The effect of surfactants on wicking flow in fiber networks

The Effect of Surfactants on Wicking Flow in Fiber Networks K E V I N T. H O D G S O N l AND J O H N C. BERG 2

Department of Chemical Engineering BF-IO, Universityof Washington, Seattle, Washington 98195 Received September 9, 1986; accepted February 18, 1987 Wicking flow in random fiber networks is examined for various pure liquids and surfactant solutions. Although the pore geometry of the fiber structures is extremely complex, it is found that all liquids used obey the rate law of the simple Lucas-Washburn theory. Imbibition of surfactant solutions is found to differsignificantlyfrom that of pure liquids of equivalent surfacetension, indicatingdepletion of surfactant from the wetting front by adsorption onto the fiber surfacesduring penetration. For fibernetworks which are wet out by the imbibing liquid, wicking rate is directly proportional to an effectivesurface tension at the meniscus. The difference between this wicking-equivalent tension and the equilibrium surface tension varies between different surfactants. Fiber structures which are partially wet exhibit penetration rates proportional instead to the adhesion tension, and for surfactant solutions, there are differences between the wicking-equivalentand equilibrium values, Differencesin wickingperformance among the surfactants are attributed to differencesin both the extent of their adsorption at the fiber surfaces and their diffusivities. © 1988 Academic Press, Inc. INTRODUCTION

the effective capillary dimensions. In its integrated form, neglecting gravitational effects, it yields the familiar result that the penetration distance is directly proportional to the square root of time:

Wicking flow, i.e., the spontaneous liquid penetration of porous materials under the influence of capillary forces, is essential to the function of m a n y products, including paper tissue and toweling, absorbent dressings, and a variety of absorbent hygiene products. The desired result is rapid and complete penetration of the porous solid. Because interfacial forces control the process, the use of surfactants is often proposed as a means of achieving this result (1). The present work concerns the effect of surfactants on the rate of liquid penetration into fibrous structures, particularly of cellulosic materials. Wicking is c o m m o n l y described by the theory of Lucas (2) and Washburn (3), which models the porous m e d i u m as a bundle of cylindrical capillary tubes and assumes quasisteady creeping flow. The Lucas-Washburn equation gives the rate of penetration as a function of the solid and liquid properties and

[ra

cos

h = [ ~ ]

0]l/2v~

=

kVt

.

[1]

h is the nominal distance traveled by the liquid from the reservoir, while the actual distance traveled is hr, where r is an appropriate tortuosity factor. # and p are the liquid viscosity and density, respectively, 0 is the dynamic advancing contact angle, and cr is the liquid surface tension. The form ofEq. [ 1] has been substantiated by experiments with pure liquids in several porous media, including some paper and textile materials (4-9) and three-dimensional fiber pads (10-12), although deviations have been observed for very short wicking times or distances and in media which are swollen by the penetrating liquid (13). The predicted variation of k with Va/~ has been verified with pure liquids, with the exception of water, in strips of cellulose (14) and glass-

1Present address: Weyerhaeuser Co., Tacoma, WA 98447. 2 To whom correspondence should be addressed. 22 0021-9797/88 $3.00 Copyright © 1988 by Academic Press, Inc. All rights of reproduction in any form reserved.

Journal of Colloid and Interface Science, Vol. 121, No. 1, January 1988

W I C K I N G F L O W IN FIBER N E T W O R K S

fiber (6) filter paper. The behavior of water is probably attributable to its inability to fully wet out the porous medium. In the case of cellulose, fiber swelling might have been a further problem. The dependence ofwicking rate on surface tension is best considered by distinguishing between liquids which fully wet out the solid and those which do not. In the former case, cos 0 = 1, and [ r~ ] 1/2 k = L2rZ#j ,

[2]

so that the wicking rate is directly proportional to ~ . For partially wetting liquids, however, we may substitute Young's equation, viz., cos 0 -

(~s~

-

o"

~sL),

[3]

where crsa and ~SLare the solid-gas and solidliquid surface energies, respectively, into Eq. [ 1] so that

rru o - o-sL)r

k= L

~

]

.

