Paolo D'Antona - Academia.edu (original) (raw)

Papers by Paolo D'Antona

Research paper thumbnail of A Rheological Study of Scleroglucan Aqueous Solutions Utilized for the Production of Edible Films

A Rheological Study of Scleroglucan Aqueous Solutions Utilized for the Production of Edible Films

Research paper thumbnail of High Pressure Viscosity of Lubricants: Effect of Polymeric Additives

High Pressure Viscosity of Lubricants: Effect of Polymeric Additives

Steinkopff eBooks, 1998

Lubricants in the automotive applications are very often subjected to very high pressures. Thus i... more Lubricants in the automotive applications are very often subjected to very high pressures. Thus in order to properly design the lubricant, it is necessary to measure rheological and tribological properties at these extreme conditions, that are not usually investigated. For instance the values of the operative conditions in an elastohydrodynamic regime (EHD), are approximately T>100°C, pressure up to 1 GPa and shear rates ranging between 105 to 108 s-1. During this regime, the lubricant properties will determine the film thickness, the load carrying capacity, the friction, etc., therefore its performance is essentially based on the the capability to reduce friction, viscous dissipation.

Research paper thumbnail of A new rheological approach helps formulation of gas impermeable cement slurries

Cement and Concrete Research, Apr 1, 1999

The prime tasks of cementing an oil well are to keep the casing in place, to prevent corrosion fr... more The prime tasks of cementing an oil well are to keep the casing in place, to prevent corrosion from formation water, and, most importantly, to avoid the flow of fluids on the outside of the casing. Sometimes gas migration in cement slurries occurs when gas present in the formation exerts pressure against the cement slurry column, causing the formation of microfractures in the setting matrix, expecially during the transition time of the slurry. Many studies have been conducted in the last two decades to help in understanding which properties the cement slurry must have to avoid the migration of such fluids. In this paper we propose a new rheological approach to evaluate the capacity of a cement slurry to stop the migration of fluids from the formation in the wells where the risk of gas migration is relatively high, especially during the transition time. Our rheological approach is based on small amplitude oscillatory measurements. We collected information on either kinetics of gelation of cements for oil well usage or the strength of their structures. This fundamental approach has been useful to formulate different cement slurries that have been used with success in several field trials where the risk of gas migration was relatively high.

Research paper thumbnail of Process for reducing the restart pressure of streams selected from waxy crude oils, water-in-crude emulsions and dispersions of hydrocarbon hydrates

Process for reducing the restart pressure of streams selected from waxy crude oils, water-in-crude emulsions and dispersions of hydrocarbon hydrates

Research paper thumbnail of Studio reologico della transizione sol-gel in sistemi usati per inibire la produzione di acqua da pozzi petroliferi

Studio reologico della transizione sol-gel in sistemi usati per inibire la produzione di acqua da pozzi petroliferi

Research paper thumbnail of Comparative analysis of tetracycline-containing dental gels: Poloxamer- and monoglyceride-based formulations

International Journal of Pharmaceutics, 1996

The aim of the paper was to develop tetracycline-containing formulations for the treatment of per... more The aim of the paper was to develop tetracycline-containing formulations for the treatment of periodontitis by direct periodontal intrapocket administration. Two different semi-solid formulations were prepared, based on poly(oxyethylene)poly(oxypropylene) block copolymer (poloxamer) and monoglycerides, respectively. Both formulations possess interesting properties as delivery systems. They are easily administered by syringe equipped with needles appropriate for intrapocket delivery, they are characterized by a sol-gel transition, becoming semi-solid once in the periodontal pocket and, finally, they represent biocompatible formulations eliminated from the body by normal routes. A rheological characterization of both formulations was performed in the presence or in the absence of tetracycline, determining the sol-gel transition temperature (To) by 'time cure tests' and the z coefficient by 'frequency sweep test'. In addition, the in vitro tetracycline release from formulations was determined. Comparative in vivo studies were conducted, in order (a) to compare the persistence of the gels on the gum and (b) to evaluate the clinical performances of the gels. These latest studies indicated that both poloxamer and monoglycerides gels, when applied subgingivally, produce a significantly improved outcome in moderate to deep periodontal pockets.

