Two-dimensional Fractal Dimension Research Articles

Quantitative evaluation of surface topographical changes of Au thin films after DNA immobilization

A quantitative evaluation, by atomic force microscopy measurements, of the nano-topography of single and double stranded DNA functionalized Au surfaces is carried out. The two-dimensional fractal dimension was quantified for the Au surface in 0.9±0.1 and 2.1±0.3 from 1μm×1μm and 5μm×5μm scans, respectively. It was quantified in 2.1±0.1 and in 2.4±0.3 for the Au surface after immobilization of single-stranded DNA film and in 2.0±0.1 and 1.9±0.3 for the Au surface after hybridization, from 1μm×1μm and 5μm×5μm scans, respectively. These results indicate a topographical conforming effect of the DNA films toward a two-dimensional Gaussian surface.

Fractal Dimension of Cohesive Sediment Flocs at Steady State under Seven Shear Flow Conditions

The morphological properties of kaolin flocs were investigated in a Couette-flow experiment at the steady state under seven shear flow conditions (shear rates of 5.36, 9.17, 14, 24, 31, 41 and 53 s−1). These properties include a one-dimensional (1-D) fractal dimension (D1), a two-dimensional (2-D) fractal dimension (D2), a perimeter-based fractal dimension (Dpf) and an aspect ratio (AR). They were calculated based on the projected area (A), equivalent size, perimeter (P) and length (L) of the major axis of the floc determined through sample observation and an image analysis system. The parameter D2, which characterizes the relationship between the projected area and the length of the major axis using a power function, , increased from 1.73 ± 0.03, 1.72 ± 0.03, and 1.75 ± 0.04 in the low shear rate group (G = 5.36, 9.17, and 14 s−1) to 1.92 ± 0.03, 1.82 ± 0.02, 1.85 ± 0.02, and 1.81 ± 0.02 in the high shear rate group (24, 31, 41 and 53 s−1), respectively. The parameter D1 characterizes the relationship between the perimeter and length of the major axis by the function and decreased from 1.52 ± 0.02, 1.48 ± 0.02, 1.55 ± 0.02, and 1.63 ± 0.02 in the low shear group (5.36, 9.17, 14 and 24 s−1) to 1.45 ± 0.02, 1.39 ± 0.02, and 1.39 ± 0.02 in the high shear group (31, 41 and 53 s−1), respectively. The results indicate that with increasing shear rates, the flocs become less elongated and that their boundary lines become tighter and more regular, caused by more breakages and possible restructurings of the flocs. The parameter Dpf, which is related to the perimeter and the projected area through the function , decreased as the shear rate increased almost linearly. The parameter AR, which is the ratio of the length of the major axis and equivalent diameter, decreased from 1.56, 1.59, 1.53 and 1.51 in the low shear rate group to 1.43, 1.47 and 1.48 in the high shear rate group. These changes in Dpf and AR show that the flocs become less convoluted and more symmetrical and that their boundaries become smoother and more regular in the high shear rate group than in the low shear rate group due to breakage and possible restructuring processes. To assess the effects of electrolyte and sediment concentration, 0.1 mol/L calcium chloride (CaCl2) and initial sediment concentration from 7.87 × 10−5 to 1.57 × 10−5 were used in this preliminary study. The addition of electrolyte and increasing sediment concentration could produce more symmetrical flocs with less convoluted and simpler boundaries. In addition, some new information on the temporal variation of the median size of the flocs during the flocculation process is presented.

Microfiltration of humic-rich water coagulated with cationic polymer: The effects of particle characteristics on the membrane performance

The main issue explored was the effects of different coagulation conditions on the particle characteristics that would also significantly affect the performance of membranes when filtering coagulated humic-rich water. The size distribution and morphological properties of flocs formed through the coagulation of natural organic matter (NOM) were characterized and the impact of Ca2+ on these characteristics and on the performance of the MF membrane was determined. The multi-cycle MF experiments with hydraulic wash between cycles were conducted for raw and coagulated humic-rich water, and the performance was evaluated by measuring the permeate water quality, resistance to filtration, and permeability recovery with cleaning. Coagulant (polydiallyldimethyl-ammonium chloride) additions from 50% to 100% of the charge neutralization dose substantially decreased fouling compared to when filtering raw humic-rich water. Short-term fouling was increased when 1mM Ca2+ was added, but the charge neutralization coagulation removed almost all of the fouling tendency that had occurred when filtering Ca-NOM and resulted in the highest permeability recovery. The median diameter and the two-dimensional fractal dimension of flocs produced were increased as the zeta potential reached close to zero, which resulted in the formation of a cake layer that was easily removed from the surface of the membrane.

