Foam fractionation of globular proteins

$Page 1: Foam fractionation of globular proteins$
Foam Fractionation of Globular Proteins*

Lynn Brownt, Ganesan Narsimhan?, and P. C. Wankat Departments of Agricultural (G. N.1 and Chemical Engineering (L. B. and P. C. W), Purdue University, West Lafayette, Indiana 47907

Accepted for publication June 5, 1990

Foam fractionation of bovine serum albumin (BSA) was studied as a model system for potato wastewater. The effects of feed concentration, superficial gas velocity, feed flow rate, bubble size, pH, and ionic strength on the enrichment and recovery of BSA were investigated in a single- stage continuous foam fractionation column. Enrichments ranged from 1.5 to 6.0 and recoveries from 5 to 85%. The feed concentrations were varied from 0.01 to 0.2 wt YO, and enrichments were found to increase with lower feed concentrations. Enrichments also increased with lower superficial gas velocities and larger bubble sizes. At sufficiently low feed flow rates, enrichment was found to increase with an increase in the flow rate, eventually becoming insensi- tive to the feed flow rate at higher values. The pH was varied from 3.5 to ZO and ionic strength from 0.001M to 0.2M. The effects of pH and ionic strength were found to be coupled with bubble size. A minimum bubble size was found at pH 4.8, the isoelectric point of BSA, resulting in a minimum in the enrichment. Bubble size, and thus enrichment, was found to increase as the ionic strength decreased from 0.2M to 0.OlM. Previous models’*2 for the hydrodynamics of foam column were extended for a single- stage continuous foam fractionation column for the prediction of enrichment and recovery. The model assumed adsorption equilibrium, infinite surface viscosity, and bubbles of the same size. Though coalescence was formally accounted for in the model by considering bubble size as a function of foam height, calculations for the experimental runs were performed only for the case of no coalescence. Quantitative predictions of enrichment and recovery could not be made with a single representative bubble size because of the broad inlet bubble size distribution as well as broadening of the distribution as a result of coalescence. The experimental enrichments were higher and recoveries were lower than the model predictions, the discrepancy being more pronounced at lower feed concentrations because of increased coalescence. The higher enrichments are due to the predominant effect of internal reflux as a result of coalescence whereas the lower recoveries are a result of detrimental effects of broadening bubble size distributions.

INTRODUCTION

Foam fractionation may be a viable method for recovery and initial concentration of proteins in dilute waste

* Paper No. 12368, Agricultural Experimental Station, Purdue

Current Address: Merck & Co. , Inc., P.O. Box 7, Elkton, University, West Lafayette, Indiana.

Virginia. * To whom all correspondence should be addressed.

effluents. Foam fractionation is based on the selective adsorption of surface active components such as proteins at a gas-liquid interface. Foam fractionation works best at low concentrations ( < 1 wt %) while other separation methods such as ultrafiltration are economi- cal only at higher concentrations. A plant for a dilute waste stream such as potato processing waste effluents which contain from 0.1 to 0.2 wt % protein3 might have a foam fractionation system followed by ultrafiltration. In this article, we study the foam fractionation of bovine serum albumin (BSA) as a model of the major protein (albumins) in potato wastewater.

Although it is not a major industrial unit operation, foam fractionation is used commercially. Lemlich4 has a general introduction and overview of foam fractionation while Okamoto and Chou,’ Somasundaran and Anathapadmanabhan,6 and Wilson and Clarke’ review the process and applications. The stability of protein foams has been extensively studied and is reviewed by Hailing.' Foam fractionation of BSA was studied in a batch process by Schnepf et al.,9 and in a continuous process by Ahmad’o,ll and by Gehle and Schugerl.’’ Ad- sorption data for BSA at air water interfaces was determined by Graham and Phill ip~.’~ In this article we greatly extend the range of variables studied for continuous foam fractionation, include bubble size measurements, and compare the results to theoretical predict ions.

A variety of models for foam fractionation have been developed starting with the early work of Miles and Schedlovsky l4 and Jacobi et al.” Leonard and Lem- li~h’~,’’ improved the early models by including surface viscosity and relaxing the assumptions on the geometry of the Plateau borders. Haas and Johnson” applied this model more directly to foam columns. Hartland and Barber19 and Desai and Kumar” accounted for thinning of the liquid lamellae and for variations of liquid holdup with foam height. Narsimhan and Ruckenstein’*’ considered the effect of capillary and disjoining pressure on the thinning of the liquid lamellae. Coales- cence due to van der Waals mediated rupture of the lamellae was also taken into account. They also accounted for a bubble size distribution. Their model, however, did not consider a continuously operating

Biotechnology and Bioengineering, Vol. 36, Pp. 947-959 (1990) 0 1990 John Wiley & Sons, Inc. CCC 0006-3592/90/09094~013$04.00

foam column. The model developed in this research is based on the model by Narsimhan and Ruckenstein,' but is written for a continuous foam fractionation column with liquid holdup decreasing up the column.

flowmeter

THEORY

A schematic diagram of a single stage continuous foam fractionation column is shown in Figure 1. Feed is in- troduced at the bottom of the column and the bottom product is withdrawn in order to maintain a constant volume of pool liquid in the column. An inert gas is bubbled through the liquid pool in order to produce a foam which moves up the column entraining some of the liquid from the pool. The foam bed consists of an ensemble of bubbles of different sizes. The bubbles in the foam are distorted in the form of polyhedra. An idealized regular dodecahedral gas bubble is shown in Figure 2. The faces of adjacent bubbles border the liquid

Y Feed (from pump)

4 impeller

ghrr f r l t s

n n n - Bottoms f

p r o t e i n

rolul lnn n I flowmeter

flowmeter

Nitrogen

Figure 1. fractionation column.

Schematic diagram of a single-stage continuous foam

I

films (lamellae), which intersect in plateau borders. A cross-sectional view of the plateau border is also shown in Figure 2. The entrained liquid in the moving foam is distributed between thin films and plateau borders. The liquid in thin films drains into the neighboring plateau borders under the action of plateau border suction and liquid drains through the interconnected network of plateau borders due to gravity. Consequently, the liquid holdup decreases with height. Protein, being surface active, is adsorbed at the gas-liquid interface. The col- lapse of the foam at the top of the column results in protein enrichment because of the recovery of adsorbed protein.