Research paper thumbnail of Gelation of waxy crude oils by ultrasonic and dynamic mechanical analysis

Gelation of waxy crude oils by ultrasonic and dynamic mechanical analysis

Rheologica Acta, 2007

Research paper thumbnail of Wax crystallization and aggregation in a model crude oil

Wax crystallization and aggregation in a model crude oil

Journal of Physics: Condensed Matter, 2005

The high-molecular-weight paraffinic (&am... more The high-molecular-weight paraffinic ('wax') fraction separates from crude oils at low temperatures, a process that can lead to a sol-gel transition when the mass of wax solids exceeds 1-2%. Attractive interactions between the micron-size wax solids suspended in the non-polar medium have been suggested to be responsible for gel formation. The present study reports an optically transparent model oil system,

Research paper thumbnail of Rheologic and NMR characterization of monoglyceride-based formulations

Rheologic and NMR characterization of monoglyceride-based formulations

Journal of Biomedical Materials Research, 2000

ABSTRACT

Research paper thumbnail of A new rheological approach helps formulation of gas impermeable cement slurries

Cement and Concrete Research, 1999

The prime tasks of cementing an oil well are to keep the casing in place, to prevent corrosion fr... more The prime tasks of cementing an oil well are to keep the casing in place, to prevent corrosion from formation water, and, most importantly, to avoid the flow of fluids on the outside of the casing. Sometimes gas migration in cement slurries occurs when gas present in the formation exerts pressure against the cement slurry column, causing the formation of microfractures in the setting matrix, expecially during the transition time of the slurry. Many studies have been conducted in the last two decades to help in understanding which properties the cement slurry must have to avoid the migration of such fluids. In this paper we propose a new rheological approach to evaluate the capacity of a cement slurry to stop the migration of fluids from the formation in the wells where the risk of gas migration is relatively high, especially during the transition time. Our rheological approach is based on small amplitude oscillatory measurements. We collected information on either kinetics of gelation of cements for oil well usage or the strength of their structures. This fundamental approach has been useful to formulate different cement slurries that have been used with success in several field trials where the risk of gas migration was relatively high.

Research paper thumbnail of Study of Gelling Behavior of Poly(vinyl alcohol)-Methacrylate for Potential Utilizations in Tissue Replacement and Drug Delivery

Biomacromolecules, 2004

The need of innovative, multifunctional biomaterials for the partial or complete tissue replaceme... more The need of innovative, multifunctional biomaterials for the partial or complete tissue replacement is the driving force for the search of improvements of the performances of the available materials and in the formulation of new ones. Addressing the focus to vitreous substitution, we have explored the possibility of using injectable aqueous solutions of poly(vinyl alcohol), PVA, derivatives able to form hydrogels in the ocular cavity upon UV-vis irradiation with visible light. In particular, we describe the features of hydrogels from methacrylate grafted PVA, PVA-MA, in terms of structural characteristics, degradation processes, release of low-and high-molecular weight molecules, and in vitro gelation kinetics. The mechanical properties, drug delivery tests, and rheology tests suggest that PVA-MA derivatives have the potential to become a useful material for vitreous substitution.

Research paper thumbnail of Viscoelastic Measurement at Very Low Temperature on Lubricant Systems

Viscoelastic Measurement at Very Low Temperature on Lubricant Systems

Rheological behavior of lubricant base oils is very important especially at low temperature becau... more Rheological behavior of lubricant base oils is very important especially at low temperature because it can be very helpful in predicting the onset of possible motor failure. It is well known that oils that have passed official standard requirements may nevertheless show failures, depending on some particular conditions to which the engine may be exposed.

Research paper thumbnail of A weak gel model for foods

Research paper thumbnail of Concentration and temperature effect on the viscosity of binary sugar solutions

Concentration and temperature effect on the viscosity of binary sugar solutions

Research paper thumbnail of Viscosity of multicomponent solutions of sugars

Viscosity of multicomponent solutions of sugars

Research paper thumbnail of A weak gel model for foods

Research paper thumbnail of Rheological Behavior and Structural Interpretation of Waxy Crude Oil Gels