Influence of single- and dual-flocculant conditioning on the geometric morphology and internal structure of activated sludge

Polymeric ferric sulfate (PFS) and cationic polyacrylamide (CPAM) were used as flocculants in single- and dual-chemical conditioning to treat activated sludge (AS). The corresponding changes in the AS geometric and internal network structure were determined according to the size, fractal dimensions, and rheological properties of AS flocs/aggregates. Results showed that at similar capillary suction time (CST) level, the flocculant dosage was lower under dual-chemical conditioning than under single-chemical conditioning. At the optimum dosage of PFS-CPAM combination, the corresponding CST and zeta potential were 11.03s and −1.65mV, respectively. In addition, the median diameters were 0.81, 0.89 and 2.73mm, and the two-dimensional (D2) fractal dimensions were 1.98, 1.95 and 1.41 for the AS conditioned with PFS-CPAM, PFS and CPAM at their respective optimum dosage. Moreover, raw and conditioned AS exhibit thixotropic (shear thinning) properties, gel-like and weak-link structures. The mass fractal dimension values were 2.52, 2.65, 2.24, and 2.70 for the raw AS and the AS conditioned with PFS, CPAM, and PFS-CPAM, respectively. These findings indicate that inorganic flocculant conditioning facilitates the compactness of the AS flocs/aggregates. PFS hydrogel and CPAM molecules can serve as backbones of the newly formed AS flocs/aggregates.

Treatment of Micro-Polluted Surface Water by Ballasted Flocculation and its Floc Structural Characteristics

In current paper, compared to the conventional coagulation, micro-sand (MS) and magnetic powder (MP) ballasted flocculation were investigated during the treatment of micro-polluted surface water by simulating ActifloTM and SiroflocTM process. Under an optimized operation condition, the optimal turbidity, CODMnand TP removal, 94.5%, 75.1% and 93.0%, respectively could be achieved by the MP process. In further research, pollutants removal efficiency at various settling time (5, 10, 15, 20 min), flocs two-dimensional fractal dimension and average size were simultaneously studied and the relationship among them was also discussed.

Effect of conditioning by PAM polymers with different charges on the structural and characteristic evolutions of water treatment residuals

Three types of polyacrylamide (PAM) flocculants with different charges (cationic PAM WD4960, nonionic PAM M351, and anionic PAM WDA110) were used for water treatment residuals (WTRs) conditioning, and the physicochemical, morphological and structural characteristics of raw and conditioned WTRs were investigated. Rheological methods were employed to analyze the internal structural transition between the raw and conditioned WTRs under a typical dosage of WD4960. Results showed that when the raw WTRs were conditioned with the polymers, the optimum dosage of WD4960 was 4.82 g/kg total suspended solid (TSS) while that of both M351 and WDA110 was 7.24 g/kg TSS. The residual PAM content in the supernatant of the WTR matrix conditioned at the optimum WD4960 dosage was 5.59 mg/L, which is the least among the supernatants obtained with the three types of PAM. Furthermore, the visible fulvic acid (FA) in the supernatant disappeared and the intensity of the ultraviolet FA decreased. The average diameter of irregularly shaped aggregates in the WTR suspensions increased from 35.73 μm to several hundred micrometers with increasing PAM dosage. The size of WTR aggregates conditioned at the optimum WD4960 dosage was much larger than that of aggregates obtained at the optimum M351 or WDA110 dosages. Two-dimensional fractal dimension (D2) values presented an increasing trend with increasing PAM dosage. D2 values of the conditioned WTR aggregates were 1.87, 1.76, and 1.83 at optimum WD4960, M351, and WDA110 dosages, respectively. The cationic PAM (CPAM) WD4960 thus appears to be a more ideal conditioner for WTRs. Consistent relationships were observed among the capillary suction time (CST), average particle size, and D2 values of the conditioned WTR aggregates at the optimum WD4960 dosage. Mass fractal dimensions (Df) indicated that both the raw and WD4960-conditioned WTRs behave like weak-link flocs/aggregates. Df values (log G′–log TSS) of the WTR aggregates before and after conditioning with the optimum WD4960 dosage were 2.79 and 2.81, respectively. Although the transition from an alum/ferric hydrogel to a cross-linked gel occurred during the WD4960-conditioning process, only a small amount of the alum/ferric hydrogel was destroyed, and the conditioned WTR aggregates showed a gel-like matrix in which residual alum–ferric hydrogels were embedded in cross-linked WD4960 molecules.