[4]

The quantity (C~sa - rsc) is referred to as the adhesion tension. According to Eq. [4], wicking rate should be independent of surface tension except insofar as liquids of different surface tensions will generally produce different values of rsc for a given solid. The role of surface tension can then be determined explicitly only if an independent measurement of the contact angle can be made. For situations displaying Lucas-Washburn kinetics, experimental k-values for liquids assumed to be fully wetting (0 = 0 °) have been used to obtain "wicking-equivalent" pore radii in porous media (4, 5, 12), and comparison of k-values for partially wetting liquids (0 > 0 °) and assumed fully wetting liquids have been used to obtain "inferred" contact angles (8). Although again it would be preferable to measure the contact angle directly, and, in particular, to determine in a given case whether or not a liquid is fully wetting, the general validity of Lucas-Washburn kinetics appears to be well established for pure liquids.

23

Lucas-Washburn theory has not been convincingly verified, however, for multicomponent penetrating liquids, particularly surfactant solutions. Using sinking time tests for various partially wettable textile yarns in surfactant solutions, investigators (15, 16) have found apparent agreement with the form of the Lucas-Washburn rate law, but no correlation of the rate constant with equilibrium surface tension. In a similar study, Fowkes (17) found good agreement with Lucas-Washburn kinetics 3 for weakly adsorbing surfactants but none for those strongly adsorbed at the fiberliquid interface. In the latter case, sinking time correlated closely with the inverse of the surfactant diffusion rate, a result corroborated by later studies of Komor and Beiswanger (19) and Schwuger (20). Such results are qualitatively understood by considering the simultaneous adsorption of surfactant at the liquidvapor interface, with the consequent reduction in surface tension, and at the solid-liquid interface of the porous medium. As pointed out recently by Pyter et al. (21), both effects are critical to the wetting of a solid by a surfactant solution. During wicking, it is the dynamic balance between these adsorptions which governs the penetration kinetics. Depletion of the advancing meniscus of adsorbed surfactant can increase the effective surface tension well above the equilibrium value, while the adsorption at the solid-liquid interface can alter o-so and hence the effective contact angle. The contact angle might be either increased or decreased depending upon the orientation of the adsorbed surfactant molecules (22). It is also possible that surfactant adsorption on the solid right at the advancing interline is negligibly low. In view of the uncertainties and discrepancies in the literature on wicking rates, particularly with respect to surfactant solutions, 3 Although Fowkes' equation was derived for the case of liquid penetration in a direction n o r m a l rather than parallel to the fiber axis, it can be shown (18) that it reduces to the L u c a s - W a s h b u r n equation for contact angles less than 30 ° . Journal of Colloid and InterfaceScience, Vol. 121, No. I, January 1988

24

HODGSON AND BERG

the objective of the present work is to investigate further the kinetics of wicking into fiber networks to determine the range of applicability of the Lucas-Washburn rate law. Wicking into paper strips and pads of a variety of fibrous materials by a range of pure liquids as well as surfactant solutions is examined. In contrast to earlier work, the contact angles of the penetrating liquids against individual fibers abstracted from the networks are measured independently using the fiber-balance technique developed in the authors' laboratory (23) and elsewhere (24, 25). It permits the determination of advancing and receding contact angles and wetting heterogeneities for fibers as small as 7 #m in diameter, and in parallel runs in the same system, yields the equilibrium surface tension of the liquid. Thus fully-wetring conditions are distinguished a priori from those of partial wetting and are analyzed accordingly so that, in particular, the effects of adsorption disequilibrium during wicking can be unambiguously discerned. METHODS AND MATERIALS Two types of wicking experiments were performed, the first using strips of paper (1.0 cm wide by I0 cm long) cut from a filter circle or handsheet and the second using unbonded pads of fibers. In the former case, representing most of the wicking studies performed, strips were hung from a wire inside a cylindrical flask 20 cm high and 3 cm in diameter. The test liquid in each case, contained in a reservoir at the bottom of the flask, was raised until it just contacted the bottom of the strip, and the liquid front was timed as it reached each of a series of marks imprinted on the strip prior to the run. The instrument used for the pad experiments was a modified commercial absorbency tester for fluffed wood pulp, known as the FAQ (fluff absorbency quality) tester, described in detail elsewhere (11). A 4.0-g pad of dry fibers was air laid into a cylindrical tube with a screen at the bottom. With a constant load applied to the top of the pad, liquid was brought into contact with the bottom. As liqJournal of Colloid and Interface Science, Vol. 121, No. t, January 1988

