Ind. Eng. Chem. Res. 1992, 31, 1549-1554 9, = path of the optimal differential reactor lying in the
1549
boundary of the attainable region, defined by eq 9 *q = equilibrium curve 9 , = maximum rate curve Subscripts C8 = dd-ehot lll&?rid which CO~eeponds kld d feed material
The Necessary Conditions. It is necessary that the attainable region A with feed(s) Cfo is such that (a) it is convex, (b) no reaction vector on the boundary of A points outward, (c) no reaction vector in the complement of A can be extrapolated backward into A, and (d) no two points on a plug flow trajectory in the complement of A can be extrapolated back into A.
Superscript * = mixing point
Literature Cited
Appendix The attainable region is defined as the set of all outlet variables which can be achieved by any possible steadystate reactor system from a given feed. The variables define a space represented by characteristicvector C. We can define a reaction vector R(C) in the following way: if we allow material with properties described by the characteristic vector C to only react, then the instantaneous change in the characteristic vector dC will be described by dC = R(C) dcp, where cp is a positive scalar quantity with units of time. The characteristic vector is defined in such a way so that the elements of the vector obey a linear mixing rule. The change in the characteristic vector of material described by characteristic vector C1 caused by adding material of property C2 is in the direction (C, - CJ, which is referred to as the mixing vector. If we allow reaction and mixing to occur simultaneously, then the characteristic vector C1 must change locally in the direction given by the resultant vector g as follows: 0 I /9 I 1 (AI) 8 = flR(C1) + (1- fl)(C2- CJ Thus locally any combination of reaction and mixing can firstly only take us in a direction that lies in the plane of the reaction vector and the mixing vector and secondly must lie between the mixing and reaction vectors. Geometry of the Ideal Reactors. The plug flow reactor has a trajectory in the space such that the reaction vector is tangent to the trajectory at every point. The CSTR has the property that the vector defined as the difference between the feed and the exit characteristic vector is collinear with the reaction vector at the exit conditions.
Aris, R. Optimal Design of Chemical Reactors; Academic Press: New York, 1961; pp 40-44. Dyson, D. C.; Horn, F. J. M. Optimum Distributed Feed Reactors for Exothermic Reversible Reactions. J. Optim. Theor. Appl. 1967, 1,4042.
Glasser, D.; Hildebrandt, D.; Crowe, C. A Geometric Approach to Steady Flow Reactors: The Attainable Region and Optimization in Concentration Space. Znd. Eng. Chem. Res. 1987, 26, 1803-1810.
Hellinch, L. G.; Van Rompay, P. V. Optimal Adiabatic Bed Reactor with Cold Shot Cooling. Znd. Eng. Chem. Process Des. Dev. 1968, 7, 595-596.
Hildebrandt, D.; Glasser, D. The Attainable Region and Optimal Reactor Structures. Chern. Eng. Sci. 1990,2, 2161-2168. Hildebrandt, D.; Glasser, D.; Crowe, C. The Geometry of the Attainable Region Generated by Reaction and Mixing; With and Without Constraints. Znd. Chem. Eng. Res. 1990,29, 49-58. Lee, K. Y.; Aris, R. Optimal Adiabatic Bed Reactors for Sulfur Dioxide with Cold Shot Cooling. Znd. Eng. Chem. Process Des. Deu. 1963,2, 300-306.
Maleng6, J. P.; Villermaux, J. Optimal Adiabatic Bed Reactor with Cold Shot Cooling. Znd. Eng. Chem. Process Des. Dev. 1967, 6, 535-536.
Maleng6, J. P.; Vincent, L. M. Optimal Design of a Sequence of Adiabatic Reactors with Cold-Shot Cooling. Znd. Eng. Chem. Process Des. Dev. 1972,11,465-468. Omoleye, J. A.; Adesina, A. A.; Udegbunam, E. 0. Optimal Design of Nonisothermal Reactors: Derivation of Equations for the Rate-Temperature-Conversion Profile and the Optimal Temperature Progression for a General Class of Reversible Reactions. Chem. Eng. Commun. 1989, 79,95-107. Westerterp, K. R.; van Swaaij, W. P. H.; Beenackers, A. A. C. M. Chemical Reactor Design and Operation, 2nd ed.; Wiley: New York, 1984; pp 188-209. Zwietering, TH. N. The Degree of Mixing in Continuous Flow Systems. Chem. Eng. Sci. 1959,11, 1-15.