Langmuir, 2005

A waxy crude oil which gels below a threshold temperature has been investigated under static and ... more A waxy crude oil which gels below a threshold temperature has been investigated under static and dynamic conditions, using a combination of rheological methods, optical microscopy, and DSC. Particular attention is given in this work to the influence of the mechanical history on gel strength and to describing the time-dependent rheological behavior. The gels display a strong dependence of the yield stress and moduli on the shear history, cooling rate, and stress loading rate. Of particular interest is the partial recovery of the gel structure after application of small stress or strain (much smaller than the critical values needed for flow onset) during cooling, which can be used to reduce the ultimate strength of the crude oil gel formed below the pour point. A second focus of this study is to further develop the physical interpretation of the mechanism by which wax crystallization produces gelation. Gelation of the waxy crude oil studied is suggested to be the result of the association between wax crystals, which produces an extended network structure, and it is shown that the system displays features common to attractive colloidal gels, for one of which, fumed silica (Aerosil 200) in paraffin oil, rheological data are reported. The colloidal gel model provides a simple and economical basis for explaining the response of the gelled oil to various mechanical perturbations and constitutes a fruitful basis from which to develop technologies for controlling the gelation phenomenon, as suggested by the rheological results reported.

Research paper thumbnail of Structure of waxy crude oil emulsion gels

Journal of Non-Newtonian Fluid Mechanics, 2008

The phase separation of paraffinic solids from crude oil constitutes a major operating issue for ... more The phase separation of paraffinic solids from crude oil constitutes a major operating issue for the petroleum industry, in view of the fact that the association of wax crystals into a disordered spanning network can lead to severe flow assurance problems. Although the presence of water in crude oil is quite common, its impact on waxy crude oil gelation and rheology has not received much more attention in the literature.

Research paper thumbnail of Massive AGB models of low metallicity: the implications for the self-enrichment scenario in metal-poor globular clusters

Astronomy and Astrophysics, 2009

Context. We present the physical and chemical properties of intermediate-mass stars models of low... more Context. We present the physical and chemical properties of intermediate-mass stars models of low metallicity, evolved along the thermal pulse phase. Aims. The target of this work is to extend to low metallicities, Z=1,2 and 6 × 10 −4 , the models previously computed for chemistries typical of Globular Clusters of an intermediate metallicity (Z=0.001), and for the most metal-rich clusters found in our Galaxy (Z=0.004); the main goal is to test the self-enrichment scenario also for metal poor Globular Clusters Methods. We calculated three grids of intermediate-mass models with metallicities Z = 10 −4 , 2 × 10 −4 , and 6 × 10 −4 ; the evolutionary sequences are followed from the pre-main sequence throughout the AGB phase, almost until the ejection of the whole envelope. We discuss the chemistry of the ejecta, and in particular the mass fractions of those elements that have been investigated during the many, deep, spectrocopic surveys of Globular Clusters Results. Although the data for oxygen and sodium are scarce for low metallicity Globular Clusters, the few data for the unevolved stars in NGC 6397 are compatible with the models. Further, we find good agreement with the C-N anticorrelation of unevolved stars in the cluster M15. In this cluster, however, no stars having low oxygen ([O/Fe]∼ −1) have been detected. The most massive, very metal poor clusters, should contain such stars, according to the present models. At the lowest metallicity Z = 10 −4 , the ejecta of the most massive AGBs have C/O> 1, due to the dramatic decrease of the oxygen abundance. We discuss the possible implications of this prediction.

Research paper thumbnail of Wax crystallization and aggregation in a model crude oil

Journal of Physics: Condensed Matter, 2005

The high-molecular-weight paraffinic ('wax') fraction separates from crude oils at low temperatur... more The high-molecular-weight paraffinic ('wax') fraction separates from crude oils at low temperatures, a process that can lead to a sol-gel transition when the mass of wax solids exceeds 1-2%. Attractive interactions between the micron-size wax solids suspended in the non-polar medium have been suggested to be responsible for gel formation. The present study reports an optically transparent model oil system, based on a mixture of linear and branched paraffins. Rheological measurements and optical microscopy show that the model system reproduces essential features of crude oil gels. Small-angle light scattering studies conducted at temperatures intermediate between the cloud point (58 • C) and sol-gel transition (39 • C) show that phase separation and wax solid aggregation are rapid processes, leading to the formation of dynamically arrested structures well above the sol-gel transition determined rheologically. Analysis of gravity settling effects has provided a rough estimate for the yield stress of the wax particle network formed (greater than 0.7 Pa at 45 • C and 0.07 Pa at 55 • C). Clusters formed by the aggregated wax solids possess a fractal dimension of about 1.8, consistent with diffusion-limited cluster-cluster aggregation.

