Flocculation Model Research Articles

Stability analysis of a flocculation model incorporating cell size, time delay, and control

The influence of algal cell size on nutrient absorption, and the time delay in reproduction is paramount in biological terms. Furthermore, the control is necessary during algal flocculation harvesting and sewage treatment. Therefore, we investigated the properties of a single cell algal flocculation model with time delay, size structure and control. First, we introduced a dimensionless model. Then, we analyzed the existence of positive equilibrium states and studied the equilibrium states of the model. Finally, the numerical simulation revealed that the model exhibits backward bifurcation.

Exploring Cohesive Sediment Flocculation With Surface Heterogeneity: A Theoretical Lagrangian‐Type Flocculation Model

AbstractThe flocculation of cohesive sediments significantly influences the particle size, concentration, and settling velocity and further influences sediment transport and pollutant transformation in the natural environment. The population balance equation (PBE) was used to model flocculation processes, including aggregation and floc breakup. This paper presents a theoretical Lagrangian‐type flocculation dynamic model established by solving the PBE using moment methodology and similarity transformation. The influence of surface heterogeneities (F2a) of the particles was incorporated. Sensitivity tests revealed that the model performance was significantly related to the aggregation and breakup parameters, which varied with ambient conditions. Furthermore, the effects of the shear rate, sediment concentration, particle size, and surface heterogeneity were analyzed theoretically. A critical shear rate distinguishes two cases: an increasing shear rate tends to increase the equilibrium floc size (Dfe) under low‐shear conditions, whereas a negative correlation exists at high‐shear levels. The dependence of Dfe on sediment concentration is complex, and increasing the initial concentration can enhance or limit the propensity to flocculate at different shear levels. Additionally, the enlargement of the primary particle size and surface heterogeneity reduces the propensity for flocculation. This study proposes a preliminary theoretical analysis method of flocculation processes considering factors such as surface heterogeneity, showing the possibility of further enhancing the knowledge of cohesive sediment transport.

Applying a logistic growth equation to model flocculation of sediment in the presence of living and dead organic matter

In the present study, we aim to parameterize a flocculation model, based on a logistic growth equation, by conducting laboratory experiments. The flocculation experiments are performed using two types of natural sediments and different flocculating agents: salt (monovalent and divalent), extracellular polymeric substances, and living and dead microalgae Skeletonema costatum. It was found that the median size of flocs (D50) did not exceed the Kolmogorov microscale when salt-induced flocculation was performed (in the absence of organic matter), which is in line with previous studies. Flocs with organic matter reach sizes that are larger than the Kolmogorov microscale, and both their growth and steady-state size are salinity-dependent. In particular, divalent salts are shown to promote flocculation of sediment to organic matter. The logistic growth model can be used to study either the evolution of a class volume concentration as function of time or the change in size of a given class as function of time. The fine particle volume concentration decreases in time, whereas the coarse particle volume concentration increases, during the flocculation process. The mass balance between the two classes as defined by Chassagne and Safar (Modelling flocculation: Towards an integration in large-scale sediment transport models. Marine Geology. 2020 Dec 1;430:106361) is estimated.

A dynamic 2DH flocculation model for coastal domains

A dynamic 2DH flocculation model for coastal domains

A storm driven turbidity maximum in a microtidal estuary

Many macro- and mesotidal estuaries are characterized by Turbidity Maxima Zones (TMZs), regions with suspended solid concentrations that are much higher than those found throughout the rest of the estuary. Such regions are located near the upriver limit of salt intrusion and their position and extent are modulated and driven by tidal oscillations, especially in estuaries where tidal forcing is large. Hence, pronounced TMZs are not typically expected in micro-tidal estuaries. Field experiments were carried out in the microtidal estuary of the Misa River (northeast coast of Italy) with the aim to analyze riverine-coastal ocean interactions during different climatic conditions, freshwater discharge and tidal forcing. The goal was also that of identifying factors and episodic conditions that could lead to the evolution of ephemeral TMZs in this microtidal estuarine system. Observational results, combined to a flocculation model suite, describe the hydrodynamics, morphological bed evolution, water chemistry and floc dynamics within the estuary during wintertime quiescent and stormy periods. Pronounced TMZs with different location and extent were observed during two storms with different intensities, when enhanced freshwater discharge, wave action and tidal oscillation generated significant stratification of the lower estuarine water column. Higher turbidity values were observed throughout the TMZ during the smaller/weaker storm, while stronger surface mixing during the stronger storm led to greater dispersion of the (re-)suspended particulate load throughout the upper water column, providing a less pronounced TMZ along the bed of the lower estuary. Observations in the Misa River, potentially valid for other microtidal estuaries, show that: 1) episodic storm conditions that significantly increase freshwater discharge can lead to the evolution of an ephemeral TMZ that is modulated, but not controlled, by tidal oscillations and surface mixing conditions; 2) ephemeral TMZ localization, intensity, and extent during episodic storm events is a function of storm intensity; 3) moderately enhanced freshwater flow during an episodic storm event promotes a high degree of stratification, allowing for the formation of large flocs with great settling rates, leading to a pronounced TMZ forming downriver of the landward limit of seawater intrusion; whereas higher freshwater flows during stronger storm events lead to less stratification, greater bottom turbulence and potential TMZ suppression near the riverbed, with shear conditions promoting smaller flocs with lower settling and a greater potential for suspended particulate export from the lower estuary to coastal waters.