Received for review February 6, 1991 Revised manuscript received August 8, 1991 Accepted February 11, 1992
Effect of Adhesion Time on Particle Deposition: Reentrainment and Rolling Nicolaos
T.Vatistas
Dipartimento di Zngegneria Chimica, Chimica Zndustriale e Scienza dei Materiali, Universitd di Pisa, Via Diotisalvi 2, 56100 Pisa, Italy
This paper begins with a brief study of the various types of adhesion affecting particles on a wall surface. It goes on to develop a previous attempt to take into account both the adhesion and removal effect, by considering the experimentally observed rolling of the particles along the wall surface. A relation between the sticking probability and the parameters of adhesion, removal, and rolling has been obtained. The effect of the sticking probability of particles only loosely adhered to the wall surface has also been studied. Introduction The particles of a fluid in turbulent flow are deposited on the wall according to the following mechanisms: (a) the carrying of the particles to the surface, (b) their adhesion to it, and (c) the reentrainment and rolling of particles which had only loosely adhered there. The adhesion, 0888-5885J92f 2631-1549$03.00 f 0
reentrainment, and rolling steps are interdependent processes and so need to be studied together. They are affected by both the kinetics of adhesion and the flow dynamic in the wall region. The kinetics of adhesion depends both on the type of adhesion forces involved and the particles' mode of ap0 1992 American Chemical Society
1550
Ind. Eng. Chem. Res., Vol. 31, No. 6, 1992
proach to the wall surface. It is usually assumed that the adhesion process is instantaneous, though it is well-known that the deposited particles become more stable in time. The hypothesis of instantaneous adhesion is valid only of one assumes that the area of contact between the particle and the wall reaches its final value instantaneously. This does not occur where the contact area is affected by humidity, etc. Experimental studies of the fine structure of turbulence in the wall region have revealed the presence of coherent motion (Cantwell, 1981; Robinson, 1991). These studies suggest that the wall shear stress is not constant but varies periodically because of the presence of bursts near the wall surface. Given that the effect of these bursts is the removal of loosely adhered particles, it follows that the adhesion time derives from a balance between the attraction and the removal forces. The relation between the sticking probability and the parameters of adhesion and removal has been obtained (Vatistas, 1989). It has recently been shown (Yung et al., 1989) that the principal effect of turbulent bursts on spherical particles is the rolling of the particles along the wall surface, while their part in the reentrainment process is comparatively insignificant. This paper elaborates partial results (Vatistas, 1991), regarding the sticking probability of particle deposition, by considering the following four factors: (a) the adhesion of the particles of the wall surface, (b) their removal, (c) the rolling of the particles along the surface, and (d) the effect of loosely adhered particles on the adhesion process.
Adhesion of Particles to Wall Surface The adhesion of the particles to the wall surface is due to the attraction exerted on them by Van der Waals, electrostatic, and similar forces. The kinetics of adhesion depends on the type of forces involved, as well as on the increase over time of the area of contact between the particle and the wall. For instance, in the case of the deposition of rigid particles from a gas fluid, the area of contact reaches its final value instantaneously. However, if the gas contains humidity, the area increases over time owing to a gradual capillary condensation, which thus reinforces the adhesion of the particle to the wall surface. A similar increase over time of the area of contact between particle and wall may occur in the case of a crystal, where the increase is not instantaneous. Generally in real systems a particle’s form is modified to a greater or lesser extent during the deposition process (gradually attained full contact), giving rise to a semiinstantaneous mode of adhession. Particles adhere to the wall surface with greater difficulty, when the initial attractive forces are weak, as the wall shear stress continually moves the particle and prevents it from sticking. The drag and lift forces acting on deposited particles have in the past been calculated assuming classical laminar conditions within the sublayer region (Saffman, 1965; O’Neill, 1968). However, if the existence of bursts in this region and the particles’ irregularity of form are taken into consideration, then it becomes extremely difficult to calculate these forces. Moreover, while a drag force acting on a spherical particle causes a reasonably rolling movement along the wall surface, the same force acting on an irregular particle causes a more unstable rolling movement that can easily cause the particle’s removal from the wall. Combined Adhesion, €&entrainment, and Rolling Process Descriptions of the fine structure of flow within the sublayer of the turbulent regime show that the fluid flow
