19 Oct 1999, 1545 hrs
TOWARDS UNDERSTANDING THE PRESSURE
DEPENDENCE OF HYGROSCOPIC WATER
C.M. Downing1,2 and G.D. McBain1
1
2Now at Sugar Research Institute, Mackay, 4740
Abstract
This paper presents a review of water sorption by cellulose, often referred to as hygroscopic or Brix-free water. Of particular interest is the apparent dependence of hygroscopic water on interparticulate ('effective') stress. The analysis suggests that the level of 25% currently assumed in the Australian industry is reasonable at low fibre compactions but at high compactions a much lower value, approximately 8%, may be more appropriate. It is hypothesised that a link exists between cell wall collapse and the reduction of hygroscopic water with increasing effective stress. It is concluded that hygroscopic water must be defined in terms of temperature, solution concentration, (vapour or) pore pressure and effective stress in the fibre skeleton.
KEYWORDS: Hygroscopic water, Brix-free water, sorption, effective stress.
Introduction
The preferential affinity of sugar cane cellulose for water has been know more than a century (Bruyn 1963). This affinity for water reduces the capacity of mill rolls to dewater sugar cane fibre and, to a certain extent, works in the millers favour by preferentially rejecting sucrose. The proportion of this 'hygroscopic', or Brix-free, water in cane is also of interest in making a judgement on whether it should be included as liquid or solid in numerical simulation of the rolling process (Downing et al. 1999). More recently, there has been discussion on the dependence of hygroscopic water on the interparticulate 'effective' stress carried by the fibre matrix during crushing (Murry et al. 1998).
There have been numerous experiments evaluating hygroscopic water, conducted by various authors using a range of experimental techniques. The two principle methods used have been: (a) vapour sorption, where water is sorbed by dry sugar-free cane fibre from a controlled atmosphere; and, (b) contacting solution, where dry sugar-free cane fibre is placed in a sucrose (or other) solution of known concentration, allowed to equilibrate and the hygroscopic water calculated from the change in solution concentration. Since a small quantity of sucrose may be sorbed by the fibre in addition to the water, the latter method measures the differential sorption of water over sucrose (Kelly and Rutherford 1957). This paper reviews the mechanisms of sorption, the sugar literature and the apparent dependence of hygroscopic water on stress in the fibre skeleton.
Sorption of water by cellulose
The term sorption, coined by J.W. McBain (1909), denotes the uptake of a vapour (or liquid) by a solid. It may be classified as adsorption or absorption depending on whether the uptake is superficial or volumetric. The two processes often occur together, but over different time-scales. A secondary classification may be made, although only quantitatively, according to the nature of the bonds involved--physical or chemical--these being distinguishable macroscopically by the magnitude of the heat of sorption.
Coulson et al. (1996) describe adsorption as occurring in three stages: a single layer of molecules (a monolayer) builds up over the surface of the solid by adsorption or chemisorption; if fluid concentrations are high enough, further layers (multilayers) may form by adsorption to the limit of the mesopore size (250 nm); and, finally, for adsorption from the gaseous phase, capillary condensation may occur when the partial pressure of the adsorbate reaches a critical value relative to mesopore size. Since mesopore size may vary significantly in a given solid, all three stages may be occurring simultaneously. The mass transfer rate, to the multilayer, depends upon the surface area of the solid and the concentration difference across the multilayer. Several theories have been developed to quantify gassolid adsorption, including BET theory, Gibbs adsorption isotherm, and potential theory. These theories are covered in some detail in texts such as Coulson et al. (1996). In principle, the equations derived for gassolid systems are applicable to liquidsolid systems, excepting capillary condensation.