Effect of ionic surfactants on the settling behavior of silt

Ionic surfactants are easily adsorbed by silt and clay particles, thus affecting the flocculation characteristics and settling behavior. The settling velocity, typical size, Zeta potential and surface tension of silt flocs were measured in the presence of two different kinds of ionic surfactants. The results indicated that the cetyltrimethylammonium bromide (CTAB, a typical cationic surfactant) can dramatically accelerate the settling of slit particles, while the linear alkylbenzene sulfonate (LAS, a typical anionic surfactant) slightly retarded silt sedimentation to some extent. In still water, the representative settling velocity dramatically increased from 0.36 cm s−1 to 0.43 cm s−1 with the increase of CTAB concentration, which increased by more than 20%. Oppositely, the sedimentation rate decreased from 0.36 cm s−1 to 0.33 cm s−1 with the increase of LAS concentration. In flowing water, as the flow rate increased from 0 to 20 cm s−1 and the ionic surfactant concentration increased from 0 to 10 mg L−1, the sedimentation rate decreased to 57% and 89% in the presence of CTAB and LAS respectively, which was due to an enhanced dispersion of silt particles and a breaking of flocs. The SEM image test shows that the floc particle size increased 1.5 times of the primary particle size under the high CTAB concentration. The flocculation induced by ionic surfactants greatly influences the sediment size as well as the law of settling velocity. The intrinsic influence mechanism was also discussed based on the variations of silt particle properties. This systematic study can be used for further development of flocculation models and particle size distribution of fine-grained soil.

Extractive adsorption of 1,3-propanediol on a novel polystyrene macroporous resin enclosing medium and long-chain alcohols as extractant

Extractive adsorption is an integrated separation method employing a novel resin with both particle and liquid characteristics in terms of adsorption and extraction. In this study, the novel extractive adsorption polystyrene-divinylbenzene (PS-DVB) macroporous resin was synthesized by suspension polymerization, in which n-octanol (OL-PS-DVB) or mixed alcohols of n-octanol, undecyl alcohol, and tetradecyl alcohol (MA-PS-DVB) were added as porogen and enclosed in the resin skeleton after the reaction. The characterization of the two novel resins of OL-PS-DVB and MA-PS-DVB showed that they have large specific surface areas of 48.7 and 17.4 m2/g, respectively. Additionally, the two synthesized resins have much higher static adsorption capacities of 1,3-propanediol (511 and 473 mg/g) and dynamic adsorption capacities (312 and 267 mg/g) than traditional resins, because extractants enclosed in the resin can increase the adsorption capacity. Through Langmuir equation, the theoretical static maximum adsorption capacity of the mixed alcohols resin is 515 mg/g at 298 K and Gibbs free energy change of adsorption was -3781 J/mol, indicating that the adsorption process was spontaneous. In addition, the sorbent concentration effect in the resin was generated at high 1,3-propanediol (1,3-PDO) concentrations. The fitting of the Flocculation model can reveal that there is a possible relation between adsorption and flocculation. Compared to OL-PS-DVB, MA-PS-DVB showed better performance in the recovery yield of 1,3-PDO and other byproducts, the removal rates of the inorganic salt and protein, and the efficiency of recycled resin. For MA-PS-DVB, the recovery of 1,3-PDO, butyrate acid, acetic acid, and residual glycerol was 97.1%, 94.7%, 93.3%, and 90.3%, respectively. Simultaneously, the resin of MA-PS-DVB could remove 93.8% of inorganic salts and 90.9% of proteins in the concentrated fermentation broth. The two synthesized resins of OL-PS-DVB and MA-PS-DVB still had 90% or 92% of capacity for extractive adsorption of 1,3-propanediol after 10 times of recycling, which exhibited potential application in the separation of 1,3-propanediol from fermentation broth.