is not entirely laminar (Cantwell, 1981; Robinson, 1991), as in conventional boundary-layer theory (Schlichting, 1955). A cyclic phenomenon (bursts) has since been observed involving fluid ejections from the sublayer and sweeps toward the solid-fluid interface from the outer flow region. Cleaver and Yates (1976) initially suggested that the effect of these bursts is the removal of some of the instantaneously adhered particles. The introduction of the notion of adhesion time, demanded by the phenomena of semiinstantaneous adhesion on the one hand and the removal of loosely adhered particles by turbulent bursts on the other, allows the combination of the adhesion and reentrainment processes in turbulent flow regimes (Vatistas, 1989). Recent experimental research (Yung et al., 1989) regarding the effect of turbulent bursts on deposited particles has shown that the bursts remove only some of the particles they disturb, while others roll along the surface. In both cases the adhesion process is interrupted, the difference being that in the former the particles return to the fluid, while in the latter the adhesion process begins over again at the particles’ new point of arrival. The combined adhesion and removal mechanism proposed above has been extended to include both removal and rolling. It should be noted that particles only loosely adhering to the wall surface and thus subject to the rolling effect have the same age (degree of adhesiveness acquired over time) as newly arrived particles. This means that we can now specify that not all particles arriving simultaneously and remaining on the wall surface have the same age. Regarding the fine structure of turbulence in the wall region, the mean period t b between bursts is approximately given by tb
= loO(u/u*~)
(1)
During a period of time t b a small portion p of the wall surface is affected by bursts, resulting in the removal efficiency q and rolling efficiency K of the particles occupying that area. Hence a portion 5 = KP of the loosely adhered particles is subject to the rolling effect, another qp is p not subject to removal, while the rest y = 1- ( q + ~ ) are in any way affected by the bursts. In the particle deposition process it is of special interest to consider the Parkin’s sticking probability defined as the probability that a particle which gets to the wall sticks to it (Epstein, 1988). The following relationship between the sticking probability and the parameters of adhesion, removal, and rolling has been obtained (Appendix, eq A14):
The sticking probability S(t,+,y,t) vs the dimensionless adhesion time t,+ is shown in Figure 1, for some values of the rolling efficiency of bursts K (5 = ~ p ) . Where the rolling effect is absent K = 0 (F = 0), eq 2 becomes S(t,+,y) = Yt“+
(3)
This equation was also obtained in the previous paper (Vatistas, 19891, where it was assumed that the only effect
Ind. Eng. Chem. Res., Vol. 31, No. 6, 1992 1551 1.0 VI
,O.B
;rr
L.
2a 0.6 ,. .,
I
h Y
3 0.2
I
.j0.2
0
2
v1
0.01
0.0
lo'
0.4
0'
1 '
Dimena?onleaa Adhesion T h e
:t
lo
10
'
'
'
."""
\ '
.
""'.'
.
19 ' 10 Dimensionless Adhesion Time
ti
10
'
Figure 3. Sticking probability vs dimensionless adhesion time.
Figure 1. Sticking probability vs dimensionless adhesion time.
By substituting the ntb in eq 4 with the value derived from eq 7, we get the portion of the wall surface occupied by unstable particles:
20000 5
3 15000 a 10000
where tt represents the transport time 2
Figure 2. Portion of unstable particles vs dimensionless adhesion time.
of the bursta is the removal of the loosely adhered particles from the wall surface.
Portion of Wall Surface Occupied by Unstable Particles The portion of the wall surface occupied by loosely adhered particles may be calculated if the form and dimension of the deposited particles is known. Assuming that the particles are spherical, the portion of the wall surface occupied by loosely adhered particles is xu
= (*d2d/4)ntbU(ta+,Y,E)
(4)
where U(ta+,r,()is the portion of unstable particles on the wall surface (Appendix, eq A17).
U(t,+,r,E)=
1 - (y
+ [)t,++N - ++1 - (Y + ON 1 - (7+ E )
1- (7+ 5)
4.
+
I/
Figure 2 shows the unstable portion of particles U(t,+,y,[) vs ta+,for some values of the rolling efficiency of bursts K (5 = KP). The value of ntb in eq 4 is obtained by means of the transfer rate Vt
which gives (7)
c
dP
The value of the portion increases with the adhesion time and may be greater than 1for high values of the time ratio tb/ tt. The values for the adhesion time obtained using eq 8 where xu = 1are to be considered as limiting values since where xu = 1 no portion of the wall surface is any longer occupied by fully adhered particles.