Two important measures of performance of the continuous foam column are enrichment and recovery. Enrichment e is defined as the ratio of product concentration to feed concentration:

e = cq/cF (1)

where cq and C F are the product and feed concentrations, respectively. Recovery r is the fraction of protein recovered in the tops product stream. Recovery can be calculated from

where Q and F are the product and feed stream flow rates, respectively. In the above equation, cqQ represents the total flow of protein in the tops product stream, while cFF represents the total flow of protein in the feed stream. High enrichments and high recoveries are desirable. To determine e and r we must determine cq. The protein in the top product comes from protein adsorbed on the foam surface and protein in the bulk liquid. Determination of these quantities is the goal of the theory.

As mentioned previously, the model developed in this work is based on the model by Narsimhan and Rucken- stein.'92 The major differences between their model and the one developed here include that the model developed here is for a continuous column, and it is assumed here that the surface viscosity is large enough to be approximated as infinite. Because globular proteins normally have a much higher surface viscosity than low-molecular-weight surfactants and other proteins, this assumption should be valid for relatively high

INTERSECTION OF HORIZONTAL PLANE

' - PLATEAU BORDER

PLATEAU BORDER J (INTERSECTION OF P F I L M ~ THREE FILMS)

FILM (INTERSECTION OF FACES OF TWO ADJACENT POLYHEDRA)

Figure 2. Idealized bubble of regular dodecahedra1 structure and cross-sectional view of a plateau border.

948 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 36, NOVEMBER 1990

protein concentrations.” Other researchers have veri- fied the validity of this assumption.” Surface viscosity for BSA, a globular protein, has been measured to be approximately 60 dyn s/cm at concentrations greater than wt %.’l

Coalescence is formally accounted for in this model by allowing the bubble radius to be a function of height in the column and including a coalescence frequency. Coalescence will have two effects on the enrichment. First, because coalescence destroys surface area, the contribution of surface protein to the enrichment will decrease. This will tend to decrease the enrichment. Second, coalescence serves as internal ref lux. Adsorbed protein from the destroyed surface is released into the bulk liquid and flows back down the foam and increases the concentration of the bulk liquid entrained in the foam, which increases enrichment. (Coalescence was assumed to be negligible in the numerical calculations for the simulation of the experiments.)

The model developed in this work accounts for gravity drainage through the network of Plateau borders. It also accounts for the thinning of the liquid lamellae due to Plateau border suction. Material balances are made on the liquid and protein in the films and in the Plateau borders in order to predict the liquid holdup in the foam. Enrichments and recoveries can then be estimated.

Several simplifying assumptions are employed in the development of the model. First, it is assumed that the gas phase consists of dodecahedral bubbles of uniform size at a given height in the foam and that the foam bed moves up the column in plug flow. Photographs showed that the bubbles are polyhedral. Also, the Plateau borders are assumed to be randomly oriented. Finally, it is assumed that the surface concentration of the protein is its equilibrium concentration. This assumption should be valid for high protein concentrations and if the liquid pool height is large so that the residence time of the bubble in the pool is long.

The protein in the collapsed foam comes from the bulk liquid that was entrained in the foam, and from the surface. Because most of the surface area on the bubble is from the thin films, the contribution of surface area from the Plateau borders can usually be neglected. Let N be defined as the number of bubbles per unit of volume of the foam and nf be the number of thin films per bubble. For a regular dodecahedron we set nf = 6 to avoid double counting (see Fig. 2). The total surface area per volume of foam is NnfAf where A, is the surface area per film. The total amount of protein adsorbed on the surface per unit volume of foam is NnfAfT, where r is the surface concentration (excess) of BSA.

To determine the total surface area per volume of liquid, the liquid holdup E is needed. The two contributions to the liquid holdup are the liquid in the thin films and in the Plateau borders. For a regular dodecahedron the number of Plateau borders per bubble, np, is set at 10 to avoid double counting (see Fig. 2). Also, let up be the cross-sectional area of a Plateau border and I

be the length of a Plateau border. In a dodecahedral arrangement,

1 = 6R (3)

where 6 is equal to 0.816,20 and R is the radius of the bubble. Finally, ifxf is the thickness of a thin film, then the liquid holdup is

E = NnfAfxf + Nn,a,l (4)

Once the liquid holdup is known, and assuming equilibrium data are available, the enrichment is

(5 ) NnfAfT c e = c 4 = p + -

C F C F E CF

To be able to predict the enrichment for a given feed concentration and a desired product concentration, N, c, E , and r must be known. Paramater r is a function of c depending on the form of the equilibrium data. To determine c, a material balance on the protein in the foam must be made.

Material Balance for Liquid in Films

Liquid will tend to drain out of the films at velocity V due to Plateau border suction. To determine the drainage of liquid through a circular plane parallel film of radius Rf and thickness xf, the equations of continu- ity and motion must be written with the appropriate boundary conditions. For the case of infinite surface viscosity, the no-slip boundary condition can be used, and the solution of the equations becomes the Reynolds equation

where A P is the pressure difference between the films and Plateau borders; p is the bulk liquid viscosity; and Rf is the radius of the planar face of a film. From geometrical considerations, the area of the planar face of the film, A , will be”:

(7) A, = 1.152R’ = rRf2

Solving the above equation for Rf yields:

The pressure drop responsible for thin-film drainage will be given by

Y A P = - - - n RP

(9)

where y is the surface tension; R, is the radius of curvature of the Plateau border; and II is the disjoining pres-

BROWN, NARSIMHAN, AND WANKAT FOAM FRACTIONATION OF GLOBULAR PROTEINS 949

sure. From geometrical considerations, R, will be 20:

- 1 . 7 3 2 ~ ~ + [(1.732~f)~ - 0.644(0.433~; - a,)]”’ 0.322

R, =

Disjoining pressure has two components: van der Waals attraction and double-layer repulsion. Van der Waals attraction tends to make the bubbles move closer together and causes the liquid in the film to drain faster. However, repulsion of the bubbles due to overlapping of the electric double layers tends to slow film drainage. Disjoining pressure only becomes important when the films become very thin (less than 100 nm), which requires residence times much longer than in our experiments. Thus, disjoining pressure was neglected in eq. (9).