Research paper thumbnail of A Rheological Study of Scleroglucan Aqueous Solutions Utilized for the Production of Edible Films

A Rheological Study of Scleroglucan Aqueous Solutions Utilized for the Production of Edible Films

Research paper thumbnail of High Pressure Viscosity of Lubricants: Effect of Polymeric Additives

High Pressure Viscosity of Lubricants: Effect of Polymeric Additives

Steinkopff eBooks, 1998

Lubricants in the automotive applications are very often subjected to very high pressures. Thus i... more Lubricants in the automotive applications are very often subjected to very high pressures. Thus in order to properly design the lubricant, it is necessary to measure rheological and tribological properties at these extreme conditions, that are not usually investigated. For instance the values of the operative conditions in an elastohydrodynamic regime (EHD), are approximately T>100°C, pressure up to 1 GPa and shear rates ranging between 105 to 108 s-1. During this regime, the lubricant properties will determine the film thickness, the load carrying capacity, the friction, etc., therefore its performance is essentially based on the the capability to reduce friction, viscous dissipation.

Research paper thumbnail of A new rheological approach helps formulation of gas impermeable cement slurries

Cement and Concrete Research, Apr 1, 1999

The prime tasks of cementing an oil well are to keep the casing in place, to prevent corrosion fr... more The prime tasks of cementing an oil well are to keep the casing in place, to prevent corrosion from formation water, and, most importantly, to avoid the flow of fluids on the outside of the casing. Sometimes gas migration in cement slurries occurs when gas present in the formation exerts pressure against the cement slurry column, causing the formation of microfractures in the setting matrix, expecially during the transition time of the slurry. Many studies have been conducted in the last two decades to help in understanding which properties the cement slurry must have to avoid the migration of such fluids. In this paper we propose a new rheological approach to evaluate the capacity of a cement slurry to stop the migration of fluids from the formation in the wells where the risk of gas migration is relatively high, especially during the transition time. Our rheological approach is based on small amplitude oscillatory measurements. We collected information on either kinetics of gelation of cements for oil well usage or the strength of their structures. This fundamental approach has been useful to formulate different cement slurries that have been used with success in several field trials where the risk of gas migration was relatively high.

Research paper thumbnail of Process for reducing the restart pressure of streams selected from waxy crude oils, water-in-crude emulsions and dispersions of hydrocarbon hydrates

Process for reducing the restart pressure of streams selected from waxy crude oils, water-in-crude emulsions and dispersions of hydrocarbon hydrates

Research paper thumbnail of Studio reologico della transizione sol-gel in sistemi usati per inibire la produzione di acqua da pozzi petroliferi

Studio reologico della transizione sol-gel in sistemi usati per inibire la produzione di acqua da pozzi petroliferi

Research paper thumbnail of Comparative analysis of tetracycline-containing dental gels: Poloxamer- and monoglyceride-based formulations

International Journal of Pharmaceutics, 1996

The aim of the paper was to develop tetracycline-containing formulations for the treatment of per... more The aim of the paper was to develop tetracycline-containing formulations for the treatment of periodontitis by direct periodontal intrapocket administration. Two different semi-solid formulations were prepared, based on poly(oxyethylene)poly(oxypropylene) block copolymer (poloxamer) and monoglycerides, respectively. Both formulations possess interesting properties as delivery systems. They are easily administered by syringe equipped with needles appropriate for intrapocket delivery, they are characterized by a sol-gel transition, becoming semi-solid once in the periodontal pocket and, finally, they represent biocompatible formulations eliminated from the body by normal routes. A rheological characterization of both formulations was performed in the presence or in the absence of tetracycline, determining the sol-gel transition temperature (To) by 'time cure tests' and the z coefficient by 'frequency sweep test'. In addition, the in vitro tetracycline release from formulations was determined. Comparative in vivo studies were conducted, in order (a) to compare the persistence of the gels on the gum and (b) to evaluate the clinical performances of the gels. These latest studies indicated that both poloxamer and monoglycerides gels, when applied subgingivally, produce a significantly improved outcome in moderate to deep periodontal pockets.