Effect of Unstable Particles on the Sticking Probability The particles that have fully adhered to the wall surface constitute the new stable wall surface, while those that have only loosely adhered to it constitute the new unstable surface. The combined adhesion and removal mechanism proposed above assumes that the particles are carried to a stable wall surface. Hence it is probably not valid for the unstable portion of the wall surface, for which the deposition mechanism is likely to be intermediate between the following two extreme cases: (a) The proposed mechanism also occurs in the unstable wall regions. (b) The proposed mechanism does not occur in the unstable regions. If the former situation obtains, this will not affect the sticking probability derived using eq 2. If the latter obtains, the sticking probability becomes
Applying the value for xu derived from eq 8, we get
The results obtained by means of eq 10 are shown in Figure 3 for some values of the time ratio t b / t t . In the deposition process studied here, the time ratio t b / t t is related to the mass-transfer phase, while the other terms are related to the adhesion, removal, and rolling phase.
1552 Ind. Eng. Chem. Res., Vol. 31, No. 6, 1992
Discussion The effect of the experimentally observed rolling due to bursts has been included in the model of adhesion of the particles in turbulent flow conditions, while in a previous work only the kinetics of adhesion and the reentrainment were considered (Vatistas, 1989). Perhaps the most important feature of the proposed model is ita ability to include an increasingly large number of details concerning the complex process of particle deposition. The initial (instantaneous) adhesion forces can occur through an impact mechanism while the following adhesion forces occur through the formation of liquid or solid bridges between the particles and the wall surface. The w e of impact adhesion has been the subject of a considerable number of theoretical and experimental studies (Dahneke, 1971,1973;Hiller and Loffler, 1980; Rogers and Reed, 19& Tsai et al., 1990; Wall et al., 1990). The experimental results available in this field concern the presence (or a b n c e ) of rebound of particles upon impact with solid surfaces in connection with the initial (instantaneous) adhesion forces and cannot confirm the model proposed above that also considers adhesion forces due to liquid or solid bridges which occur gradually. Moreover, the experimental studies were carried out in such a way as to avoid the effect of fluid flow. In the field of adhesion it is neccessary to improve the existing adhesion models, by further investigation of both the experimental aspects in fluid flow conditions and the theoretical aspects, using a dynamic model that includes forces throughout and after impact. Conclusions The adhesion of deposited particles increases in time, owing to the gradual increase in the contact area in which the attractive forces are operative. The increase in the contact area and consequently in the attractive forces in time is the most complex phase in the deposition process, and only the initial (instantaneous) step has been studied in the case of adhesion by impact. Taking the kinetics of adhesion as known, the sticking probability, previously obtained by including the adhesion and removal of the particles, has here been extended by including the experimentally observed rolling movement of the particles along the wall surface. This rolling movement has the effect of reducing the sticking probability, by interrupting the adhesion process of the particles involved. The adhesion process of the newly arriving particles may or may not be impeded in that part of the wall surface occupied by loosely adhered particles. Both cases have been taken into consideration in order to obtain the sticking probability. Acknowledgment The research described here was carried out with financial assistance from the Italian CNR. Nomenclature
C = bulk particle concentration, kg/m3 d, = particle diameter, m
fi(a) = portion
of particles of age a,after the period t = it,, dimensionless F ( t ) = portion of stabilized particles, after the period t = (t,+ ,+ j N b , dimensionless N = dimensionless maximum time, eq A8 ntb = number of particles transported between bursts/unit area of surface, particles/m2