Coalescence is accounted for by assuming that the bubble radius increases with height in the foam. The change in the total surface area is accounted for by monitoring the change in the number of bubbles per volume of foam with height in the column, and their size. The coalescence frequency, p, is the fraction of bubbles collapsing per unit time. Letting 77 be the number of bubbles passing through a unit cross-sectional area of the foam column per unit time, the change in 77 will be given by:

The right-hand side is divided by a factor of two in order to avoid double counting. 7 and N can be determined as:

where G is the superficial gas velocity. The volume of a bubble, vb, is

where R is the equivalent radius of the spherical bubble. Combining eqs. (11)-(13) and solving, we obtain

h N R 4 dR p = - 9G dz

As expected, the bubble radius is constant if p = 0. Equation (14) allows one to estimate p from experiments. Prediction of /3 requires a stability analysis of draining thin films subjected to thermal and mechanical perturbations which is beyond the scope of this article, It is to be noted that coalescence will result in the broadening of the bubble size distribution. The above

simplified model assumes that the broadening bubble size distribution can be represented by varying the average bubble size. Such an assumption is likely to be valid only if the bubble size distribution is sufficiently narrow everywhere in the column i.e. broadening of the distribution due to coalescence is small.

The material balance for the liquid in the films is

d N dz 2 - - (qnfAfxf) - NnfAf V - -nfAfxfp = 0 (15)

The first term represents the change due to convection, the second term represents the flow of liquid out of the films due to Plateau border suction, and the third term represents the loss of liquid due to the rupture of films leading to coalescence. Note that dxf/dz is always negative; the films are continuously thinning.

Material Balance for Liquid in Plateau Borders

There will be four contributions to the material balance for liquid in the Plateau borders. First, liquid will be sucked into the Plateau borders from the films due to the higher pressure in the films. Second, liquid from the ruptured films will be redistributed in the Plateau borders. Third, there will be a term due to convection because the foam is moving up the column. Finally, gravity will cause the liquid to drain out of the foam through the network of Plateau borders.

The velocity of gravity drainage, u, can be determined by solving the Navier-Stokes equationsz3:

where cv is the ratio of the average velocity with finite surface viscosity to the average velocity through the Plateau border for infinite surface vis~osity.’~ For infinite surface viscosity, c, is unity.

The average volumetric flow rate q, through a randomly oriented Plateau border is’

2 3

qp = -a,u

To determine the total gravity flow at a given height, the total cross-sectional area of the Plateau borders must be known. The total number of bubbles per area of foam cross section is 2RN. Then the number of Plateau borders per unit area of foam will be 2RNni, where ni is the number of Plateau borders per bubble that intersect a cross section of foam. For a regular dodecahedron, n; will be n,/5 = 2. The change in flow due to gravity is

d 4 (da,), = - - Nn,a,uR

dz 15


The material balance for liquid in the Plateau borders can be constructed:

-d dz

N - Pnf Afxf = 0 (19) 2

Material Balance for Protein in the Foam

In order to predict enrichment, the concentration of protein in the bulk liquid being entrained in the foam [c/cF in eq. (5)] must be known. Because of coalescence, this concentration changes with height in the foam. When the thin films rupture, the liquid and protein from the destroyed surface are redistributed in the Plateau borders. Thus, the concentration of protein will be different in the Plateau borders than in the films. Two extreme cases can be considered. First, if the liquid entrained in the foam is well mixed, protein concentration is the same in the films and the Plateau borders. This assumption will tend to predict concentrations that are too high, but it should be reasonable if the amount of liquid in the films is small relative to the amount of liquid in the Plateau borders. In the second case, it is assumed that the liquid in the films and plateau borders are segregated and that the liquid in the destroyed films and plateau borders upon coalescence are redistributed among the remaining plateau borders. Consequently, only the concentration in the plateau borders changes and the concentration in the films remains constant at that of the pool. This assumption tends to underpredict the concentration. The actual solution will lie somewhere between these two extreme cases. If there is no coalescence ( p = 0), the two extreme cases give the same results because the concentration of protein in the entrained liquid will not change. We will present the equations for the well- mixed case, although similar equations can easily be written for the segregated case.

The material balance for protein is

-d -[Tnpa,lc + qnfAfxfc] + dz

N N - /3nfAfr + - PnfAfxfc = 0 (20) 2 2

Note that if there is no coalescence, /3 = 0 and dc/dz = 0.’ In order to solve eq. (20), r must be known as a function of c. In the calculations done here for BSA, the isotherm is approximated as linear using an equation based on experimental dataI3:

r = 1.13 x 1 0 - ~ ~ + 3.21 x 10-7

where r is in g/cm2 and c is in wt %. The bulk concentration range eq. (21) is assumed to be valid for is from 0.004 to 0.1 wt %.

(21)

These equations can be solved simultaneously with the appropriate boundary conditions to obtain the liquid holdup, enrichment, and the recovery. If coalescence is negligible, the equations are greatly simplified. Parame- ters p and dc/dz will be zero, and the number of equations needed to solve for E is reduced to two. When /3 = 0, eq. (15) for the liquid in the films becomes

d”r= dz -[+I, While eq. (19) for the liquid in the Plateau borders is given by

Nn a R 4 - qnpl - d a p [ dz 7 5 f i p 15

p g - -Nn,uR

1 4njla,uR 15(vb + nfAfxf + n,ap1)2

+

dx, (23) = NnfAfV - 4nfAfnpa,u R

15(vb + nfAfx, + n,ap1)2 dz

Boundary Conditions

In order to solve either the set of two or four coupled equations, the values of R , xf, c, E , and G at the foam- liquid interface must be known. Also, it is necessary to know the fraction of liquid that is distributed in the films and the fraction that is in the Plateau borders. Let & be equal to the fraction of liquid in the films at the foam-liquid interface. It can be assumed that R , G, and c can be specified or controlled experimentally. It is difficult to determine E, and &f,, but E, can be estimated from the void volume of close-packed spheres and set equal to 0.26. Drainage occurs very rapidly initially, and the value of E~ does not appear to be ~ritical.’~