Numerical simulation of a mechanical flocculation process with multi-chambers in series.

A mechanical flocculation system with multi-chambers in series is commonly used as the advanced phosphorus removal technology for wastewater treatment. This work aims to numerically investigate the inner states and overall performance of industrial-scale mechanical flocculators in series. This is based on our previously developed computational fluid dynamics (CFD) flocculation model which is extended to consider the key chemical reactions of phosphorus removal. The effects of the number of flocculation chambers, locations, and sizes of the flocculation chamber connection as well as operational combinations of impeller speeds are investigated. With a decreasing number of flocculation chambers, the main vortexes and chemical reactions are weakened, while the small flocs form. Both the phosphorus removal efficiency η and the average floc size dp reduce as the number of flocculation chambers decreases. The connection location of flocculation chambers directly determines the turbulent flow, thus influencing the key performance indicators. However, the phosphorus removal efficiency η and average particle size dp are little affected by the size of the flocculation chamber connection. As the impeller speeds in series gradually increase, the gradient of floc size distribution in each chamber is enlarged and the chemical reaction is enhanced over the working volume.

On the importance of temporal floc size statistics and yield strength for population balance equation flocculation model

Many aquatic environments contain cohesive sediments that flocculate and create flocs with a wide range of sizes. The Population Balance Equation (PBE) flocculation model is designed to predict the time-dependent floc size distribution and should be more complete than models based on median floc size. However, a PBE flocculation model includes many empirical parameters to represent important physical, chemical, and biological processes. We report a systematic investigation of key model parameters of the open-source PBE-based size class flocculation model FLOCMOD (Verney, Lafite, Claude Brun-Cottan and Le Hir, 2011) using the measured temporal floc size statistics reported by Keyvani and Strom (2014) at a constant turbulent shear rate S. Results show that the median floc size d50, in terms of both the equilibrium floc size and the initial floc growth, is insufficient to constrain the model parameters. A comprehensive error analysis shows that the model is capable of predicting three floc size statistics d16, d50 and d84, which also reveals a clear trend that the best calibrated fragmentation rate (inverse of floc yield strength) is proportional to the floc size statistics considered. Motivated by this finding, the importance of floc yield strength is demonstrated in the predicted temporal evolution of floc size by modeling the floc yield strength as microflocs and macroflocs giving two corresponding fragmentation rates. The model shows a significantly improved agreement in matching the measured floc size statistics.

Vertical tubular flocculator: Alternative technology for the improvement of drinking water treatment processes in rural areas

The guarantee of access to safe drinking water for rural communities is a great challenge due to the increase in contamination and deterioration of water sources. Rural areas face technological, financial, and operational limitations, having poor water quality, generally. The purpose of this study was to evaluate the efficiency of a vertical tubular flocculator (VTF) to be used as part of the purification process in rural areas where small flows are used. An experimental treatment system (ETS) implemented in the field was used. The VTF was implemented using PVC pipes and fittings. Tests were carried out with the same raw water used from a conventional treatment plant with aluminum sulfate as a coagulant. The optimal coagulant dose applied in the ETS was determined by the jar test. In the VTF, the length, turbidity, and flow of the raw water were varied. The hydraulic behaviour of the VTF was evaluated with the analysis of the time distribution curve of concentration of a tracer applying the Wolf-Resnick model. A low residence time VTF was obtained, representing a new efficient flocculation model for the reduction of turbidity and colour. The results showed that the turbidity of the raw water, the residence time, and the degree of agitation are important parameters in the operation and efficiency of a VTF. There was a predominance of plug flow in the reactor. The obtained results were compared with the efficiency of a conventional water treatment plant used in the study site. The results obtained indicated that this ETS that integrates a VTF with settling and filtration can be a useful tool for rural areas. It was recommended to replicate this study with wastewater, other dimensions of the VTF, to establish a specific methodology for the design of the VTF, to evaluate the dosage with dose bombs for improving the results of VTF, and to elaborate a hydraulic model for VTF.

Stability and persistence analysis of a microorganism flocculation model with infinite delay.