Following Valko (1943), the usual method of correlating sorption data is to plot moisture content against the vapour pressure of the liquid in the surrounding atmosphere or, more conveniently, against relative humidity (RH) where RH is the ratio of the vapour pressure of the liquid to the corresponding saturation vapour pressure at that temperature (eg. Figure 1). The adsorption and desorption data for cellulose together form a sorption loop, i.e. a pair of BET Type II multilayer isotherms. Adamson (1982) explains: the first section of the Type II isotherm, up to the 'knee', corresponds to monolayer formation; the intermediate region indicates multilayer build-up; and, the apparent infinite film thickness at high relative humidities (asymptotic section) indicates interparticle, or capillary, condensation. The difference between adsorption and desorption curves occurs due to hysteresis effects which are not explained by BET theory. Hysteresis possibly arises from changes in the radii of the contacting liquid or the relative amounts of crystalline and amorphous cellulose material making up natural cellulose.
Water vapour sorption loops for some cellulosic materials are illustrated in Figure 1. The sorption curves for wood are noticeably higher than those for cotton cellulose. The adsorption curve for Q50 sugar cane (Foster 1956) is similar to bleached sulphite pulp. Cotton fibres freshly removed from the seed are noted to yield sorption isotherms which lay well above the standard cellulose sorption loops presented in the figure (Valko 1943). Collectively, the isotherms suggest monolayer water of about 36% sorbed water percent dry weight and multilayer water perhaps up to 10% or more. Keey (1996) quoted a monomolecular adsorption figure of 8%, at 25C for softwood, which is consistent with the 8% hygroscopic water for pure cellulose powder determined using the solution contact method (Kelly and Rutherford 1957; van der Pol, Young and Douwes-Dekker 1957).
Valko (1943) discussed the work of several authors on the subject of water take up by cellulose and the net contraction of the adsorbed water, including a number of x-ray diffraction studies. Using x-ray diffraction it has been determined that cellulose crystalline regions do not expand and, therefore, do not absorb water between the molecules. The crystalline regions may, however, build up a multilayer on the surface of the crystallites. Amorphous cellulose regions, where intermolecular cohesion is lower, preferentially sorb water. Variation in crystallinity, therefore, affects the ability of the cellulose to sorb water.
When water is sorbed by cellulose, the cellulose swells but careful examination shows that the expanded volume is less than the sum of the component volumes. X-ray diffraction analysis and fibre density measurements in helium have demonstrated that it is the water volume which contracts. Valko (1943) concluded that the first layer of sorbed water undergoes strong contraction and that the degree of contraction decreases for subsequent layers. The contraction effect is clearly demonstrated in Figure 2 where the density of the rigidly bound (ice-like) first layer of water is calculated to be 2.60 g/ml. The apparent density decreases to about 1 g/ml at a moisture content of 89%, at this stage the adsorbed water is liquid-like. Valko quoted the pressure required to achieve the apparent density of the first sorbed water at 1400 MPa and the average pressure for the entire multilayer at 200 MPa. Valko suggested that the distinction between free and sorbed water is not sharp; rather, there is graduated influence of the cellulose on the whole of the swelling water.
The difference between vapour phase adsorption and the contacting solution method is somewhat indistinct. During sorption from vapour, there is a replacement of hydrogen bonds between fibrefibre molecules by bonds between water and fibre molecules. In the case of fibre swelling in a contacting solution, some waterwater and cellulosecellulose hydrogen bonds are replaced with watercellulose bonds, the cohesion forces overcome by solvation forces. The two techniques may differ due to the contribution of capillary condensation; however, condensation of water in preformed spaces within dry fibres is not expected to be more than 23% mass on cellulose, based on microscopic cross-section measurements and x-ray determinations of the unit cell (Valko 1943). Further, Stamm (1997) states that dry cell walls are virtually free of voids that could fill with water without swelling (absorption) occurring.
Sorption of water by sugar cane fibre
Vapour Sorption. Foster (1962) stated that the chemical and physical structure of the thick walled fibre cells of sugar cane are similar to those of wood fibre. Not all the cellular material in sugar cane is cellulose, sugar cane also contains 1721% lignin (Brotherton 1985). Foster (1962) conducted vapour sorption experiments on predried Q50 cane fibre at 20C for 3595% RH (Figure 1). He subsequently extrapolated his results to 100% RH and quoted a figure of 25% for hygroscopic water. The extrapolation was into the section of the isotherm where it is almost parallel with the ordinate axis and difficult to justify. Kelly (1957) also conducted vapour sorption measurements at 27.2C and determined a value of 35% hygroscopic water at 100% RH. In the face of uncertainty regarding maximum water take-up in a saturated atmosphere, a standard value of 25% has been adopted by the Australian sugar industry.