From an overall material balance for the liquid in the foam, the difference between the rates of uptake and drainage of liquid at the foam liquid interface should be equal to the difference at the top of the foam column. The flow rates at the top of the foam column are usually much smaller than those at the foam liquid interface because the liquid holdup at the top of the column is much smaller than 0.26. Moreover, the rates of uptake and drainage at the top of the column should be more or less equal since the liquid holdup1Xz0 far from the pool liquid interface remains fairly constant. Consequently, one can approximate the rate of uptake at the foam liquid interface as equal to the rate of The rate of uptake at the foam liquid interface is

(24) G E O rate of uptake = ~

1 - 8,

At zero foam height, the rate of drainage will be the rate of gravity drainage:

4 (rate of drainage at z = 0) = -N 15 0 n P a PO R,u, (25)


Consequently,

GE, 4 -- - - N n a Rouo 1 - E , 15 O P p

Also,

1 - E , No = ~

4 - n-R? 3

The initial value for R, can also be solved for by substi- tuting xf, and a,, into eq. (10). Note that R,, cannot be negative. Equations (26)-(29) can be solved simultaneously to obtain the initial values xf, and a,,. From an overall protein balance, the pool concentration, cB, can be related to the feed concentration cF through,

where F is the feed flow rate per unit cross-sectional area of the column and r is the equilibrium surface concentration of protein at the pool concentration.

Equations (22) and (23) were solved simultaneously with the boundary conditions [eqs. (26-(2911 to obtain predictions for the liquid holdup, enrichment, and recovery for an aqueous solution of bovine serum albumin. For the simulation of experiments, coalescence was assumed to be negligible, so that p, the coalescence frequency, was zero, and the concentration of the bulk liquid in the foam did not change with height in the foam. All calculations were done with a feed flow rate of 0.02 cm’/cm’ s. The equations were solved using an International Mathematics and Statistics Library (IMSL) routine to numerically solve sets of ordinary differential equation by the Gear rneth~d.’~ Additional details are given by Br~wn. ’~

EXPERIMENTAL

Figure 1 shows the final design of the foam column. It consisted of a glass column, 4.5 cm in diameter and 22 cm high. Liquid was initially pumped into one of two feed ports located near the bottom of the column. Bottoms liquid was pumped out of the bottom of the column at a rate that allowed the liquid level to remain 5 cm from the top of the column (a liquid level of 17 cm). Dry nitrogen was sparged through three glass frits 5 mm in diameter and with pore sizes ranging from 4 to 10 pm. To obtain reproducible results, the frits had to be soaked in an acidic cleaning solution after each use to remove adsorbed protein. While the feed and

bottoms flow rates were measured and controlled by flowmeters, the tops flow rates was calculated from an overall mass balance. The foam breaker consisted of a two-blade flat impeller centered over the foam column. An optimum RPM was determined empirically. The foam was thrown to the silicone-treated wall of the outer column where it breaks, and the liquid was col- lected from a port on the bottom of the outer column. The outer column was siliconized by soaking in a solution of dichlorodimethylsilane (Eastman Kodak) and chloroform. A thin layer of the silicone compound was deposited on the column, creating a permanent, non- wetting surface that was able to break the foam in the majority of cases.

In most experiments a phosphate buffer was added to deionized water to adjust the feed solution to a pH value of 7.0 and a conductivity equal to that of 0.1M NaCl. In the measurements of the effect of ionic strength, a phosphate buffer concentration of the order of 10-4M was used to maintain pH 7.0, while sodium chloride was used to adjust the ionic strength. In the final set of experiments that investigated the effects of pH, a citrate- phosphate buffer with concentration of the order of lOP4M was used to vary the pH, while sodium chloride was again used to adjust the ionic strength.

To start the operation of the column, protein solution was added to the desired level and the nitrogen was turned on. The feed flow rate was set and the bottoms flow rate was adjusted so as to keep the liquid level in the column constant. Samples were taken every 15 min initially and analyzed for protein concentration using UV absorbance at 280 nm. Usually, about 1.5 h was needed for the system to attain steady state. Because of the presence of fine gas bubbles, the top sample was allowed to sit before reading the absorbance.

In order to compare the experimental results with a model, the size of the bubbles in the foam were measured. Two additional sections of column were added onto the experimental apparatus in order to take pictures. This allowed the foam-liquid interface to be visi- ble through the inner section of column. To simulate the actual experimental conditions, the liquid level was kept at the same height as in all of the experiments. Also, the column was run in the same manner as previously described. Pictures of the foam just above the interface were taken with a Canon AE-1 35-mm camera with auto bellows. High contrast technical pan film (Kodak, ASA 125) was used to improve the distinction between liquid and gas. In a few cases, pictures were also taken at 2.5 and 5.0 cm above the interface to determine if coalescence was taking place.

Bubble size measurements from the pictures were made with a Kontron IBAS 2000 image analysis system operating in an interactive mode because the picture quality was relatively poor. Bubble size distributions, average bubble diameters, and other statistical parameters were obtained.


RESULTS

Figures 3 through 5 show the plots of experimental as well as predicted protein enrichments versus superficial gas velocity f& different feed concentrations. Addi- tional results are given by Brown.25 The enrichment tends to decrease and then level off as the gas flow rate increases. This is expected since the amount of liquid that is entrained in the foam increases as the gas flow rate increases. The increased entrainment decreases the relative contribution from protein adsorbed on the surface which decreases the enrichment.

Figures 3-5 also show that enrichment increases as the feed concentration decreases. This is particularly

7.0 1 I I \

0 0.02 0.04 0.06 0.08 0.10 0.12 0.14

SUPERFICIAL GAS VELOCITY (CM/SEC)

Figure 3. Effect of superficial gas velocity on protein enrichment for cF = 0.1 wt %; F = 0.02 cm/s; Z = 0.1M; pH 7; and z = 5 cm. The curves refer to model predictions for different bubble radii.