In this paper, we study the global stability and persistence of a microorganism flocculation model with infinite delay. First, we make a complete theoretical analysis on the local stability of the boundary equilibrium (microorganism-free equilibrium) and the positive equilibrium (microorganism co-existent equilibrium), and give a sufficient condition for the global stability of the boundary equilibrium (applicable to the forward bifurcation and the backward bifurcation). Then, for the persistence of the model, we present an explicit estimate of the eventual lower bound of any positive solution for which only the parameter threshold $ R_0 > 1 $ is required. The obtained results extend some of the conclusions of the existing literatures on the case of discrete time delay.

Comparison between two analytical models to study the flocculation of mineral clay by polyelectrolytes

In the present article two flocculation models, given in [5] (LG model) and [36] (S model) are compared. Both models give the time evolution dL/dt where L is the size of a particle undergoing flocculation, and t is the time. The LG model is based on logistic growth theory, whereas the S model is based on the theory originally derived by Smoluchowski. Both models have the advantage of easy implementation in, for instance, large-scale sediment transport numerical models. However, it is found that they do not obey the same kinetics. A series of laboratory experiments is presented where the flocculation of a mineral clay by polyelectrolyte is studied as a function of clay concentration and shear rate. From modelling these experiments, it is found that the LG model reproduces the time dependence of the floc sizes found experimentally, whereas the S model does not. It is shown that the LG model can be used to model the data over the whole range of clay concentration and shear investigated. Based on the study presented in this article, it was found that the average floc growth in time for the clay type and conditions applied in the experiments could be modelled by: dL/dt=40×10−4G0.75×[exp(−2×10−4G0.75t)]/[1+20exp(−2×10−4G0.75t)]L.

Survival and ergodicity of a stochastic microorganism flocculation model with nonlinear response functionals

Survival and ergodicity of a stochastic microorganism flocculation model with nonlinear response functionals

Predicting the flocculation kinetics of fine particles in a turbulent flow using a Budyko-type model.

Through an analogy with the Budyko curves in catchment hydrology science, this study defines the supply and demand limits for the flocculation system of cohesive particles (the supply limit can be represented by the potential floc size growth, whereas the demand limit can be represented by the steady-state floc size) and attempts to adopt Budyko-type models to estimate the temporal evolution of floc size during flocculation. Seventeen experimental datasets are collected to test the accuracy of the Budyko model with an average high correlation coefficient of 0.9784 and average low relative error and root mean squared error values of 0.1304 and 0.0605, respectively. Either the potential floc size growth or the steady-state floc size is a monotonic function of the flow shear rate, and a simple empiric power law function can be used to describe them. Other Budyko-type models are also found to show good prediction accuracies against the experimental datasets. This study indicates that Budyko-type models have potential as a good addition to existing flocculation models for predicting the temporal variation in the size population of flocs in a turbulent flow, provided that some coefficients have been calibrated by limited data points prior.

Application of Dragon Fruit Peel’s Mucilage in Coagulation – Flocculation Process to Remove Turbidity from Water

The study determined flocculation activity of mucilage extracted from dragon fruit peel (Hylocereus undatus) and its ability in reducing synthetic coagulant polyaluminium chloride (PAC) used in coagulation – flocculation process to remove turbidity of different types of water. Investigated waters were turbid waters made from kaolin suspension (KS), suspension of river water with hill soil (FW), and To Lich river water (TL). Turbidity removal was assessed in a sequent coagulation and flocculation model using PAC and mucilage extracted from dragon fruit peel in Jar-tests. Optimal coagulation conditions of PAC with PAC dosage of 20-50 mg/L and pH range of 6-8 regardless of water types and resulted in maximum turbidity removal of about 98%. In order to obtain a comparable turbidity removal, 50%-68% of the required PAC was reduced if mucilage was used. The presence of mucilage enhanced turbidity removal of PAC by 13-22% total efficiency. Mucilage extracted from dragon fruit peel has shown its flocculation ability and its potential as a green material in water treatment.
 