Contacting Solution. The more common approach for determining hygroscopic water on sugar cane fibre is the solution contact method (Murry et al. 1998; Kelly and Rutherford 1957; van der Pol et al. 1957; Foster 1962; Steuerwald 1912; Qin and White 1991; Mangion and Player 1991). A review of the results obtained using this method follows.
Steuerwald (1912) determined a value of 22.4% for hygroscopic water, using the solution contact method. Steuerwald also used a pressing technique where pure sucrose solution was added to 'fresh' cane fibre and pressed to obtain a residue. Following this method hygroscopic water was found to decrease to 16.5% as applied pressure was increased to 30 MPa. Foster (1962) initially attributed the decrease to variation in Brix in the stalk, in particular, to fibrovascular water. Fibrovascular water is the very low Brix (< 0.8) solutions in the large vessels (in xylem), sieve tubes (in phloem) and fibre lumen that make up the vascular bundles. The fibrovascular water amounts to approximately 3% of the weight of cane and is in relatively large cavities. The water in the large vessels and sieve tubes of the fibrovascular bundles is relatively easily removed (Douwes-Dekker 1961); however, the low sugar liquid in the thick-walled shorter tissues surrounding these elements is much more strongly held (Foster 1956). After conducting press tests, Foster (1962) concluded that there is some variation in hygroscopic water due to expression. Foster reports: hygroscopic water on bagasse at 10.8% by Brix balance, corresponding to 18.4% by Pol balance; and, 9.013.8% on prepared cane fibre at 40 MPa. Foster also notes that increasing the sucrose concentration reduces sorbed water due to increased affinity of the sucrose for water molecules. The pressure dependency of hygroscopic water is also reported for cotton (Valko 1943).
Mangion and Player (1991) investigated varietal and location effects on hygroscopic water using 10 Brix solution and found: an average hygroscopic water level of 20.6% with a standard deviation of 2.2 units for 250 data points; a small spread in hygroscopic water for six varieties, 17.020.3%; tops/green leaf had a slightly higher hygroscopic water, 23.524.1%; trash and stalk both had similar levels of hygroscopic water; a much lower hygroscopic water level was observed for roots, 4.56.7%; and, growing location did not consistently affect hygroscopic water. Mangion and Player also developed a Soxhlet extraction technique for determining hygroscopic water on cane fibre.
A much stronger varietal effect was found by Kelly and Rutherford (1957); i.e., Q50 adsorbed approximately twice the water that three other varieties sorbed. Van der Pol et al. (1957) determined that fibre and leaf both sorbed an average of 29% hygroscopic water when in contact with 20 Brix solution after the fibre samples has been dried at various temperatures. Interestingly, van der Pol et al. point out that the fibre retained 5% water after cold extraction at 60C in the presence of P2O5, the last remaining water appearing to be tightly bound. In both articles, pure cellulose powder was tested as a reference material and the adsorbed water value was reported to be 8%. It is not specified in either article how the cellulose had been prepared.
Qin and White (1991) report on the development of a variation to the solution contact method where smaller volumes of solution are added to the fibre specimen; i.e., solution to fibre ratios closer to three than the traditional 20. The specimen and solution are repeatedly pressed, giving improved mixing and increased accuracy. For a 5Brix solution at room temperature, the hygroscopic water is determined for rind 11.9%, fibrovascular bundles 18.3% and pith 22.1%. The decrease in hygroscopic water from pith to fibrovascular bundles to rind to root is thought to be due to increasing cell wall thickness, i.e. less available surface area (decreasing specific surface) for adsorption of nonsolvent water, and change in the cell wall material, particularly lignification. The hygroscopic water values appeared to be independent of temperature effects over the range 1555C; however, this maybe due to the limited amount of data available. Valko (1943) and Nelson (1983) both report that increasing temperature reduces vapour sorption up to 85% RH, beyond which point the effect of temperature is not consistent.