0 0.02 0.04 0.06 0.08 0.10 0.12 0.14


Figure 4. Effect of superficial gas velocity on protein enrichment for CF = 0.05 wt %; F = 0.02 cm/s; I = 0.1M pH 7; and z = 5 cm. The curves refer to model predictions for different bubble radii.

0 0.02 0.04 0.06 0.08 0 10 0.12 0.14


Figure 5. Effect of superficial gas velocity on protein enrichment for CF = 0.01 wt %; F = 0.02 cm/s; I = O.lM, pH 7; and z = 5 cm. The curves refer to model predictions for different bubble radii.

true at lower gas flow rates. The BSA isotherm shape is one reason for this. The second reason is illustrated in Figure 6 which shows that the measured average bubble size increases as feed concentration and gas flow rate decreases. The larger bubbles decrease the liquid holdup because of faster drainage and therefore enrichment increases. As can be seen from Figures 3-5, the predicted protein enrichments for the measured average bubble sizes are always smaller than the experimental values, this discrepancy being more pronounced at lower feed concentrations.

Predicted and experimental recoveries are shown in Figures 7-9. Qualitatively, both experiment and theory

A A

A

0.17

I '* 0 0.18

A food aono. = 0.01 wtA

0 ford aana. I 0.0s wtA

food aorta. = 0.20 rt::

~ 0.15

E a

0 P

0.13

/ ' , ' I . , ' I . -.--

0.0 0.02 0.04 0.06 0.08 0.10 c ta

GES Flow R a t e (cm/sec)

Figure 6. Effect of gas flow rate on the average bubble size at the foam-liquid interface for F = 0.02 cm/s; z = 0 cm; I = O.lM, and pH 7.


1 -~ 1.0 ,

0 0 0 2 0.04 0.06 0 0 8 0 10 0 12 0 14


Figure 7. Effect of superficial gas velocity on protein recovery for CF = 0.1 wt %; F = 0.02 cm/s; I = 0.1M, pH 7; andz = 5 cm. Curves refer to model predictions for different bubble radii.

1 .o

0 0.02 0.04 0.06 0.08 0.10 0.12 0 14


Figure 8. Effect of superficial gas velocity on protein recovery for CF = 0.05 wt %; F = 0.02 cm/s; I = 0.1M, pH 7; and z = 5 cm. Curves refer to model predictions for different bubble radii.

1 0 ,

o l l , l l l l l l , l ] l l , 0 0.02 0.04 0 OF, 0.08 0 10 0.12 0.14


Figure 9. Effect of superficial gas velocity on protein recovery for cp = 0.01 wt %; F = 0.02 crn/s; I = 0.1M; pH 7; and z = 5 cm. Curves refer to model predictions for different bubble radii.

show that recovery increases as gas flow rate increases due to increased entrainment. The theory also predicts that recovery increases for lower feed concentrations but this is not borne out by the experiments.

Before discussing additional experimental results, it is worthwhile to explore bubble size in more detail. Figure 10 is a histogram of the bubble diameter distribution from the image analysis. This histogram is rea- sonably representative of the other histogram^.^' Note that the distribution is quite broad. Because there is distribution of bubble sizes, the single bubble size used in the model calculations should represent an average size. In the material balance equation for liquid in the films, the appropriate average to use is the area average diameter.' However, the number average diameter may be more appropriate in the material balance equation for liquid in the Plateau borders. If the size distribution is narrow, these two averages will differ only slightly. However, for the broad distribution shown in Figure 10, the area average size will be much larger than the number average, and one single appropriate average size will not exist. Figure 11 is a comparison of theory and experiment where both the average and the maximum

1 4 0 . 0 0

3 0 . 0 0

2 0 . 0 0

1 0 . 0 0

B wee

C O U N T S 233 I N R U N G E 233

l i f R f A L p 3 L s E - e l I W T E R V D L

kbkt f iO&635S9 k.hk0.607596 . . . . 8 . 3 6 3 1 2 7 S T . 0 v ke b 6 3 5 4 2 E - 0 1

k b b g 8 . 3 6 3 7 3 4 .... 0 . 3 7 3 6 9 7

DCIRCLE

diameter, m m

Figure 10. cf = wt %; G = 0.10 crn/s; pH 7; I = 0.1M; and z = 0 cm.

Histogram for inlet bubble size distribution. with

R = O . O l E c m ( a v e r a g e ) R=O 04cm (maximum)

3.0

0 0.02 0.04 0.06 0 08 0.10 0.12 0.14


Figure 11. Predicted and experimental protein enrichment vs. superficial gas velocity for C F = 0.05 wt %; F = 0.02 cm/s; I = O.lM, pH 7; a n d z = 5 cm.


bubble size were used. The experimental enrichments are higher than model predictions even for the maximum bubble size. It is also clear from Figures 7-9 that experimental recovery results are lower than model predictions. For a broad bubble size distribution large bubbles control the drainage and hence the liquid holdup while the small bubbles control the surface area. Thus it is likely that a single avezage bubble size cannot adequately model this broad distribution.

A second problem with bubble size is coalescence. Coalescence was observed for feed concentrations of 0.01 and 0.05 wt %. This is illustrated in Figure 12 since bubbles are increasing in size as one moves up the foam. More coalescence was observed at the lowest feed concentration. This is understandable since the adsorption of protein at gas-liquid interface, responsible for stabilization of the foam, is lower at lower protein concentrations. Coalescence acts as internal reflux, decreases surface area, and broadens the bubble size distribution. Internal reflux would increase the enrichment and recovery because of the increase in the bulk and the subsequent increase in the surface concentration of proteins. However, the decrease in the surface area would decrease enrichment and recovery. As will be discussed later, preliminary evaluations of the effect of bubble size distribution indicate that the broadening of the distribution is detrimental both to enrichment as well as recovery. In our experiments, it appears that protein enrichment is controlled mainly by the first effect whereas recovery is influenced predominantly by the other two effects. This would explain the higher experimental enrichments and lower recoveries than the model predictions especially at lower feed concentrations. This discrepancy between the experiments and the model predictions is discussed later.