Research paper thumbnail of Gelation of waxy crude oils by ultrasonic and dynamic mechanical analysis

Gelation of waxy crude oils by ultrasonic and dynamic mechanical analysis

Rheologica Acta, 2007

Research paper thumbnail of Wax crystallization and aggregation in a model crude oil

Wax crystallization and aggregation in a model crude oil

Journal of Physics: Condensed Matter, 2005

The high-molecular-weight paraffinic (&am... more The high-molecular-weight paraffinic ('wax') fraction separates from crude oils at low temperatures, a process that can lead to a sol-gel transition when the mass of wax solids exceeds 1-2%. Attractive interactions between the micron-size wax solids suspended in the non-polar medium have been suggested to be responsible for gel formation. The present study reports an optically transparent model oil system,

Research paper thumbnail of Rheologic and NMR characterization of monoglyceride-based formulations

Rheologic and NMR characterization of monoglyceride-based formulations

Journal of Biomedical Materials Research, 2000

ABSTRACT

Research paper thumbnail of A new rheological approach helps formulation of gas impermeable cement slurries

Cement and Concrete Research, 1999

The prime tasks of cementing an oil well are to keep the casing in place, to prevent corrosion fr... more The prime tasks of cementing an oil well are to keep the casing in place, to prevent corrosion from formation water, and, most importantly, to avoid the flow of fluids on the outside of the casing. Sometimes gas migration in cement slurries occurs when gas present in the formation exerts pressure against the cement slurry column, causing the formation of microfractures in the setting matrix, expecially during the transition time of the slurry. Many studies have been conducted in the last two decades to help in understanding which properties the cement slurry must have to avoid the migration of such fluids. In this paper we propose a new rheological approach to evaluate the capacity of a cement slurry to stop the migration of fluids from the formation in the wells where the risk of gas migration is relatively high, especially during the transition time. Our rheological approach is based on small amplitude oscillatory measurements. We collected information on either kinetics of gelation of cements for oil well usage or the strength of their structures. This fundamental approach has been useful to formulate different cement slurries that have been used with success in several field trials where the risk of gas migration was relatively high.

Research paper thumbnail of Study of Gelling Behavior of Poly(vinyl alcohol)-Methacrylate for Potential Utilizations in Tissue Replacement and Drug Delivery

Biomacromolecules, 2004

The need of innovative, multifunctional biomaterials for the partial or complete tissue replaceme... more The need of innovative, multifunctional biomaterials for the partial or complete tissue replacement is the driving force for the search of improvements of the performances of the available materials and in the formulation of new ones. Addressing the focus to vitreous substitution, we have explored the possibility of using injectable aqueous solutions of poly(vinyl alcohol), PVA, derivatives able to form hydrogels in the ocular cavity upon UV-vis irradiation with visible light. In particular, we describe the features of hydrogels from methacrylate grafted PVA, PVA-MA, in terms of structural characteristics, degradation processes, release of low-and high-molecular weight molecules, and in vitro gelation kinetics. The mechanical properties, drug delivery tests, and rheology tests suggest that PVA-MA derivatives have the potential to become a useful material for vitreous substitution.

Research paper thumbnail of Viscoelastic Measurement at Very Low Temperature on Lubricant Systems

Viscoelastic Measurement at Very Low Temperature on Lubricant Systems

Rheological behavior of lubricant base oils is very important especially at low temperature becau... more Rheological behavior of lubricant base oils is very important especially at low temperature because it can be very helpful in predicting the onset of possible motor failure. It is well known that oils that have passed official standard requirements may nevertheless show failures, depending on some particular conditions to which the engine may be exposed.

Research paper thumbnail of A weak gel model for foods

Research paper thumbnail of Concentration and temperature effect on the viscosity of binary sugar solutions

Concentration and temperature effect on the viscosity of binary sugar solutions

Research paper thumbnail of Viscosity of multicomponent solutions of sugars

Viscosity of multicomponent solutions of sugars

Research paper thumbnail of A weak gel model for foods

Research paper thumbnail of Rheological Behavior and Structural Interpretation of Waxy Crude Oil Gels