uid penetrated it, the pad collapsed. The sample height was measured as a function of time, yielding data equivalent to those obtained in the paper strip experiments. Contact angles of the various liquids against single fibers abstracted from the strips or pads were measured using the fiber-balance technique described in detail elsewhere (23). The instrument uses the Wilhelmy principle to determine the contact angle from the measured wetting force on the fiber dipping into a liquid. Force traces measured during fiber immersion and emersion yielded advancing and receding contact angles, respectively, and the condition of full wetting was clearly recognized when the two force traces were mirror images of one another. Measurements were made at the constant interline velocity of 750 um/min, well below the point where the contact angle became velocity-dependent due to viscous effects or diffusional disequilibrium at the interline (in the case of surfactant solutions). Contact angles reported in his work are advancing angles obtained in this manner. The various fiber sources used for the wicking experiments are listed in Table I. Whatman No. 40 filter paper was used as purchased, while the remaining three samples were commercial wood pulps supplied by the Weyerhaeuser Co., Tacoma, Washington. The TMP and OA Fir fibers were formed into handsheets according to TAPPI standard "T205om-81," and the OA Fir sheets were further oven-aged for 16 h at 105°C, inducing self-sizing of the fiber surfaces. Both the FAC and TMP samples were defiberized into flufffor bulk absorbency testing. The advancing contact angle measured for each of the fiber types with water is listed to indicate a relative degree of hydrophilicity. The liquids used in the experiments were triply distilled water, ethylene glycol, formamide, hexamethyldisiloxane, isopropyl alcohol, methylethyl ketone, 1,1,2,2-tetrabromoethane, and toluene. The surfactants used are listed in Table II. Critical micelle concentrations (CMC) are listed where available. The first four surfactants were chosen as representative examples of anionic, cationic, and non-

25

WICKING FLOW IN FIBER NETWORKS TABLE I Fiber Sources for Wicldng Experiments Designation

Composition

Pulpingprocess

Whatman No. 40 TMP OA Firb FACc

Cotton-99% c~-cellulose 100% Hemlock 100% Douglas fir 100% Hemlock

Watercontact anglea(°) 0 55.3 49.8 14.0

Thermomechanical Kraft Sulfite

a Determined for single fibers at 100% R.H. b Oven-aged (self-sized) fir. c Pulp grade designation.

ionic types. T h e two Berocell surfactants are c o m m e r c i a l c o m p o u n d s used in p u l p m a n u facture for d e b o n d i n g a n d anti-self-sizing applications. T h e y b o t h c o n t a i n t e r m i n a l l y e t h o x y l a t e d q u a t e r n a r y a m m o n i u m salts. RESULTS AND DISCUSSION T h e r e m a r k a b l e general result was o b t a i n e d t h a t all w i c k i n g e x p e r i m e n t s d o n e with p a p e r strips, either fully o r p a r t i a l l y wet, b o t h with p u r e liquids a n d with surfactant solutions, o b e y e d the f o r m o f Eq. [1] to w i t h i n experi-

m e n t a l precision. T h e d a t a o f Fig. 1, showing wicking height vs square r o o t o f t i m e for several o f the liquids s t u d i e d i m b i b i n g into W h a t m a n No. 40 filter paper, are typical o f the linearity achieved. In the a b o v e circumstances, a c o n v e n i e n t p r o c e d u r e for representing the wicking perf o r m a n c e o f various liquids in a given p o r o u s m e d i u m is to c o m p u t e its "wicldng-equivalent surface tension," 0*. This can be d o n e b y using a nonswelling reference liquid (if possible, one which wets o u t the fibers) to n o r m a l i z e the L u c a s - W a s h b u r n slope for each liquid. T h e

TABLE II Surfactants Used in Wicking Studies Compound

Abbreviation

CMC"(M)

Surfactanttype

Sodium dodecyl sulfate b

SDS

8.1 × 10-3

Anionic

Sodium dodecylbenzene sulfonate b

SDBS

1.6 X 10-3

Anionic

Cetyltrimethylammonium bromideb

CTAB

9.2 × l0 -4

Cationic

Triton X- 100 (octylphenoxy polyethoxy ethanol)