A 0 - 0.06 em/

0 = 0.10 om/

:

0.0 1.0 a.0 8.0 4.0 6.0

HofOht in Form (om)

Figure 12. Change in average bubble diameter with foam height, CF = 0.01 wt %; I = 0.1M; and pH 7.

Additional experiments were done to explore the effect of feed flow rate, ionic strength, and pH. The effects of the feed flow rate on the enrichment and recovery are shown in Figure 13. The feed flow rate has a significant effect on the enrichment only at values below 0.2 cm/s where the enrichment decreases. At low feed flow rates, the residence time of the liquid in the pool is large, and the concentration of entrained bulk liquid are decreased, the enrichment decreases. The recovery decreases as feed flow rate is increased, but the mass of protein in the top product actually increased. The entrainment depends on the gas rate and is insensi- tive to the liquid rate. Thus at higher feed rates the fraction of feed entrained decreases and the fraction of feed recovered also decreases.

The effects of ionic strength on enrichment and recovery are shown in Figure 14. At lower values of ionic strength, the enrichment decreases with increasing ionic strength. Above a concentration of approximately 0.1M NaC1, the addition of more salt appears to have

1.7 -

1.0 - o rnrlohm-n i erroovery 1 - 0.0 p

b h

-0.0 ' - O.' i - 0.0 : - 0.0

i - 0.4

0 ::=! ; , . I , , , I !jj 1 1.0 0.0

0.0 0.08 0.04 0.08 0.08 0.10

F--d Flow R ~ t r (om/mao)

Figure 13. recovery, with cF = 0.05 wt %; z = 5 cm; I = 0.1 M, and pH 7.

Effect of feed flow rate on protein enrichment and

8.0 1.0

- 0.9 0 0

A onrtrhmot

A rrr.- - 0.0 a b - O.' a - 0.0 If

8.8

*

- 0.4

- 0.8 j -0.1 &

1.0 -

0.0

10-1 10.

1.0 . . . . ...., . . . . . ...( , . . . ...., . . . .I.. I-

10- 10- 10-

Ionio Stranstlx. Y

Figure 14. Effect of ionic strength on protein enrichment and recovery, with CF = 0.05 wt %; F = 0.02 cm/s; G = 0.053 cm/s; pH 7; and z = 5 cm.

i3ROWN, NARSIMHAN, AND WANKAT: FOAM FRACTIONATION OF GLOBULAR PROTEINS 955

little effect on the enrichment. The bubble size in the foam increased as the ionic strength de~reased.’~ As described earlier, larger bubbles in the foam tend to make the foam drain faster, have less liquid holdup, and, therefore, higher enrichment. The size of a gas bubble produced through a frit is proportional to the square root of the surface tension of the liquid through which the gas is being bubbled.26 Since the surface tension of BSA solutions increases as the ionic strength decreases:’ the increase in bubble size with decreasing ionic strength is expected. No theoretical calculations were done, since adsorption equilibrium data are not available at varying ionic strengths.

The effect of pH on enrichment is shown in Figure 15 at an ionic strength of 0.01M. Note that there is a minimum in enrichment at a pH around 4.8 which is the isoelectric point of BSA. At an ionic strength of 0.1M this minimum did not occur and enrichment was lower at pH 3.6. The enrichment becomes higher as the feed concentration is decreased. The results shown in Figure 15 were unexpected since Schnepf and Gaden’ and Ahmad” reported maximum enrichments at the PI. Schnepf and Gaden’ reported a maximum at PI for feed concentrations ranging from 5 x to 2.5 x

wt %. As the concentration increased, however, the maximum became less pronounced. At a concentration of 5 x pH is reported to have no effect on the enrichment. Also, neither article reports the ionic strength of the solutions used, but it is probably lower than 0.01M because the only electrolyte added to the solution was in the adjustment of pH. Thus, it is difficult to make a direct comparison of the results. Previ- ous studies made no mention of the size of bubbles produced. In the experiments done here, there was a shallow minimum at the PI followed by a large increase

10.0 -

0.0 -

8.0 - 4J 1 7.0 I a 8 0.0 :

0.0 1 *

IJ 4.0 -

food oonon - 0.01 rt%

0 f.-d oonon - 0.0s r t X i

€ f x I H

1 . 0 ; . . , , . . . , . . . , . , . , ‘ . . I . . .

8.0 5.0 4.0 0.0 8.0 7.0 8.0

p H of Feed

Figure 15. Effect of pH on protein enrichment at different feed concentrations, with F = 0.02 cm/s; G = 0.08 cm/s for CF = 0.05 wt %; G = 0.01 cm/s for cF = 0.01 wt %; I = 0.01M; and z = 5 cm.

in the bubble size at pH 3.5. The change in bubble size can be explained once again by the difference in surface tension at different pH values, since surface tension has a minimum at the PI.’’ This change in bubble size may mask any other effect caused by a pH change. Also, a maximum in stability at the isoelectric point has been reported.’.” The foam at the isoelectric point would be less likely to coalesce. Because coalescence serves as internal reflux, the enrichments would be higher at pH values away from the PI.

DISCUSSION

Clearly, the quantitative predictions of enrichment and recovery by the model do not agree well with the experimental data especially at lower feed concentrations. The major deficiencies in the model are the use of a single bubble size to represent a broad distribution of bubble sizes and the assumption of no coalescence (p = 0). The distribution of bubble sizes can be accounted for,’ although the model becomes significantly more complicated. The use of two bubble sizes may be adequate to describe the effect of bubble size distribution. Though coalescence was formally accounted for in the model by considering bubble size as a function of foam height, simulation of experimental runs were performed only for the case of no coalescence. It is ex- tremely difficult to predict the coalescence frequency a priori from the stability analysis of thin films to imposed thermal and mechanical perturbations since the nature of the imposed perturbations is not known. Moreover, estimation of coalescence frequency from the experimental measurements of bubble size at different foam heights may be difficult because p may be a function of height.