= number of unstable particles/unit area of surface, particles/ m2 p = portion of wall surface affected by bursts during t b , dimensionless S = sticking probability, dimensionless t = time, s t , = adhesion time, s t,+ = dimensionless adhesion time ( = t , ~ * ~ / 1 0 0 v ) t b = mean period between bursts, s U = portion of unstable particles, dimensionless u* = wall friction velocity, m/s [=(r,/p)1/2] V , = transfer rate/unit surface area, m/s zu= portion of wall surface occupied by unstable particles, dimensionless Greek Letters a = age of particle, s = portion subject to aging, dimensionless [l - (7 + k ) p ] 7 = removal efficiency of bursts, dimensionless K = rolling efficiency of bursts, dimensionless Y = kinetic viscosity, mz/s 5 = portion subject to rejuvenating, dimensionless ( ~ p ) p, = density of deposit, kg/m3 7, = wall shear stress, N/m2 R,
Appendix To determine the relations deriving from the combined adhesion, removal, and rolling mechanism, let us consider the behavior of ntbparticles carried to the unit area of the wall surface over a period of time tb The quantity y is that portion of the overall number of particles which is subject to aging, while the quantity 4 is that subject to rejuvenation. Hence, whereas initially (t = 0) the whole portion of particles are equally ageless fO(0)= 1 by the end of the given period (t = portions of the various ages are
tb)
(AI) the respective
while their sum is fi(0) + fdl) = Y + 5 (A21 By the end of a second period (t = 2tb) the respective portions of the various ages are f.(a)=
b+
age a = 0 age a = t b age a = 2 t b
while their sum is fi(0)+ fdl) + f i ( 2 ) = (7+
o2
(A31
By inference, by the end of the adhesion time period (t = t,+tb) the respective portions of the various ages are
i
((7 +
age a = 0
rfcr + 5 ) fa+-2 qt,(y +
age a = tb age a = 2 t b age a = 3tb
End. Eng. Chem. Res., Vol. 31, No. 6, 1992 1553 while the portion of unstable particles is f,(O)
+ f,(l) + ... + j,(a - 1) = (7+
-
[)'a+
By the end of a further period [t = (t,' spective portions of the various ages are
(A4)
++
+ l)tb] the re-
agea=O age a = tb age a = 2tb age a = 3tb ff,'+lb)
= age a = (ta+- 2)tb age a = (fa+ - 1)tb age a = t.+tb age a = (t,+ + 1)tb
while the portion of unstable particles is ft,++AO)
+ fb++1(1)+ + ft,++1 (y
+
-
(a 1) = - (7 25)+'
+
#a++'
(A5)
By the end of a still further period [t = (t,+ + 2)tbl the respective portions of the various ages are
The above equation may be written in a more convenient form, as follows:
s(ta+,r,t) ++ +
+ + 5) + (y + [)2 + ... + (y + 5)t*++N-1] + + 5) + (y + [)2 + ... + (y + 5)N-'] p a + [[l + 2(r + 5) + 3(y + 5)2 +
yt.'[[l (y y2"+[[1 (y
age a = 0 age a = tb
... + ( N - l)(y + 5 P 2 ]
age a = 2 t b age a = 3tb
or
- 2)tb age a = (ta+- 1)tb
S(ta+,y,f)= ++
age a = (t,'
+ ++5
t,++N-1
C
i=O
(A10)
(y + E)' -
age a = ta+tb age a = (ta++ 1)tb age a = (ta++ 2)tb
while the portion of unstable particles is ft.++2(0)
+ ft,++2(1) + .* + ft,++2(a - 1) = (y + 5)tl++2- (Y + E)(r + 3 W '
(A61
By inference, by the end of an (t,+ + n)th period [t = (t,++ n)tb] the portion of unstable particles is ft,++n(o)
+ ft,++n(1) + ... + ft,+n(a - 1) = (y + [)t*++n - (Y + [)"-'[y + (n + I)[]++
(A7)
The minimum value of this equation must be zero, meaning that n may not be greater than the maximum value N, derived from
[ +:) + i)
N(t,+,r,[)= (1
1]( 1
Finally, combining eqs A12 and A13 gives us the sticking probability:
W+,r,U= (A8)
Sticking Probability. The portion of stabilized particles is derived by means of eq Al-A7 according to the following law: the portion of particles stabilized after the period t = (t,' n)tb is given by multiplying yt'+ by the value of the unstable portion at t = (n - 1)tb.
+
While there should be no difficulty in calculating the respective s~ of the initial geometric progressions, the s u m of the final combined arithmetic and geometric progression is (Perry, 1984)
Znd. Eng. Chem. Res. 1992,31,1554-1562
1554
Portion of Unstable Particles on the Wall Surface. The portion of unstable particles on the wall surface is equal to the sum of the unstable particles at times 0, 1, 2, ..., t,+ + N a n d is given by t,++N-1
U(t,+,r,U =
c
i=O
(7+ [Ii - ++ yta+[
N-1
c (7+ 5)’ -
i=O N-2 i=O
(i + l ) ( y + t)i (A15)
Literature Cited Cantwell, B. J. Organized motion in turbulent flow. In Annual Reviews of Fluid Mechanics; Dyke, M. V., et al., Eds.; Annual Reviews: Palo Alto, CA, 1981;Vol. 13,pp 457-515. Cleaver, J. W.; Yates, B. The effect of re-entrainment on particle deposition. Chem. Eng. Sci. 1976,31, 147-151. Dahneke, B. Capture of aerosol particles by surfaces. J. Colloid Interface Sci. 1971,34,342-353.