TX- 100

2.4 × 10-4 c

Nonionic

Berocell 564

564

Terminally ethoxylated cationic

Berocell 584

584

Mixture of nonionic and terminally ethoxylated cationic

Mukerjee, P., and Mysels, K. J., Nat. Bur. Stand. Ref. Data Ser., NBS-36, U.S. Govt. Printing Office, Washington, DC, 1971. b Reagent grade. c Fowkes, F. M., J. Phys. Chem. 57, 98 (1953). Journalof Colloidand InterfaceScience, Vol.121,No. 1,January1988

26

HODGSON AND BERG I []

that referencing the wicking of each solution to pure water yielded

z~o

xl2

AO AO

0

xO

AO xO ~,0 x [] z~O xn ¢ ~0 xO 0 ~0 xO 0

m4 .c: L~ .o_ 2

0

xn

AO

~* = 72.0 ~

¢

~C~O

0

,

0

I

I0

,

I

,

I

,

I

50

20 .30 40 square root time (sec I/z)

FIG. 1. Lucas-Washburn plot of wicking into strips of Whatman No. 40 filter paper: (ZX)water, (©) 0.01 wt% TX-100, (×) ethanol, (ffl)0.005 M SDS, (0) 0.1 M CTAB.

wicking-equivalent surface tension is computed as (7* = O ' r e f ~ }

mN/m.

[6]

0

,

[5]

in which all the quantities on the right-hand side were measured independently. Leastsquares slopes of the Lucas-Washburn plots were used for the required k values. The value used in each case was the average of those obtained in at least two experiments for each liquid/fiber strip combination. For pure liquids, a* should be equal to the measured surface tension of the liquid, ¢. Table III shows results for several pure liquids wicking into cellulose and T M P strips. The cellulose was wet out by all the solvents with which it was tested, while the T M P was only partially wet by its test solvents. Toluene was found to wet out both materials and was used as the reference liquid. Except for water, formamide, and ethylene glycol in cellulose, reasonable agreement between a and a* was found in all cases. The latter three solvents were presumed to swell cellulose, reducing the effective pore radius. Wicking-equivalent surface tensions were also used to characterize the wicking of aqueous surfactant solutions into cellulose strips. Complete wetting of the fibers occurred in all cases, and the viscosity of all solutions was effectively the same as that of water, so Journal of Colloid and Interface Science, Vol. 121, No. 1, January 1988

Tacit in using Eq. [6] was the assumption that any swelling of the fibers by the surfactant solutions is identical to that induced by pure water. Results comparing a* and ~ for solutions of SDS, CTAB, and Triton X-100 as a function of surfactant concentration are shown in Fig. 2. Results for the two Berocell surfactants are shown in Fig. 3. While the wicking data did show scatter, the trends were unmistakable. The wicking-equivalent surface tensions in all cases were substantially higher than the corresponding equilibrium surface tensions, until they converged at the higher concentrations. It was evident that there was substantial depletion of surfactant from the advancing meniscus due to its adsorption onto the fiber surfaces during wicking. As bulk surfactant concentration was increased, the depletion effect was eventually overwhelmed. The concentration needed to achieve this condition was equal to or in excess of the C M C in each case. Literature data for the CMC-values of the Bero-

TABLE III Results of Wicking Pure Liquids into Paper Strips-Reference Liquid, Toluene Liquid

~r (mN/m)

o'* (mN/m)

0 (°)

Cellulose strips (Whatman No. 40) Water Formarnide Ethylene glycol Methylethyl ketone Isopropyl alcohol ltexamethyl disiloxane

72.0 58.2 47.7 24.6 21.7 15.9

33.9 26.3 24.0 27.5 27.3 16.1

0 0 0 0 0 0

TMP strips Water Formamide Diiodomethane Tetrabromoethane Ethylene glycol

72.0 58.2 51.1 48.8 47.4

77.6 62.2 45.2 48.8 47.7

55.3 21.8 34.8 29.9 21.3

WICKING FLOW IN FIBER NETWORKS 80

i

,IL,,,,

I

i

i ,i,,u

,

\o

70

60

,~d,

(a) "~,\ •

50

"-,e

\

40_ CMC

,la,,~,l , ~,,,,IL , ,,,,m~ 80 ........ I ............... '. z 70 --~ (b) E 60 ~ N"o\ 20

•~

i

5C

~

40 3

50

\ CMC

80

' ' ''''q

To

--°-o-

60

-"•f

........ I -

•-

......e •

........

