C. A few drops of toluene were added to these solutions had properties similar to those prepared by prevent any bacterial action. The solutions were then methods which will be described later, their chief disadvantage lay in the fact that they could not be prepared in introduced into parchment bags which were allowed to reconceiitratioiis greater than 0.5 per cent. Since the solu- main in the dialyzing tank for about 2 weeks. A colorimetric method was used for determining the amount of tions were diluted in reactions by addition of reagents, insufficient fibroin was present for many of the determina- calcium thiocyanate or lithium bromide remaining in the solution. B y means of this method it was found that after tions carried out in this research. dialysis for 1 meek the solution contained about 1 part of 1 Received March 21, 1930. Constructed from a thesis submitted salt in 1000 parts of solution, and after 2 weeks, 1 part in by Mr. Harris in partial fulfilment of the requirements for the degree of 10,000. The fibroin concentration of the resulting solution doctor of philosophy in the Graduate School of Yale University, June, 1929. was obtained by determining the total nitrogen. B y this 2 Holder of the Cheney Brothers Research Fellowship, 1928-29.
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ECEXT studies of the