On reviewing the work of Munro (1964), Murry (1997) determined that hygroscopic water as a mass fraction on fibre, Hw, appeared to decrease both with increasing preparation and increasing Brix extraction (i.e. increasing compression pressures 055 MPa). There is a possible error in this observation due to the potential inclusion of low Brix fibrovascular water. There are also conflicting reports of the effect of beating on the equilibrium moisture content of paper: Valko (1943) states that the beating of pulp has no effect on the hygroscopic water, while Higham (1968) states that there is an increase in equilibrium water with beating (the consistency of the definitions 'hygroscopic' and 'equilibrium' has not been confirmed).
Subsequently, Murry et al. (1998) reported experiments at controlled pressures using the solutionpress apparatus developed by Qin and White (1991). The results of the latter tests show a clear decrease in hygroscopic water with increasing compaction; there is also a suggestion that below compactions of 300 kg/m3 hygroscopic water averaged approximately 22% and above compactions of 400 kg/m3 averaged 7.5%. During these tests (Khatri 1997), a bagasse density of 450 kg/m3 was achieved at pressures of 27 MPa with corresponding hygroscopic water levels of 79% (note, much higher compactions would normally be expected at this pressure). Murry et al. correlated their data using linear and sigmoidal curve fits. The sigmoidal regression captures the perceived step change in hygroscopic water. No explanation for the change in hygroscopic behaviour was offered.
In summary, hygroscopic water in sugar cane:
a. decreases with increasing concentration of the contacting solution, but is independent of the juicefibre ratio used (Qin and White 1991);
b. depends on cane variety (Kelly and Rutherford 1957; Mangion and Player 1991);
c. has a mean value of 20.6% by contacting solution at 10Bx, pressure unspecified (Mangion and Player 1991);
d. depends on the portion of fibre being tested, i.e. rind 11.9%, fibrovascular bundles 18.3%, pith 22.1% and root 4.56.7% (Qin and White 1991; Mangion and Player 1991);
e. may decrease with comminution (possible error due to the potential inclusion of fibrovascular water) (Murry 1997);
f. depends on pressure applied to fibre matrix, reducing to 16.5% at 30 MPa (Steuerwald 1912), 9.013.8% at 40 MPa (Foster 1962), to 79% at 27 MPa (Khatri 1997);
g. appears independent of temperature under fully saturated conditions, 1555C (Qin and White 1991); and
h. is independent of growing locality (Mangion and Player 1991).
Apparent dependence of hygroscopic water on fibre effective stress
References to the pressure dependence of hygroscopic water will now be considered in detail. It is also important to distinguish between vapour or pore (hydraulic) pressure, and the interparticulate effective stress in the fibre skeleton. A load very slowly applied to a (wet) specimen by a platen or plunger will allow pore pressure to abate leaving the fibre skeleton to carry the entire platen load. A specimen held at a constant volume achieves the same type of pore pressurefree, effective stress state with time. The reported effective stress dependence of hygroscopic water is a concern for milling engineers who routinely monitor the extraction and dewatering performance of their mills. A decrease in hygroscopic water at mill pressures implies that the Brix may be mixed with a larger volume of water than expected and, therefore, be more difficult to extract. Lower hygroscopic water also implies that dewatering performance is far worse than it should be; i.e., the proportion of fixed water in the bagasse is lower and there is more free water available for expression. If a definition for hygroscopic water including 'pressure' or fibre effective stress is to be used, then a much smaller value than the Australian industry standard value of 25% should be used. How much smaller should the hygroscopic water value be and why is hygroscopic water pressure dependent?
During milling the fibre skeleton experiences stresses exceeding 20 MPa (Murry and Holt 1967). As stated above, the apparent density of the first sorbed water is 1400 MPa and the average pressure for the entire multilayer (89% water, Figure 2) is 200 MPa. It is unlikely that the pressures applied during milling would affect the multilayer water to any great extent and a logical lower limit of 8% is established for hygroscopic water. Given the 200 MPa average pressure in the bound layers, it may be inferred that effective stress in the fibre skeleton at milling pressures is carried through the bound liquid film directly. This conclusion does not negate the principle of effective stress but does discount direct point contact between solid cellulose particles. If the upper limit to hygroscopic water at 10?Bx is taken to be 20.6%, assuming a small unstated stress level (Mangion and Player 1991); then, between the upper and lower limits, hygroscopic water must be defined in terms of temperature, solution concentration, (vapour or) pore pressure and effective stress in the fibre skeleton.