...(c) _'%%-

5O 40

CMC 20 ,I . ,,,,,4 , , , f,,,,I , . iO-4 10-3 10-2 surfactant concentration ( M )

I0-1

FIG. 2. Comparison of wicking-equivalentsurfacetension (---) with equilibriumsurfacetension (--) for aqueous solutions of(a) SDS, (b) CTAB,and (c) TX-100,imbibing into strips of Whatman No. 40 filterpaper strips.

to the square root of time. The magnitude of ~* must be governed in each case by the concentration of surfactant in the solution, the extent of adsorption at the fiber surfaces, the dependence of surface tension on concentration, and the diffusivity of the surfactant in solution. Significant differences in the performance of the different surfactants were observed. The meniscus depletion effect (difference between ~* and ~) was least for the SDS solutions and greatest for the Triton X-100 and Berocell solutions, with the CTAB solutions showing intermediate performance. Furthermore, the concentration required for convergence of ~* and ~ was approximately equal to the CMC for SDS, but about 10 times the CMC for CTAB and over 100 times the CMC for the Triton X-100 and Berocell surfactants. The two principal reasons for the differences were differences in the extent of adsorption at the fiber surface and the effective diffusivity of the surfactant in solution. High adsorption and low diffusivity should favor large and persistent disequilibria, as measured by ~* - ~. The difference in behavior between the SDS and

80

cell surfactants were not available, but from the observed "break" in the equilibrium surface tension curves, they appeared to be approximately 0.003 wt% in each case. It was notable that despite the significant disequilibrium with respect to surfactant distribution at the advancing meniscus in all cases, the Lucas-Washburn rate law was always observed over the entire course of imbibition. This suggested that a dynamic balance was established very quickly (and maintained) between the depletion of surfactant from the meniscus by adsorption at the fiber surfaces and its replenishment by diffusion from the bulk solution. This is in retrospect not so surprising, since as the meniscus advances, both the required diffusion distance (proportional to h) and the diffusion path length (proportional to V-~) are proportional

27

........ I

........ I

........ I

........ I

.......

"",,, 40 z

20

'~ 8o

....... I ........ I '

"'"

L-

. . . . .

........ J

-o- ~o~.

'."1

'

'""q

70

........ I '

'"""1

, ,,,,.,

(b) '

'""'

~

-

~=5o

~

3o20

, . . . . . . ,I

~ ,Im.I

,

IIIIHI~

I II,hHI

I ,,1111,

[0-5 10-4 10-3 [0-2 iO-I iOO surfactont concentration (wt%) FIG. 3. Comparison o f wicking-equivalent surface tension (---) with equilibrium surface tension ( - - ) for aqueous solutions o f (a) Berocell 564 and (b) Berocell 584, imbibing into strips o f W h a t m a n No. 40 filter paper strips. Journal of Colloid and Interface Science, V o l .

121, N o . l, J a n u a r y

1988

28

H O D G S O N AND BERG

CTAB was evidently due mainly to differences in adsorption onto the fiber surfaces, since the measured diffusivities of the two compounds in water are essentially identical both below and above the CMC (26), and the effects of the two surfactants on the surface tension of water are nearly the same. The much greater disequilibria shown by the Triton X-100 and Berocell solutions, however, were attributable primarily to the low diffusivities of these compounds. The diffusion coefficient for Triton X-100 in water is an order of magnitude lower than that for SDS or CTAB (27) due to its much larger molecular size. Its hydrophilic portion consists of a chain of 9.5 (on the average) hydrated ethoxylate units. The Berocells possess similar structure (28, 29) and would thus also be expected to have much lower diffusivities than SDS or CTAB. The importance of diffusivity is consistent with the conclusions of Schwuger (20), who examined systematically the effect of chain branching (hence diffusivity) in hexadecyl sulfate surfactants on the immersional absorbency of their solutions into porous materials. Wicking experiments were also performed with strips of fibers which were only partially wet by aqueous surfactant solutions. For such materials, neither the surface tension nor the contact angle was expected to be at its equilibrium values at the location of the advancing meniscus. Thus the slopes of the LucasWashburn plots were analyzed using Eq. [4]. The extent of disequilibrium during wicking was quantified by comparing the "wickingequivalent adhesion tension" (aso - aSL)* to the equilibrium adhesion tension (asG - crSL). The equilibrium adhesion tension was obtained by using Eq. [3] and independently measured equilibrium values for 0 and a. (trsG aSL)* was obtained by computing the ratio of the Lucas-Washburn slope for the surfactant solution in each case to that obtained for pure water, the reference liquid. Eq. [ 1] was thus applied in the form -

(~sG- crsL)* = 72.0 ~

mN/m.