 

A Mechanistic Model for Mud Flocculation in Freshwater Rivers

AbstractThe transport and deposition of mud in rivers are key processes in fluvial geomorphology and biogeochemical cycles. Recent work indicates that flocculation might regulate fluvial mud transport by increasing mud settling velocities, but we lack a calibrated mechanistic model for flocculation in freshwater rivers. Here, we developed and calibrated a semi‐empirical model for floc diameter and settling velocity in rivers. We compiled a global data set of river suspended sediment concentration‐depth profiles and inverted them for in situ settling velocity using the Rouse‐Vanoni equation. On average, clay and silt (diameters <39 μm) are flocculated with settling velocity of 1.8 mm s−1 and floc diameter of 130 μm. Among model variables, Kolmogorov microscale has the strongest positive correlation with floc diameter, supporting the idea that turbulent shear limits floc size. Sediment Al/Si (a mineralogy proxy) has the strongest negative correlation with floc diameter and settling velocity, indicating the importance of clay abundance and composition for flocculation. Floc settling velocity increases with greater mud and organic matter concentrations, consistent with flocculation driven by particle collisions and binding by organic matter which is often concentrated in mud. Relative charge density (a salinity proxy) correlates with smaller floc settling velocities, a finding that might reflect the primary particle size distribution and physical hosting of organic matter. The calibrated model explains river floc settling velocity data within a factor of about two. Results highlight that flocculation can impact the fate of mud and particulate organic carbon, holding implications for global biogeochemical cycles.

Dynamical Behavior of a Stochastic Microorganism Flocculation Model with Nonlinear Perturbation

Dynamical Behavior of a Stochastic Microorganism Flocculation Model with Nonlinear Perturbation

Evaluation of flocculation performance of polysaccharide-protamine complex flocculant by flocculation model

Flocculation experiments were conducted with three kinds of polysaccharide-protamine complex flocculants. Alginate, κ-carrageenan, and pectin were used as typical polysaccharides. The polysaccharides have carboxyl and sulfate groups, and it can be considered that the polysaccharides could bind basic protein, such as protamine, at around the neutral pH (pH 6.5–7.5). The relative absorbance was used as an index of the flocculation efficiency. Influences of the mass ratio (polysaccharide/protamine) and dosage of the complex flocculants on the flocculation efficiency were investigated. Judging from the results, the optimum mass ratio of polysaccharide and protamine was found as 0.4 for alginate and 1.0 for κ-carrageenan and pectin. The previously proposed flocculation model was applied to the data successfully and the proportional constant, stoichiometric coefficients, and the equilibrium adsorption constant regarding as forming flocs were determined by fitting to the data and using a least square method. Judging from the model parameters, the total number of acidic groups, and the molecular weight of each polysaccharide, the alginate-protamine complex could be the most effective flocculant.

Optimising the Flux Enhancer Dosing Strategy in a Pilot-Scale Anaerobic Membrane Bioreactor by Mathematical Modelling.

Flux enhancers (FEs) have been successfully applied for fouling mitigation in membrane bioreactors. However, more research is needed to compare and optimise different dosing strategies to improve the filtration performance, while minimising the use of FEs and preventing overdosing. Therefore, the goal of this research is to develop an optimised control strategy for FE dosing into an AnMBR by developing a comprehensive integrated mathematical model. The integrated model includes filtration, flocculation, and biochemical processes to predict the effect of FE dosing on sludge filterability and membrane fouling rate in an AnMBR. The biochemical model was based on an ADM1, modified to include FEs and colloidal material. We developed an empirical model for the FE-induced flocculation of colloidal material. Various alternate filtration models from the literature and our own empirical models were implemented, calibrated, and validated; the best alternatives were selected based on model accuracy and capacity of the model to predict the effect of varying sludge characteristics on the corresponding output, that is fouling rate or sludge filterability. The results showed that fouling rate and sludge filterability were satisfactorily predicted by the selected filtration models. The best integrated model was successfully applied in the simulation environment to compare three feedback and two feedforward control tools to manipulate FE dosing to an AnMBR. The modelling results revealed that the most appropriate control tool was a feedback sludge filterability controller that dosed FEs continuously, referred to as _10. Compared to the other control tools, application of the _10 controller resulted in a more stable sludge filterability and steady fouling rate, when the AnMBR was subject to specific disturbances. The simulation environment developed in this research was shown to be a useful tool to test strategies for dosing flux enhancer into AnMBRs.

An analysis approach to permanence of a delay differential equations model of microorganism flocculation

<p style='text-indent:20px;'>In this paper, we develop a delay differential equations model of microorganism flocculation with general monotonic functional responses, and then study the permanence of this model, which can ensure the sustainability of the collection of microorganisms. For a general differential system, the existence of a positive equilibrium can be obtained with the help of the persistence theory, whereas we give the existence conditions of a positive equilibrium by using the implicit function theorem. Then to obtain an explicit formula for the ultimate lower bound of microorganism concentration, we propose a general analysis method, which is different from the traditional approaches in persistence theory and also extends the analysis techniques of existing related works.</p>