To explore the discrepancy between the experimental data and the model predictions, two sets of calculations were done. In the first, enrichments and recoveries were calculated for different values of constant coalescence frequencies. As pointed out earlier, coalescence leads to (1) enrichment of the liquid due to internal reflux (2) faster rates of liquid drainage because of coarsening of bubble sizes, and (3) lower interfacial ar- eas. The first two effects tend to increase protein enrichment whereas the last two would decrease the recovery. A typical plot of normalized enrichment and normalized recovery versus dimensionless coalescence frequency p6 is shown in Figure 16. Here, 6 is the residence time of foam and the dimensionless enrichment and recovery were obtained by normalizing with respect to the corresponding values in the absence of coalescence. As can be seen from Figure 16, coalescence increases both the enrichment and recovery though the latter is a much weaker function of coalescence. When coalescence is not very significant (small values of P O , i.e., p6 < l), therefore, the predominant effect of coalescence seems to be the enrichment of the liquid as a result of internal reflux.


.2

0 0 2 .4 .a .a

0 0

Figure 16. Effect of coalescence frequency on enrichment and recovery, with F = 0.02 cm/s; G = 0.02 cm/s; cF = 0.01 wt %; z = 5 cm; and R = 0.02 cm. The enrichment and recovery are normalized with respect to the corresponding values in the absence of coalescence. Parameter 8 is the residence time of foam.

In the second set of calculations, the effect of broad bubble size distribution on enrichment and recovery is investigated by assuming that the foam bed consisted of bubbles of two different sizes. In these calculations, the average bubble size is assumed to be constant and the standard deviation of the bubble population is varied by varying the bubble sizes. Moreover, coalescence is assumed to be absent so that the bubble sizes do not change with foam height. The appropriate balance equations for film and plateau border drainage are given in the Appendix. A typical plot of normalized enrichment and normalized recovery versus the coefficient of variation of the bubble sizes is shown in Fig- ure 17. The dimensionless enrichment and recovery were obtained by normalizing with respect to the corresponding values when foam bed consisted of uniform bubble sizes (i.e., u = 0). Larger bubbles tend to hasten the rate of liquid drainage and provide much smaller interfacial area whereas smaller bubbles yield large interfacial area at the cost of much slower rate of drainage. As can be seen from Figure 17, the overall

=/ R Effect of coefficient of variation of the bubble size dis-

tribution on enrichment and recovery. The bubble population is assumed to consist of bubbles of two different sizes. Parameter values are F = 0.02 cm/s; G = 0.02 cm/s; cF = 0.01 wt %; z = 5 cm; and R , = 0.02 cm. The enrichment and recovery are normalized with respect to the corresponding values for uniform bubble sizes.

effect of broadening of the bubble size distribution is detrimental both to enrichment as well as recovery.

These calculations accounted for the effects of coalescence and bubble size distributions separately on enrichment and recovery and indicated that the former (for not too significant coalescence frequencies) is bene- ficial whereas the latter is detrimental. The combined effect of the two, of course, would depend on the relative importance of the two. Both the above effects can be expected to be more pronounced at lower feed concentrations since coalescence leads to broadening of the bubble size distribution. Since the experimental enrichments were higher and recoveries were lower than the predictions by the model which did not account for either coalescence or bubble size distribution, it is be- lieved that the enrichment is influenced predominantly by coalescence whereas the detrimental effect of bubble size distribution is reflected more on the recovery.

Some experimental difficulties should be mentioned. Because of the very low tops flow rates, the tops flow rate, Q, was determined from a mass balance as feed flow rate minus bottoms flow rate. Since there were

BROWN, NARSIMHAN, AND WANKAT: FOAM FRACTIONATION OF GLOBULAR PROTEINS 957

some fluctuations in flow rates and two approximately equal numbers were subtracted, Q and hence r are not very accurate.

A second experimental problem is that the bubbles which were photographed for determination of the bubble size distributions may not be representative. Only bubbles at or very near the wall were photographed. These bubbles may differ from the bubbles in- side the column.

Initially, the foam fractionation results could not be duplicated. After considerable refinement of the experimental technique, we realized that the glass frits had to be cleaned every night. Results were reproducible when the frits are soaked overnight in a hot solution of 50/50 concentrated sulfuric/nitric acid. All of the data shown here was taken after this was discov- ered. Alternate materials for the frits might foul less and require less cleaning.

More extensive bubble size distribution measurements at different foam heights are to be undertaken in order to infer the coalescence frequency from population balance analysis. For industrial applications multistage systems will be required to achieve acceptable overall enrichments and recoveries. At low protein concentrations where the isotherm is steep countercurrent flow of liquid and foam is desirable. The single stage shown in Figure 1 was designed so that it can be cas- caded. At higher protein concentrations where r is constant, a cross-flow system may be advantageous. One of the next steps in this research will be to design and construct a multistage cascade.

CONCLUSIONS

The effects of different operating variables on the enrichment and recovery of BSA were experimentally evaluated in a single-stage continuous foam fractionation column. Enrichments ranged from 1.5 to 6.0 whereas the recoveries varied from 5 to 85%. Higher enrichments were obtained at lower feed concentrations, lower superficial gas velocities, and larger bubble sizes. The feed flow rate was found to affect the enrichment only at very low values. The effects of pH and ionic strength were found to be masked by that of bubble size since bubble sizes could not be independently controlled at different pH and ionic strength because of the variation of surface tension. Minimum enrichment was obtained at pH 4.8, the isoelectric point of BSA, as a result of minimum bubble size. Lower enrichments were obtained at lower ionic strengths because of smaller bubble sizes. A model for the prediction of enrichment and recovery was proposed which accounts for the gravity drainage from the plateau border as well as the drainage of thin films due to capillary pressure. The model assumed adsorption equilibrium, infinite surface viscosity, and dodecahedra1 bubbles of the same size. Though the model formally accounted for coalescence by considering bubble size as a function of foam height,

enrichment and recovery for the experimental runs were predicted only for the case of no coalescence. Be- cause of the broad inlet bubble size distribution as well as coalescence, quantitative predictions of enrichment and recovery could not be made with a representative bubble size. The experimental enrichments were higher and recoveries were lower than the model predictions. The discrepancy between the model predictions and the experimental data is larger at lower feed concentrations because of increased coalescence as a result of lower surface concentrations of protein. Evaluations of the effects of coalescence and bubble size distributions through simple models indicated that the enrichment is influenced predominantly by internal reflux as a result of coalescence whereas the detrimental effect of bubble size distribution is reflected more on the recovery.