Study on pore characteristics of flocs and sludge dewaterability based on fractal methods (pore characteristics of flocs and sludge dewatering)

To study the influence of floc characteristics on dewatering performance of excess sludge, a fractal method is adopted to characterize the sludge flocs formed at different flocculation time. The sludge is conditioned with cationic polyacrylamide (CPAM) and the fractal dimensions (two-dimensional fractal dimension Df and one-dimensional fractal dimension D1) of flocs are solved by employing image analysis. The specific resistance to filtration (SRF) and expression tests are conducted to estimate the dewatering performance of the conditioned sludge. The results indicate that sludge flocs are multilevel structure and the fractal dimension is able to monitor the sludge conditioning process, which can be divided into three stages: (1) primary particles form flocculi; (2) flocculi collide with one another, group to form flocs; (3) equilibrium stage. The critical flocculation times of these stages are 45 s and 150 s respectively. At the beginning of flocculation, Df increases and D1 diminishes dramatically because compact and regular flocculi are formed owing to the neutralizing of the cationic contained in CPAM. Subsequently, Df decreases and D1 increases slightly because of the forming of flocs with a looser structure. Finally, the Df and D1 are almost constant (with a maximum deviation of 1.1% and 2% respectively) due to the fixed internal structure and superficial morphology of the floc. In order to improve the sludge dewaterability, the optimal CPAM dosage is 3.0 kg/t DS for a good dewaterability. Under this condition, the sludge floc is the most compact and regular with the highest (two-dimensional)/lowest (one-dimensional) fractal dimension (Df: 1.86 and D1: 1.19) on the equilibrium stage. The specific filtrate speed and the SRF of the conditioned sludge are 2.86 mL/s and 5.12 × 1011 m/kg respectively. After conditioning 45 s (flocs forming stage), a dewatering step can be applied to remove the water contained in sludge and shorten the time.

Black and brown carbon fractal aggregates from combustion of two fuels widely used in Asian rituals

Incense sticks and mustard oil are the two most popular combustion fuels during rituals and social ceremonies in Asian countries. Given their widespread use in both closed and open burning activities, it is important to quantify the spectral radiative properties of aerosols emitted from the combustion of both fuels. This information is needed by climate models to assess the impact of these aerosols on radiative forcing. In this study, we used a 3-wavelength integrated photoacoustic-nephelometer – operating simultaneously at 405, 532 and 781nm – to measure the optical coefficients of aerosols emitted from the laboratory combustion of mustard oil lamp and two types of incense sticks. From the measured optical coefficients at three wavelengths, time-varying single scattering albedo (SSA), absorption Ångström exponent (AAE), and scattering Ångström exponent (SAE) were calculated. For incense smoke particles, the time-averaged mean AAE values were found to be as high as 8.32 (between 405 and 532nm) and 6.48 (between 532 and 781nm). This spectrally-varying characteristic of AAE indicates that brown carbon – a class of organic carbon which strongly absorbs solar radiation in the blue and near ultraviolet – is the primary component of incense smoke aerosols. For aerosols emitted from the burning of mustard oil lamp, the time-averaged mean AAE values were ∼1.3 (between 405 and 781nm) indicating that black carbon (BC) is the primary constituent. Scanning electron microscopy combined with image processing revealed the morphology of incense smoke aerosols to be non-coalescing and weakly-bound aggregates with a mean two-dimensional (2-d) fractal dimension (Df)=1.9±0.07, while the mustard oil smoke aerosols had typical fractal-like BC aggregate morphology with a mean 2-d Df=1.85±0.09.