To understand why hygroscopic water is pressure dependent, a mechanistic approach is adopted. Consider the elastic moduli of sugar cane fibre, 8.3 GPa (Pidduck 1955) and cellulose, 25 GPa (Downing et al. 1999). At pressures of 20 MPa the strain in the cellulose material is quite small (approximately 0.001) and would not be expected to affect the mesopore volume or absorbed water. The 20 MPa pressure is, however, high enough to compact bagacillo platelets into close proximity and to elastically or plastically collapse many of the cell walls of the fibrovascular bundles bringing cell wall faces into contact. When the cellbagacillo surfaces come into contact there is a reduction in exposed surface area and, it is speculated, loosely bound water may be displaced. The displacement of loosely bound fluid results in an apparent decrease in the hygroscopic water. The decrease in hygroscopic water is likely to depend upon: the particleparticle contact pressure; the flexibility of the cell wall material, hence elastic and plastic collapsing stresses; the surface areas in contact and voids ratio; the curvatures of the surfaces; the roughness of the cellulose; the apparent viscosity of the film; and, capillary pressure as the two surfaces approach. In reality, the loosely bound water is probably not a continuous film and the reduction in sorbed water is more likely to be the result of a decrease in 'shared' hygroscopic water volume as the cellulose particles approach one another.
It is hypothesised that a link exists between cell wall collapse, where collapsing stresses increase with increasing cell wall thickness and reducing cell wall length (refer to honeycomb model presented by Downing et al. 1999), and the variation in hygroscopic water, from nominally 2025% down to 8%, with increasing compression pressure. Since the hypothesis is based on the physical response of the cell walls, it stands to reason that the expulsion of loosely bound hygroscopic water would be reversible within the capacity of the cell walls to recover elastically, or viscoelastically, from the deformation. Due to the high degree of scatter in the hygroscopic watercompaction data (Murry et al. 1998), it is not possible to confirm the suitability of a cellular collapse model for the hygroscopic behaviour and the hygroscopic watercompaction tests should be repeated on a larger scale.
The implications of a low (8%) hygroscopic water value on related matters, such as the cane payment formula, have not been considered at this point in time.
Conclusions
A review of the literature has demonstrated that sorbed water is bound to cellulose fibre with a varying degree of attraction. Total bound water may be as high as 35% (Kelly 1957); however, the firmly bound multilayer water is limited to about 8% on fibre dry weight, corresponding to approximately 1% of the total cane mass and a little over 1% of the total liquid phase in cane. This small liquid fraction may be included as free liquid in numerical models of the rolling process (Downing et al. 1999).
The reduction in hygroscopic water with increasing effective stress in the solid phase is perceived to be an effect caused by the displacement of loosely bound water as fibre particles approach. It is hypothesised that a link exists between cell wall collapse, where collapsing stresses increase with increasing cell wall thickness and reducing cell wall length, and the reduction in hygroscopic water from nominally 2025% down to 8% with increasing compression pressure. Recent work by Murry et al. (1998), however, shows too much scatter to conclusively demonstrate the hypothesis using a cellular collapse model (Downing et al. 1999) and the experiments should be repeated on a larger scale. Further, it is clear that hygroscopic water must now be defined in terms of temperature, solution concentration, (vapour or) pore pressure and effective stress in the fibre skeleton.
Acknowledgments
The financial assistance of the Bureau of Sugar Experiment Stations (BSES), Australia is gratefully acknowledged by the first author. Technical comments by Professor E.T. White, Univ. Queensland and the late Dr. C.R. Murry assisted in the compilation of the text.
REFERENCES
Adamson, A.W. (1982). Physical Chemistry of Surfaces, 4th ed., Ch. 16, Wiley, NY.