APPENDIX: BALANCE EQUATIONS FOR FOAM BED CONSISTING OF BUBBLES OF TWO SIZES

Here, a simple case of bubble size distribution is considered. The foam bed is assumed to consist of bubbles of two sizes, having a mean R , and standard deviation of u. If R I is one bubble size, the other bubble size, R I , is given by:

The fraction of bubbles f, of radius R1 is given by,

and the fraction of bubblesf2 of radius RZ is

fz = 1 - fi

(321

(33)

The balance equation for liquid in films in this case can be written as:

where t , j refers to the two bubble sizes. The area of the film between bubbles of sizes I and] is given by,

A,I = (A, ,AII)”Z = 1.152R,RI

The rate of drainage Kl of the film between bubbles of size i and given by,

is

(35)

The balance equation for liquid in the plateau border is given by:

where, f; and f, are the fraction of bubbles of size i and j , respectively, and t , = 6R,.

The above equations are solved with the boundary condition

G E ~ 4 -- - - N n a u R , 1 - 9 , 15 o p p ‘ J O

(37)


at the foam-liquid interface, where

1 - E , No = __

Vh,av

2

Vh,av = 2 v t j , = I

EodVo . 2 N q A Y

Xfat = , i = 1,2

1.J

apopg u -- a - 2ov3.L

E, = 0.26

(1 - 4 f o ) E o

No n p SRrn ap0 =

The concentration of proteins in the top product is given by;

NOMENCLATURE

cross-sectional area of plateau border area of film bulk concentration of BSA velocity coefficient for gravity drainage of plateau border enrichment feed flow rate per unit cross sectional area of foam column acceleration due to gravity superficial gas velocity length of plateau border number of films per bubble number of plateau borders per bubble number of plateau borders per bubble on a horizontal plane number of bubbles per unit volume of the foam bed pressure average volumetric flow rate through plateau border flow rate of top product recovery bubble radius radius of film radius of curvature of plateau border velocity of gravity drainage volume of a bubble velocity of film drainage thickness of thin film axial distance

Greek Symbols p coalescence frequency y surface tension r surface excess of BSA 6 constant = 0.816 p density of BSA solution

7) number of bubbles per unit area of the foam bed per unit time

p viscosity E liquid holdup II disjoining pressure 4 0 residence time

Subscripts B bottom product F feed o foam-liquid interface q top product

fraction of liquid in films

References

1. G. Narsimhan and E. Ruckenstein, Langmuir, 2(2), 230 (1986). 2. G. Narsimhan and E. Ruckenstein, Langrnuir, 2(4), 494 (1986). 3. Y.T. Hung, Am. Pot. I , 60, 543 (1983). 4. R. Lemlich, Progress in Separation and Purification, Volume I ,

E. S. Perry, Ed. (Interscience, New York, 1968). 5. Y. Okamoto and E. J. Chou, “Foam Separation Processes,” in

Handbook of Separation Techniques for Chemical Engineers, P. A. Schweitzer, Ed. (Wiley, New York, 1979), Sec. 2.5.

6. P. Somasundaran and K . P. Ananthapadmanathan, “Bubble and Foam Separations-Ore Floatation,” in Handbook of Sepa- ration Process Technology, R.W. Rousseau, Ed., (Wiley, New York, 1987), Chap. 16.

7. D. J. Wilson and A. N. Clark, “Bubble and Foam Separations- Waste Treatment,” in Handbook of Separation Process Technol- ogy , R.W. Rousseau, Ed., (Wiley, New York, 1987), Chap. 17.

8. 9.

10. 11. 12.

13.

14. 15.

16. 17. 18. 19.

20. 21.

22.

23. 24.

25.

P J . Halling, CRC Crit. Rev. Fooh Sci. Nutr., 15(2), 155 (1981). R.W. Schnepf and E. L. Gaden, I Biochem. Microbiol. Technol. Eng., 1(1), 1 (1959). S. I. Ahmed, Sep. Sci., 10(6), 673 (1975). S . I. Ahmed, Sep. Sci., 10(6), 689 (1975). R. D. Gehle and K. Schugerl, Appl. Microbiol. Biotechnol., 20, 133 (1984). D. E . Graham and M. C. Phillips, I Colloid Interface Sci., 70, 415 (1979). G. D. Miles and R. Schedlovsky, I Phys. Chem., 49,93 (1945). W.M. Jacobi, K .E . Woodcock, and C.S. Grove, Jr. , Z&E.C., 48(11), 2046 (1956). R. A. Leonard and R. Lemlich, AZChE I , 11(1), 18 (1965). R. A. Leonard and R. Lemlich, AZChE I , 11(1), 25 (1965). P. A. Haas and H. F. Johnson, I E. C. Fundam., 6(2), 225 (1967). S. Hartland and A. D. Barber, Trans. Znst. Chem. Eng., 52, 43 (1974). D. Desai and R. Kumar, Chem. Eng. Scc., 38(9), 1525 (1983). D. E. Graham and M. C . Phillips, J. Colloid Znterface Sci., 76(1), 240 (1980). J.T. Davies and E . K. Rideal, Interfacial Phenomana, (Aca- demic, New York, 1961). D. Desai and R. Kumar, Chem. Eng. Sci., 37(9), 1361 (1982). C.W. Gear, Numerical Initial Value Problems in Ordinary Dijfer- ential Equations (Prentice-Hall, Englewood Cliffs, NJ, 1971). L. K . Brown, M.S. thesis, Purdue University, West Lafayette, IN, 1988.


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Foam fractionation of globular proteins