Dahneke, B. Measurements of bouncing of small latex spheres. J. Colloid Interface Sci. 1973,45,584-590. Epstein, N. Particulate fouling of heat transfer surface: Mechanism and models. In Fouling science and Technology; Melo L. F., et al. Eds.; Kluwer: Dodrecht, 1988,Chapter 4. Hiller, R.; Loffler, F. Influence of particles impact and adhesion on the collection efficiency of fibre filtres. Ger. Chem. Eng. 1980,3, 327-332. ONeill, M. E. A sphere in contact with a plane wall in a slow linear shear flow. Chem. Eng. Sci. 1968,23,1293-1298. Perry, J. H. Chemical Engimeer’s Handbook; McGraw-Hill: New York, 6th ed.; 1984;Chapter 2. Robinson, S. K. Coherent motion in the turbulent boundary layer. In Annual Review of Fluid Mechanics; Lamley, J. L., et al., Ma.; Annual Reviews: Palo Alto, CA, 1991;Vol. 23,pp 601-639. Rogers, L. N.; Reed, J. The adhesion of particles undergoing an elastic-plastic impact with a surface. J. Phys. D: Appl. Phys. 1984,17,677-689. Saffman, P. G. The lift on a small sphere in a slow shear flow. J. Fluid Mech. 1965,22,385-403. Schlichtina, H. Boundary-Layer - Theory; McGraw-Hik New York, 1955;Chapter la. Tsai. C. J.: Pui. Y. H.: Liu. B. Y. H. CaDture and rebound of small particles upon impact k t h solid surfaces. Aerosol Sci. Technol. 1990,12,497-507. Vatistas, N. The effect of adhesion time on particle deposition. Chem. Eng. Sci. 1989,44,1603-1608. Vatistas, N. The adhesion of particles to surface under turbulent flow conditions. In Particles on surface 3 detection, adhesion, and removal; Mittal, K. L., Ed.; Plenum Press: New York, 1991; in press. Wall, S.; John, W.; Wang, H. C.; Goren, S. L. Measurements of kinetic energy loss for particles impacting surfaces. Aerosol Sci. Technol. 1990,12,926-946. Yung, B.P. K.; Merry, H.; Bott, T. R. The role of turbulent bursta in particle reentrainment in acqueous system. Chern. Eng. Sci. i989,44,a73-882. Receiued for review March 8, 1991 Revised manuscript receioed December 12, 1991 Accepted January 14, 1992
Amine Extraction of Hydroxycarboxylic Acids. 1. Extraction of Citric Acid with 1-0ctanolln -Heptane Solutions of Trialkylamine Vladislav Bbek,* J a n HoriEek, Roman b i i c h a , and Michaela Kou6ovi Znstitute of Chemical Process Fundamentals, Czechoslovak Academy of Sciences, Rozvojov6 135, 16502 Praha 6,Suchdol, Czechoslovakia
Extraction of citric acid from aqueous solutions with TAA, a mixture of tertiary aliphatic amines, dissolved in l-octanolln-heptane mixtures, and coextraction of water have been studied as a function of acid, amine, and octanol concentrations a t different temperatures. Using a “chemical modeling” approach, two complexes [acid-amine.hllH20 and a ~ i d . ( a m i n e ) ~ - h ~ ~have H ~ Obeen ] assumed to exist in the organic phase, and the corresponding equilibrium constants,apparent enthalpies, and entropies of complex formation have been evaluated. The overall equilibrium constants, Bill and Fl2,and hydration numbers, hll and hI2,have been correlated with the concentration of amine and with various properties of the mixed solvents. The solubility of water in acid-free organic phase has been found to be the best fitting parameter. According to IR spectra, the amineacid interaction is represented by an equilibrium between the extreme types of an H-bond (“neutral” O-H.-NR3 and ionic O--. H-+NR3). A mathematical model of acid extraction and water coextraction has been formulated. Introduction Amine extraction has been found to be a prospective method of separation of carboxylic or hydroxycarboxylic acids from aqueous solutions. More than 50 papers have been published on this subject up to 1988 (see Kerbs and King (1986) and Tamada and King (1989)). At least seven more papers have emerged since 1989 (Bauer et al., 1989; Chen et al., 1989; Tamada et al., 1990, Tamada and King,
1990a,b;Poole and King, 1991; Yang et al., 1991). Various aspects of this complex subject were elucidated. Nevertheless, many interesting problems have been left for future work, e.g., quantitative description of the influence of amine concentration, the effect of diluent, and coextraction of water. Thirteen papers were found to be devoted to amine extraction of citric acid. Pyatnitskii et al. (1970a,b, 1971,
0888-588519212631-1554$03.00/0 1992 American Chemical Society