Recognition of plant leaf image based on fractal dimension features

This work proposed a new method of describing the characteristics of plant leaves based on the outline fractal dimension and venation fractal dimension. First, using multiple threshold edge detection method to separate leaf edge and vein, and get multiple veins. Then, the two-dimensional fractal dimension of the leaf edge image and multiple vein images will be calculated, and a new ring projection wavelet fractal feature for leaf shape is also adopted. Finally, these two kinds’ fractal dimension features are used to plant leaves classification and recognition. The experimental results demonstrated the effectiveness of the fractal dimension feature method.

Determination of the aggregate fractal dimensions in colloidal nanofluids

Owing to the significant technological implications of nanoscale colloidal suspensions (nanofluids), it is necessary to develop suitable techniques to characterize the nanostructured aggregates in suspension. In the present work, a fractal dimension approach is applied to characterize the agglomerate structure using image analysis by scanning electron microscope photographs of the nanoparticle aggregates. Aqueous suspensions of aluminum oxide nanoparticles (nanofluids) are used for the study. A simple and direct method of projected image manipulation has been used to calculate the aggregate fractal dimensions in colloidal nanofluid. The fractal dimension provides quantitative information about important morphological features of the aggregate structure. A functional relationship is established between the two-dimensional fractal dimension ( d f2) and the three-dimensional fractal dimension ( d f3). The present study demonstrates that the optical image analysis technique can be effectively used for fractal dimension analysis of colloidal nanoparticle aggregates.

Fractal characteristics of Al-humic flocs

Abstract The characteristics of Al-humic flocs were studied through a series of experiments using microscopic and online optical monitoring techniques. It was verified that Al-humic flocs are of fractal nature and the two-dimensional fractal dimension D 2 derived from image analysis characterizes their morphological properties. At pH 5.0, the structure of Al-humic flocs formed was more compact with higher fractal dimension of 1.43 than that formed at pH 7.0 with lower fractal dimension of 1.17. The difference in floc structure was considered to be related to the different characteristics of hydrolysis and precipitation of aluminum sulfate under these two typical pH values: at pH 5.0 with a low alum dose, the products of aluminum hydrolysis are mainly soluble, while at pH 7.0 at the same alum dose, precipitates form quickly. Alum dose also affected the structure of Al-humic flocs. At pH 5.0 and at a dose to bring about charge-neutralization to |ζ| < 10 mV, flocs formed are more compact with a fractal dimen...

Fractal characteristics of Al-humic flocs

The characteristics of Al-humic floes were studied through a series of experimental work using microscopic and online optical monitoring techniques.It was verified that AI-humic floes are of fractal nature and the two-dimensional fractal dimension Df derived from image analysis characterizes their morphological properties.At pH 5.0,the structure of Al-humic flocs formed was more compact with higher fractal dimension of 1.43 than that formed at pH 7.0 with lower fractal dimension Of 1.17.The difference in floc structure was considered to be related to the difierent characteristics of hydrolysis and precipiration of aluminum sulfate under these two typical pH values:at pH 5.0 with a low alum dose,the products of alurninum hydrolysis are mainly soluble maner,While at pH 7.0 at the same alum dose.precipitates form quicldv Alum dose also affected the structure Of Al-humic floes.Under pH 5.0 and at a dose to bring about charge-neutralization to 1.1<1OmV,floes formed are more compact with a fractal dimension ranging from 1.43 to 1.49.while at a higher dose when hydrolyzed aluminum precipitates form,flocs are more open and looser with a much lower fractal dimension.During growth.the fractal dimension of the floes decreased graduauY until an equilibdum state was reached.This implies a faster increase of floc volume than the number of primary particles the floc contains.