Langmuir, 2005

A waxy crude oil which gels below a threshold temperature has been investigated under static and ... more A waxy crude oil which gels below a threshold temperature has been investigated under static and dynamic conditions, using a combination of rheological methods, optical microscopy, and DSC. Particular attention is given in this work to the influence of the mechanical history on gel strength and to describing the time-dependent rheological behavior. The gels display a strong dependence of the yield stress and moduli on the shear history, cooling rate, and stress loading rate. Of particular interest is the partial recovery of the gel structure after application of small stress or strain (much smaller than the critical values needed for flow onset) during cooling, which can be used to reduce the ultimate strength of the crude oil gel formed below the pour point. A second focus of this study is to further develop the physical interpretation of the mechanism by which wax crystallization produces gelation. Gelation of the waxy crude oil studied is suggested to be the result of the association between wax crystals, which produces an extended network structure, and it is shown that the system displays features common to attractive colloidal gels, for one of which, fumed silica (Aerosil 200) in paraffin oil, rheological data are reported. The colloidal gel model provides a simple and economical basis for explaining the response of the gelled oil to various mechanical perturbations and constitutes a fruitful basis from which to develop technologies for controlling the gelation phenomenon, as suggested by the rheological results reported.

Research paper thumbnail of Structure of waxy crude oil emulsion gels

Journal of Non-Newtonian Fluid Mechanics, 2008

The phase separation of paraffinic solids from crude oil constitutes a major operating issue for ... more The phase separation of paraffinic solids from crude oil constitutes a major operating issue for the petroleum industry, in view of the fact that the association of wax crystals into a disordered spanning network can lead to severe flow assurance problems. Although the presence of water in crude oil is quite common, its impact on waxy crude oil gelation and rheology has not received much more attention in the literature.

Research paper thumbnail of Massive AGB models of low metallicity: the implications for the self-enrichment scenario in metal-poor globular clusters

Astronomy and Astrophysics, 2009

Context. We present the physical and chemical properties of intermediate-mass stars models of low... more Context. We present the physical and chemical properties of intermediate-mass stars models of low metallicity, evolved along the thermal pulse phase. Aims. The target of this work is to extend to low metallicities, Z=1,2 and 6 × 10 −4 , the models previously computed for chemistries typical of Globular Clusters of an intermediate metallicity (Z=0.001), and for the most metal-rich clusters found in our Galaxy (Z=0.004); the main goal is to test the self-enrichment scenario also for metal poor Globular Clusters Methods. We calculated three grids of intermediate-mass models with metallicities Z = 10 −4 , 2 × 10 −4 , and 6 × 10 −4 ; the evolutionary sequences are followed from the pre-main sequence throughout the AGB phase, almost until the ejection of the whole envelope. We discuss the chemistry of the ejecta, and in particular the mass fractions of those elements that have been investigated during the many, deep, spectrocopic surveys of Globular Clusters Results. Although the data for oxygen and sodium are scarce for low metallicity Globular Clusters, the few data for the unevolved stars in NGC 6397 are compatible with the models. Further, we find good agreement with the C-N anticorrelation of unevolved stars in the cluster M15. In this cluster, however, no stars having low oxygen ([O/Fe]∼ −1) have been detected. The most massive, very metal poor clusters, should contain such stars, according to the present models. At the lowest metallicity Z = 10 −4 , the ejecta of the most massive AGBs have C/O> 1, due to the dramatic decrease of the oxygen abundance. We discuss the possible implications of this prediction.

Research paper thumbnail of Wax crystallization and aggregation in a model crude oil

Journal of Physics: Condensed Matter, 2005

The high-molecular-weight paraffinic ('wax') fraction separates from crude oils at low temperatur... more The high-molecular-weight paraffinic ('wax') fraction separates from crude oils at low temperatures, a process that can lead to a sol-gel transition when the mass of wax solids exceeds 1-2%. Attractive interactions between the micron-size wax solids suspended in the non-polar medium have been suggested to be responsible for gel formation. The present study reports an optically transparent model oil system, based on a mixture of linear and branched paraffins. Rheological measurements and optical microscopy show that the model system reproduces essential features of crude oil gels. Small-angle light scattering studies conducted at temperatures intermediate between the cloud point (58 • C) and sol-gel transition (39 • C) show that phase separation and wax solid aggregation are rapid processes, leading to the formation of dynamically arrested structures well above the sol-gel transition determined rheologically. Analysis of gravity settling effects has provided a rough estimate for the yield stress of the wax particle network formed (greater than 0.7 Pa at 45 • C and 0.07 Pa at 55 • C). Clusters formed by the aggregated wax solids possess a fractal dimension of about 1.8, consistent with diffusion-limited cluster-cluster aggregation.