Journal of Colloid and Interface Science, Vol. 121, No. 1, January 1988

[71

Results for sodium dodecylbenzene sulfonate (SDBS) and Berocell 564 solutions wicking into TMP strips are shown in Table IV and for the same solutions wicking into OA Fir (self-sized) strips in Table V. Both materials were poorly wet by water, as indicated by the contact angles shown in Table I. The equilibrium contact angle was reduced by the addition of surfactant to the solution in all cases, as shown in Tables IV and V. The equilibrium adhesion tension was also seen to fall as surfactant concentration increased, although the eventual drop was sometimes preceded by a slight increase at lower surfactant concentrations. Assuming that the dry solid surface energy, aso, was unchanged by the presence of surfactant in the solution, the drop in adhesion tension may be interpreted as an increase in the solid-liquid surface energy, CrSL,due to adsorption. Such a result suggests that the surfactant adsorbed at the solid surface is in a "head-down" orientation. It should be recalled in making any such interpretation that it is

TABLE IV Wicldng into TMP Strips--Reference Liquid, Water

Concentration SDBS 1X 5X 1X 5X 1X 5X 1X 5X

solutions (M) 10-5 10-5 10-4 10-4 10-3 10-s 10-2 10-2

(#sG- asL) (mN/m)

(~sa - #sL)* (rnN/m)

0 (°)

44.9 43.0 33.6 42.4 36.8 30.7 29.7 27.8

43.7 42.6 44.8 48.0 46.1 43.7 39.0 31.4

50.0 49.7 48.0 30.0 24.7 19.3 20.6 23.2

46.0 45.3 52.9 46.5 32.1 29.8 28.9 27.7 27.7

42.2 37.7 40.5 43.2 42.6 42.9 42.1 32.1 27.5

50.0 49.5 26.2 25.3 23.7 24.5 26.6 27.6 24.5

Berocell 564 solutions

(wt%) 1X 1X 5X 1X 1X 5X 0.1 0.5 1.0

10-5 10-4 10-4 10-s 10-2 10-2

WICKING FLOW IN FIBER NETWORKS TABLE V Wicking into OA Fir (Self-Sized)Strips-Reference Liquid, Water Concentration

(aso - ,~sL) (mN/m)

(~sG - ~sL)* (raN/m)

0 (°)

SDBS solutions (M) 5 × 10-6 1 × 10-4 5 × 10-4 1 X 10-3 1 × 10-2 5 × 10-2

44.2 38.3 36.0 29.1 29.5 29.6

26.3 22.2 25.4 26.9 29.3 26.9

51.9 52.6 47.2 44.1 21.3 13.7

Berocell 564 solutions (wt%) 1 × 10-4 1 × 10-3

46.6 32.9

47.0 47.1

47.6 49.1

5 × 10 -3

34.4

44.6

33.4

1 X 10-2

32.6 28.5 26.0 27.7 27.4

46.8 50.5 44.5 50.4 49.8

28.5 26.6 34.7 24.7 22.6

5 X 10-2 0.1 0.5 1.0

the advancing contact angle which was used in computing (~s~ - f f S L ) , reflecting the conditions of the least-wettable portions of the surface. Corresponding receding contact angles were m u c h lower and only negligibly affected by the presence of surfactant. The disparity between the equilibrium and wicking-equivalent adhesion tensions again reflected the diffusion lag in the attainment of adsorption equilibrium at the advancing meniscus. It again tended to vanish as surfactant concentration increased, although more slowly for the slower-diffusing Berocell surfactant. The wicking-equivalent adhesion tension for Berocell 564 solutions in the self-sized strips remained effectively constant all the way up to 1 wt% surfactant. Limited experiments were done with threedimensional fiber networks, specifically airlaid pads of fluffed wood pulp fibers. Ifwicking behavior is found to be similar to that seen with the paper strips, then a basis exists for drawing conclusions about liquid penetration into such pads from the more extensive data available for the strips. A plot of pad height