Physical characteristics of conditioned anaerobic digested sludge – A fractal, transient and dynamic rheological viewpoint

The changes in the physical characteristics of unconditioned and conditioned anaerobic digested sludge (ADS) biosolids, such as capillary suction time (CST), yield stress, average size and fractal dimensions, were investigated through a CST test, transient and dynamic rheological test and image analysis. The results showed that the optimum polymer dose range was observed when CST or its reciprocal value was employed as an indicator. There were good correlations between the yield stresses determined from both a controlled shear stress test and a strain amplitude sweep test. The yield stress and storage modulus ( G′) increased as the polymer dose increased in most cases. A frequency sweep test revealed that polymer conditioning could extend the frequency sweep ranges for their elastic behaviors over viscous behaviors as well as the gel-like structure in the linear viscoelastic range. These results implied that more deformation energy was stored in this rigid structure, and that elastic behavior became increasingly dominant with the addition of the polymer in most cases. In addition, both the average sizes and two-dimensional fractal dimensions for conditioned ADS biosolids presented a similar up-climax-down variation trend as the polymer doses increased, whereas the critical polymer doses at the highest average sizes or two-dimensional fractal dimensions, were different. Correlation analysis revealed that the conditioned ADS dewaterability was not correlated with the yield stresses, while the average sizes or the two-dimensional fractal dimensions for conditioned ADS biosolids could be taken as the indication parameters for ADS dewaterability.

Fractal dimensions of flocs between clay particles and HAB organisms

The impact of harmful algal blooms (HABs) on public health and related economics have been increasing in many coastal regions of the world. Sedimentation of algal cells through flocculation with clay particles is a promising strategy for controlling HABs. Previous studies found that removal efficiency (RE) was influenced by many factors, including clay type and concentration, algal growth stage, and physiological aspects of HAB cells. To estimate the effect of morphological characteristics of the aggregates on HAB cell removal, fractal dimensions were measured and the RE of three species of HAB organism, Heterosigma akashiwo, Alexandrium tamarense, and Skeletonema costatum, by original clay and modified clay, was determined. For all HAB species, the modified clay had a higher RE than original clay. For the original clay, the two-dimensional fractal dimension (D2) was 1.92 and three-dimensional fractal dimension (D3) 2.81, while for the modified clay, D2 was 1.84 and D3 was 2.50. The addition of polyaluminum chloride (PACl) lead to a decrease of the repulsive barrier between clay particles, and resulted in lower D2 and D3. Due to the decrease of D3, and the increase of the effective sticking coefficient, the flocculation rate between modified clay particles and HAB organisms increased, and thus resulted in a high RE. The fractal dimensions of flocs differed in HAB species with different cell morphologies. For example, Alexandrium tamarense cells are ellipsoidal, and the D3 and D2 of flocs were the highest, while for Skeletonema costatum, which has filamentous cells, the D3 and D2 of flocs were the lowest.

Effect of polyferric chloride (PFC) doses and pH on the fractal characteristics of PFC–HA flocs

Changes in the fractal characteristics of PFC–HA flocs with polyferric chloride (PFC) doses and coagulation pHs were investigated in this study. A type of PFC coagulant with a hydrolysis degree ( B*) of 0.6027 and a Fe(III) concentration of 0.202 mol/L was employed to coagulate HA solutions at five constant coagulation pHs. Zeta potential tests were employed to reveal the coagulation mechanisms. The physical properties of flocs formed in the coagulation process were analyzed by their CCD image morphology, size distribution, and fractal dimensions. Next, microscopic observations and nitrogen-adsorption–desorption methods were conducted to characterize the pore structure and surface fractal dimensions of powders prepared from these flocs through a cryofixation–vacuum-freeze-drying procedure. The PFC doses and coagulation pHs had an obvious effect on the physical characteristics of PFC–HA flocs and their corresponding powders. Generally, in the low PFC dose range, PFC–HA flocs formed under acidic coagulation pHs and charge neutralization mechanisms were larger, had less irregular boundaries or surfaces (lower D 1 value), a more compact structure (lower D 2 value) and more irregular pore surface or pore size distribution in their dried powder than those formed under neutral and alkaline coagulation pHs and physical enmeshment and/or fresh precipitate adsorption mechanisms involved in the coagulation process. After the PFC doses exceeded this range, a gradual reversal phenomenon occurred. Furthermore, there were different specific PFC dosages that were above the critical reversal point for each property of these flocs or powders, such as the median diameter, one-dimensional fractal dimension, two-dimensional fractal dimension, and pore surface fractal dimension. In addition to these characteristics, the most compact PFC–HA flocs were formed at coagulation pH = 6.00 ± 0.05 and a PFC dosage of 4.04 × 10 −4 mol/L (Fe 3+), and the loosest flocs were produced at coagulation pH = 7.00 ± 0.05 and a PFC dose of 1.01 × 10 −4 mol/L (Fe 3+).