Brotherton, G.A. (1985). Development of small scale tests to predict the milling characteristics of cane varieties, BSES.
Bruyn, J. (1963). Brix-free water in cane fibre. S.M.R.I. Bulletin - No. 25. The Sth Afr. Sugar Journal, Oct. 1963, pp. 757-765.
Coulson, J.M., Richardson, J.F., Backhurst, J.R. and Harker, J.H. (1996). Chemical Engineering: Particle Technology and Separation Processes, vol. 2, 4th ed., Reed Elsevier, UK.
Douwes-Dekker, K. (1961). Sth Afr. Sugar Technol. Assoc., 35th Conf., 7994.
Downing, C.M., Loughran, J.G. and Domanti, S.A. (1999). Crushing soil contaminated sugar cane. Proc. Aust. Soc. Sugar Cane Technol., 21: 294300.
Foster, D.H. (1956). Analytical methods used in assessing mill tandem performance. Proc. Int. Soc. Sugar Cane Technol., vol. 2, 9: 426-436.
Foster, D.H. (1962). Fibre water and juice. Proc. Qld Soc. Sugar Cane Technol., 29: 179184.
Higham, R.R.A. (1968). A Handbook of Papermaking: The Technology of Pulp, Paper and Board Manufacture, Oxford Univ. Press, London.
Khatri, K. (1997). Effect of applied pressure on hygroscopic water in sugar milling. Univ. Qld, BEng thesis.
Keey, R.B. (1996). Recent developments in the understanding of wood drying: An Australasian View. Heat and Mass Transfer Australia, Sydney, 6: 409426.
Kelly, F.H.C. (1957). Water adsorption on sugar cane fibre. Int. Sugar J., 59: 3638.
Kelly, F.H.C. and Rutherford, B.J. (1957). Water adsorption on sugar cane fibres. I.S.J., 59: 152155.
Mangion, M.J. and Player, M.R. (1991). Hygroscopic water in sugarcane. Proc. Aust. Soc. Sugar Cane Technol., 13: 285290.
McBain, J.W. (1909). The mechanism of the adsorption ("sorption") of hydrogen by carbon. Philosophical Magazine, S. 6, 18, 108, 916935.
Munro, B.M. (1964). An investigation into crushing of bagasse and the influence of imbibition on extraction. University of Queensland, PhD Thesis.
Murry, C.R. (1997). An alternative model for the extraction performance of first mills. Proc. Aust. Soc. Sugar Cane Technol., 19: 322329.
Murry, C.R. and Holt, J.E. (1967). The Mechanics of Crushing Sugar Cane, Elsevier.
Murry, C.R., Katri, K and White, E.T. (1998). Hygroscopic water and compression. Proc. Aust. Soc. Sugar Cane Technol., 20: 404406.
Nelson, R.M. (1983). A model for sorption of water vapor by cellulosic materials. Wood Fiber Sci., 15: 822.
Pidduck, J. (1955). Physical properties of bagasse. Proc. Qld Soc. Sugar Cane Technol., 22: 147155.
van der Pol, C., Young, C.M. and Douwes-Dekker, K. (1957). The determination of certain qualities of individual consignments of cane. Sth. Afr. Sugar J., 41: 544552.
Qin, L.J., and White, E.T. (1991). A press method for evaluating hygroscopic water for cane fibres. Proc. Aust. Soc. Sugar Cane Technol., 13: 291297.
Stamm, A.J. (1997). Wood Technology: Chemical Aspects, ACS Symposium Series 43, Washington D.C.
Steuerwald, L.G.L. (1912), Archief voor Java Suikerindustrie, 1315. (In Bruyn 1963, above.)
Valko, E.I. (1943). Cellulose and Cellulose Derivatives, ed. Emil Ott, Interscience Publ. Inc., NY, 379423.
Figure 1 - Type II isotherms for cellulosic materials (standard cellulose and pulp data at 20C, Valko 1943; white spruce at 25C, Nelson 1983; Q50 sugar cane fibre at 20C, Foster 1956)
Figure 2 - Apparent density of water sorbed by cotton (Valko 1943)