29

vs square root of time is shown in Fig. 4 for water absorbing into a hydrophilic fluff pad. As in the strip experiments, a linear relationship was observed, except at the very early stages of flow. The nonlinearity shown in the first fraction of a second has been observed in other work and referred to as a "wetting delay" (30, 31). This region was not detected in the strip experiments since in them the first data point was recorded a few seconds after the strip was contacted with the liquid. Only the slope of the linear region was used in the subsequent calculations for the pads. Water and two different concentrations of Berocell 564 were used to penetrate pads of hydrophilic and poorly wet fibers, respectively. Results are listed in Table VI and represent the average of five runs for each entry. Water was used as the reference liquid. The values of o-* for the two different concentrations of Berocell 564 solutions wicking into almost completely wetted FAC fluff pads both showed surfactant depletion affecting the penetration rate, as was observed in the Whatman filter strip results. The absolute values of a*, however, were higher than those in the strip experiments, suggesting that meniscus depletion was even greater for wicking into the fluff pads. The results o f runs with both concentrations of Berocell 564 solutions into poorly wet T M P fluff pads also indicated that adsorption equilibrium was not reached at the wetting front during penetration. As before, a

2O

E

I

'

[

'

J

'

I

'

I

'

I

'

I

~ ~ '

I

is 14

•"o I0

0

Ra .E ~

1

2

1

0

/

[] 0

-

0 C3

6

~4

[]

o

g 2 0

[] ,

0

[]

0

I

0.2

0.4

0.6 0.8 1.0 1.2 1.4 1.6 squore root time (sec I/2)

t,8

2.0

FIG. 4. Lucas-Washburn plot of water wicking into

three-dimensionalpad of FAC fibers. Journal of Colloid and Interface Science, Vol. 121, No. 1, January 1988

30

HODGSON AND BERG

decrease was seen in the equilibrium adhesion tension. Comparing these results to the analogous entries in Table IV, it is seen that about the same extent of adsorption was reached for Berocell 564 wicking into the three-dimensional fluffpads as that in the two-dimensional strips. CONCLUSIONS Solutions of a variety of different surfactants over wide ranges in concentration have been shown to obey Lucas-Washburn wicking kinetics (liquid penetration distance proportional to the square root of time) in all cases. For networks of fibers which are wet out by the penetrating liquid, the wicking rate was proportional to an effective surface tension at the meniscus, higher than the equilibrium surface tension for the surfactant solution. The difference, which decreased as the surfactant concentration increased, was attributed to surfactant depletion from the advancing meniscus caused by adsorption at the fiber-liquid interface. The concentration required for convergence of the wicking-equivalent and equilibrium surface tensions was equal to or above the C M C for all surfactants examined. Differences between the wicking performances of SDS and CTAB solutions were attributed to

the greater extent of adsorption of the CTAB on the fiber surfaces. Even greater differences were observed between wicking-equivalent and equilibrium surface tensions for solutions of Triton X-100 and the Berocell surfactants. These were attributed to differences in surfactant diffusivity. For strips of partially wetted fibers, liquid penetration rates were proportional not to any surface tension, but to a wicking-equivalent adhesion tension, i.e., the difference between the solid-gas and solid-liquid surface energies. Again a difference (decreasing with surfactant concentration) was observed between the wicking-equivalent and equilibrium adhesion tensions. The equilibrium adhesion tension, obtained independently in single-fiber wetting experiments, indicated that the adsorption of surfactant onto the low-energy portions of the fiber surface occurred in such a way that the solid-liquid interfacial energy increased, suggesting that the surfactants were adsorbedthere with their hydrophobic portions directed outward. Wicking studies with three-dimensional, collapsing fiber networks (fluff pads) showed Lucas-Washburn penetration kinetics (following a "wetting delay" of less than 1 s), closely resembling the results obtained for paper strips, for both pure water and surfactant solutions.

TABLE VI

ACKNOWLEDGMENTS

Wicking into Three-Dimensional Fiber Networks (Fluff Pads)--Reference Liquid, Water

This work was supported in part by the Weyerhaeuser Company, Tacoma, Washington, and the Engineering Center for Surfaces, Polymers and Colloids at the University of Washington.