The effect of polymer doses and extended mixing intensity on the geometric and rheological characteristics of conditioned anaerobic digested sludge (ADS)

The effect of polymer doses and extended mixing intensity (EMI) on the geometric and rheological characteristics of conditioned anaerobic digested sludge (ADS) was investigated. The results revealed that polymer doses had a distinct effect on the CST values of conditioned ADS, but that extended mixing intensity (EMI) did not show such effect at specific polymer dosage. The polymer doses, at which the maximum values of the initial peak height and area in the two kinds of rheograms appear, were as same as or close to 20.36kg/ton producing the lowest CST value for conditioned ADS-1. The maximum size and two-dimensional fractal dimensions of the conditioned ADS-1 aggregates were observed at a polymer dosage of 13.57kg/ton, while their one-dimensional fractal dimensions decreased as more polymer was added. The floccky test for conditioned ADS-2 at different extended mixing intensities during conditioning indicates distinct effects on the peak height and area under the rheograms. However, the minimum values of peak height and area in the Haake RV20 rheograms were given at an EMI of 30rpm (G=28.98s−1), while the maximum values were obtained at an EMI of 80rpm (G=126.21s−1). At an EMI equal to 28.98s−1, the most compact and largest aggregates were produced with less irregular boundaries and surfaces than at other EMIs. For ADS-1 and ADS-2, there were no good correlations between the rheological parameters and aggregate sizes, D2L or D2P. Moreover, the EMIs from 28.98s−1 to 425.95s−1 provided available hydraulic conditions for flocculation, while mixing intensities higher than 425.95s−1 led to stronger shear and deflocculation.

Assessment of 2D and 3D fractal dimension measurements of trabecular bone from high‐spatial resolution magnetic resonance images at 3 T

In vivo two-dimensional (2D) fractal dimension (D2D) analysis of the cancellous bone at 1.5 T has been related to bone structural complexity and shown to be a potential imaging-based biomarker for osteoporosis. The objectives of this study were to assess at 3 T the in vivo feasibility of three-dimensional (3D) bone fractal dimension (D3D) analysis, analyze the relationship of D2D and D3D with osteoporosis, and investigate the relationship of D3D with spinal bone mineral density (BMD). A total of 24 female subjects (67 +/- 7 yr old, mean +/- SD) was included in this study. The cohort consisted of 12 healthy volunteers and 12 patients with osteoporosis. MR image acquisitions were performed in the nondominant metaphysis of the distal radius with a 3 T MR scanner and an isotropic resolution of 180 microm. After segmentation and structural reconstruction, 2D and 3D box-counting algorithms were applied to calculate the fractal complexity of the cancellous bone. D2D and D3D values were compared between patients with osteoporosis and healthy subjects, and their relationship with radius BV/TV and spinal BMD was also assessed. Significant differences between healthy subjects and patients with osteoporosis were obtained for D3D (p < 0.001), with less differentiation for D2D (p = 0.04). The relationship between fractal dimension and BMD was not significant (r = 0.43, p = 0.16 and r = 0.23, p = 0.48, for D2D and D3D, respectively). The feasibility of trabecular bone D3D calculations at 3 T and the relationship of both D2D and D3D parameters with osteoporosis were demonstrated, with a better differentiation for the 3D method. Furthermore, the D3D parameter has probably a different nature of information regarding the trabecular bone status not directly explained by BMD alone. Future studies with subjects with osteopenia and larger sample sizes are warranted to further establish the potential of D2D and D3D in the study of osteoporosis.

The effect of high speed mixing and polymer dosing rates on the geometric and rheological characteristics of conditioned anaerobic digested sludge (ADS)

Wastewater sludges are non-Newtonian fluids because their shear rates change with shear stress and no linear relationship is observed between their shear stress and shear rate. Therefore, it is necessary to condition sludges with polyelectrolytes prior to dewatering to increase in the dewaterability. Since 1978, researchers have observed that the yield strength of conditioned sludge increased with the addition of polymer up to the optimum dose. Then sludge rheogram was used as a control parameter to optimize the addition of polymers, and the peak height in the shear stress vs. shear rate curve was an indication of sludge conditionablity, where the optimum polymer conditioning corresponding to the highest peak was obtained. However, few studies have addressed the effects of distinct conditioning factors on the appearance of peaks in such rheograms. In this study, the impact of factors such as high speed mixing and polymer dosing rates on the geometric and rheological characteristics of conditioned anaerobic digested sludge (ADS) with the polymer zetag7557 were investigated through the jar test method. The results showed that both the high speed mixing time and polymer dosing time had important effects on the emergence of the initial peak in test curves obtained using the Haake RV20 and Flokky rheometers for evaluation of conditioned ADS. A high speed mixing time within 60 s or a polymer dosing time of 5 s was sufficient for observation of the initial peak in flow curves, and both peak height and area decreased as the high speed mixing times were prolonged in most cases in this study. As same as the high speed mixing time, the extension of zetag7557 dosing time can also lead to the gradual decrease in the initial peak size of test curves, and form small aggregates with a decrease in two-dimensional fractal dimensions ( D 2). Although the initial peak in the test curves was observed when high speed mixing intensities increased up to 300 rpm, there were several differences in the peak height and area observed on the Haake RV20 test rheograms and Floccky test curves. In addition, a high speed mixing intensity of 300 rpm was found to lead to the formation of smaller and less compact aggregates than other mixing intensities. All of the rheological and geometric parameters were somewhat correlated with fractal dimension- D 2P (based on regression analysis of the logarithmics of area and perimeter). However, D 2L(based on regression analysis of the logarithmics of area and maximum diameter) did not show good correlation with any other parameters. The median diameters of the aggregates were well correlated with one-dimensional fractal dimensions ( D 1).

Morphological characterization of suspended particles under wind-induced disturbance in Taihu Lake, China

Sediments are disturbed by wind frequently, especially in the shallow lakes. The characteristics of resuspended sediment particles in Taihu Lake were studied under different wind velocities. It showed that sediment particles suspended obviously and particle number in overlying water increased directly under high wind-induced disturbance. Suspended solid (SS) concentration was less than 50 mg/l when the wind velocity was below 3.0 m/s, however, it increased to more than 300 mg/l when the wind velocity was 10.0 m/s. Two methods were used to measure the fractal characteristics of particles. One was light scattering and the other was image analysis. The three-dimensional fractal dimensions of suspended particles, measured by light scattering, were between 2.26 and 2.44; correspondingly, the two-dimensional fractal dimensions, calculated by image analysis, were between 1.44 and 1.77. Moreover, the three-dimensional fractal dimensions were directly proportional to two-dimensional fractal dimensions. The characteristic length of particles was calculated by image analysis. The minimum characteristic length was close to 8.5 microm when the wind velocity was 1.5 m/s at 50 cm beneath lake surface, while, the maximum characteristic length was approximate to 24 microm when the wind velocity was 10 m/s at the depth of 150 cm.

Rock salt dilatancy boundary from combined acoustic emission and triaxial compression tests

This paper presents an experimental investigation of rock salt dilatancy boundary based on combined acoustic emission and triaxial compression tests carried out on the rock salt samples from the Asse Salt Mine, Germany. The experimental results were evaluated to determine the dilatancy boundary under specified stress, stress loading rate and pore pressure. Pore volume changes caused by deviatoric stresses were measured during triaxial compression tests. The dilatancy boundary was then determined from the maximum compression on a stress–strain curve which separates the compression and dilatancy regions. Variations in acoustic emissions that occur during microcrack development under triaxial compression were recorded with ten sensors mounted on the outer surface of the cylindrical samples. A spontaneous increase observed in the cumulative number of acoustic events is consistent with the dilatancy boundary determined from the minimum pore volume. It is confirmed that the dilatancy boundary depends on both stress loading rate and pore pressure. The dilatancy boundary slightly decreases with increasing the loading rate, but increases with increasing the minor normal stress. High pore pressures accelerate the dilatancy. A Biot coefficient of 0.25 for Asse rock salt was determined from the dilatancy boundary. An analysis of two-dimensional (2D) fractal dimensions determined for several samples shows that the samples with smaller dimensions have slightly higher dilatancy boundaries. The dilatancy boundary values of Asse rock salt are lower than those reported for crystalline rocks, although both rock types show similar dilatancy behaviour.