Liquid

(naN/m)

(raN/m)

0 (°)

REFERENCES FAC fluffpulp 0.1% Berocell 564 0.5% Berocell 564 Liquid

32.5 31.3

74.3 58.3

0 0

( ~ s o - aSL)

(~SO -- ~SL)*

(raN/m)

(mN/m)

0 (°)

39.8 36.4

26.6 27.6

TMP fluffpulp 0.1% Berocell 564 0.5% Berocell 564

29.1 27.7

Journal of Colloid and Interface Science, Vol. 121, No. 1, January 1988

1. Berg, J. C., in "Absorbency" (P. K, Chatterjee, Ed.), Elsevier, Amsterdam, 1985. 2. Lucas, R., Kolloid-Z. 23, 15 (1918). 3. Washburn, E. W., Phys. Rev. 17, 273 (1921). 4. Simmonds, F. A., Tech. Assoc. Pap. 17, 401 (1934). 5. Back, E. L., Sven. Papperstidn. 68, 614 (1965). 6. Everett, D. H., Haynes, J. M., and Miller, R. J. L., in "Fibre-WaterInteractionsin Papermaking" (Fundamental Research Committee, Eds.), p. 519. Clowes, London, 1978.

WICKING FLOW IN FIBER NETWORKS 7. Minor, F. W., Schwartz, A. M., Buckles, L, C., and Wulkow, E. A., Amer. Dyest. Rep. 49, 37 (1960). 8. Minor, F. W., Schwartz, A. M., Wulkow, E. A., and Buckles, L. C., Text. Res. J. 19, 931 (1959). 9. Laughlin, R. D., and Davies, J. E., Text. Res. Z 31, 904 (1961). 10. Aberson, G. M., in TAPPI Spec. Tech. Assoc. Publ. Vol. 8 (D. Page, Ed.), p. 282, TAPPI, New York, 1970. 11. Martinis, S., Ferris, J. L., Balousek, P. J., and Beetham, M. P., Preprint No. 7-3, in "Proceedings, Tech. Assoc. Pulp Pap. Ind., Chicago, IL, March 2-5, 1981," pp. 1-8. 12. Graef, D. A., Weyerhaeuser Co. Technical Report, November 4, 1982. 13. Hoyland, R. W., in "Fibre-Water Interactions in Papermaking" (Fundamental Research Committee, Eds.), p. 557. Clowes, London, 1978. 14. Peek, R. L., and McLean, D. A., Ind. Eng. Chem., Anal, Ed. 6, 85 (1934). 15. Lenher, S., and Smith, J. E., Amer. Dyest. Rep. 22, 689 (1933). 16. Caryl, C. R., Ind. Eng. Chem. 33, 731 (1941). 17. Fowkes, F. M., J. Phys. Chem. 57, 98 (1953). 18. Hodgson, K. T., Ph.D. dissertation, University of Washington, Seattle, 1985.

31

19. Komor, J. A., and Beiswanger, J. P. G., J. Amer. Oil Chem. Soc. 43, 435 (1960). 20. Schwuger, M. J., in "Anionic Surfactants: Physical Chemistry of Surfactant Action, Surfactant Science Series," Vol. 11 (E. K. Lucassen-Reynders, Ed.), Chap. 7. Dekker, New York, 1981. 21. Pyter, R. A., Zografi, G., and Mukerjee, P., J. Colloid Interface Sci. 89, 144 (1982). 22. Gionotti, J. C., M. S. thesis, University of Washington, Seattle, 1982. 23. Berg, J. C., in "Composite Systems from Natural and Synthetic Polymers" (L. Salmen et al., Eds.), p. 23. Elsevier, Amsterdam, 1986. 24. Miller, B., Penn, L. S., and Hedvat, S., Colloids Surf. 6, 49 (1983). 25. Okagawa, A., and Mason, S. G., in "Fibre-Water Interactions in Papermaking (Fundamental Research Committee, Eds.), p. 581. Clowes, London, 1978. 26. Lindman, B., Puyal, M-C., Kamenka, N., Rymden, R., and Stilbs, P., Z Phys. Chem. 88, 5089 (1984). 27. Wenheimer, R. M., Evans, D. F., and Cussler, E. L., J. Colloid Interface Sci. 80, 357 (1981). 28. Technical bulletin on Berocell 564, Berol Kemi AB, 1982. 29. Technical bulletin on Berocell 584, Berol Kemi AB, 1982. 30. Bristow, J, A., Sven. Papperstidn. 70, 623 (1967). 31. Lyne, M. B., and Aspler, J. S., TAPPIJ. 65, 98 (1982).

Journal of Colloid and Interface Science, VoI. 121, No. 1, January 1988