Creaming and Rheology of Oil-in-Water Emulsions Containing Sodium Dodecyl Sulfate and Sodium Caseinate

The kinetics of bridging flocculation of polystyrene latex (PSL) particles induced by addition of excess polyethylene oxide (PEO) in the initial stage was studied using standardized mixing flow generated in an end-over-end rotation apparatus. To clarify the effect of the rate of polymer supply, flocculation experiments were performed by changing polymer concentration (C(p)). As was found in previous investigation, the progress of flocculation is divided into two stages. The first stage is characterized by an enhancement of the rate of flocculation by polymer addition. The increase in polymer concentration results in a higher enhancement but in a shorter duration for this stage. In the second stage, the flocculation is essentially stopped due to the appearance of steric stabilization. It was found that the ultimate degree of flocculation goes through a maximum against C(p). That is, when C(p)>==1.0 ppm, the ultimate degree of flocculation decreases with increased C(p). In this region, a clear crossover from the first stage to the second stage was observed. In the extreme case, evidence of a slight setback of flocculation was confirmed, which implies the breakup of metastable bridges by the application of additional fluid shear. When C(p)<==1.0 ppm, the ultimate degree of flocculation decreases with decreased C(p). The crossover from the first stage to the second stage appears more gradual at lower C(p). These results were observed irrespective of ionic strength. This result was interpreted as the elimination of a bare surface due to the spreading of a steric layer of adsorbed polymer. The characteristic time for reconformation of the polymer at a bare colloidal surface was estimated to be a few seconds. Copyright 2000 Academic Press.     

Stability and Adsorption Properties of Suspensions of Finely Dispersed Silica in the Presence of Cationic Surfactants

Interrelation between the coagulation rate, adsorption and electrokinetic properties of silica polydisperse suspensions in the presence of cationic surfactants is studied. The highest coagulation rate is observed in a certain concentration range of the cationic surfactants. When pH values increases, an increasing amount of cationic surfactant is required to achieve maximal coagulation rate. For bisquaternary cationic surfactants, ethonium and decamethoxine, maximal coagulation rate is observed at concentrations by an order of magnitude lower than for monoquaternary cetyltrimethylammonium bromide. It is concluded that the suspensions lost their stability as a result of both neutralization of particle surface charge and flocculating effect of the cationic surfactants. Moreover, the flocculation mechanism depends on the cationic surfactant nature and physicochemical parameters of the medium, ionic strength and pH.     

Effect of cationic polyacrylamide adsorption kinetics and ionic strength on precipitated calcium carbonate flocculation

The effect of polymer adsorption kinetics and ionic strength on the dynamics of particle flocculation was quantified using a model system consisting of precipitated calcium carbonate (PCC) and cationic polyacrylamide (CPAM) at a low shear rate. All early flocculations detectable by a photodispersion analyzer (PDA) happened in nonequilibrium polymer adsorption regimes. We observed discrepancies in flocculation rates with the surface coverage theory, which is based on a simple monolayer adsorption model, in both early and late flocculation stages. For instance, the same amount of adsorbed CPAM reached at different polymer doses demonstrated different flocculating capabilities. This highlighted the importance of polymer adsorption kinetics upon flocculation. The transient conformation of the adsorbed CPAM during the kinetic process sometimes even superceded the adsorbed amount in the determination of PCC flocculation. Both antagonistic and synergetic effects of increased ionic strength on the CPAM-induced PCC aggregation were observed during early flocculation. However, late-stage PCC flocculation shared some similarities, irrespective of polymer dose and ionic strength. Despite the decreased amount of adsorbed polymer from the increased ionic strength, the combination of CPAM and salt, at certain concentrations, demonstrated a synergy to promote PCC aggregation more efficiently than the same amount of the respective components.     

Salt concentration influence on the efficiency of two cationic polymeric flocculants

The influence of the increase of the solution ionic strength on the flocculation of charged latex particles in the presence of cationic polymers is reported. Empirical flocculation rate constants are experimentally determined using particle counting and for two cationic polymers, one linear and the second with two branches. Comparisons are made with a solution containing monovalent salt only at different ionic concentrations in the absence of polymers. In all cases, polymer-induced flocculation is significantly more efficient than charge screening effects using salt only. Analysis of zeta potential measurements indicates that the charge neutralization and surface charge variations dictate the stability of the latex suspensions. Moreover, the addition of a small amount of salt in the polymer–particle mixtures results in a dramatic decrease of the polymer efficiency which is more pronounced for the linear polymeric flocculant. By increasing further the ionic strength, the rates of polymer flocculation are found to increase again but remain smaller than in the absence of salt.     

Flocculation and stabilization of colloidal silica by the adsorption of poly-diallyl-dimethyl-ammoniumchloride (PDADMAC) and of copolymers of DADMAC with N-methyl-N-vinyl- acetamide (NMVA)

 The stabilization and flocculation behavior of colloidal silica-particles with cationic polyelectrolytes (PE) is investigated. The zetapotentials, diffusion coefficients and flocculation rate constants of silica particles have been measured as a function of the adsorbed amount of cationic polyelectrolytes poly(diallyl-dimethyl-ammoniumchloride) (PDADMAC) of different molar masses and of statistic copolymers of DADMAC and N-methyl-N-vinyl-acetamide (NMVA) of various compositions at different salt concentrations and pH-values. Very fast flocculation due to van der Waals attraction occurs if the zetapotential is small. At low ionic strength this condition occurs just below the plateau of the adsorption isotherms where the surface charges are screened by adsorbed polycations. Additionally with high molecular polycations slow mosaic flocculation is observed at lower PE concentrations. At high ionic strength fast flocculation takes place at low macroion concentration due to the screening of the surface charges by adsorbed polycations and salt ions. At medium concentrations of polycations below plateau adorption slow bridging flocculation is observed. At plateau adsorption the suspensions become stabilized up to high ionic strength. At low salt concentration charge reversal at full coverage with polycations results in electrostatic repulsion. At high ionic strength the particles are stabilized sterically due to the osmotic repulsion of the long adsorbed PE tails. Therefore macroions of high molar mass are necessary to stabilize the suspension at high ionic strength. Received: 27 January 1998 Accepted: 23 March 1988     

Improving primary treatment of urban wastewater with lime-induced coagulation

The enhancement of primary treatment efficiency through the coagulation process may yield several advantages, including lower aeration energy in the subsequent biological unit and higher recovery of biogas from sludge digestion. In this work sewage coagulation with lime was studied at pilot plant level, using degritted sewage from the city of Rome. The work aimed at optimising the operating conditions (coagulant dosage or treatment pH, and mixing conditions in the coagulation and flocculation tanks), in order to maximise the efficiency of suspended Chemical Oxygen Demand (COD) removal and to minimise sludge production. Lime dosage optimisation resulted in an optimal treatment pH of 9. Lime addition up to pH 9 may increase COD removal rate in the primary treatment from typical 30-35% of plain sedimentation up to 55-70%. Within the velocity gradients experimented in this work (314-795 s(-1) for the coagulation tank and 13-46 s(-1) for the flocculation tank), mixing conditions did not significantly affect the lime-enhanced process, which seems to be controlled by slow lime dissolution. Sludge produced in the lime-enhanced process settled and compacted easily, inducing an average 36% decrease in sludge volume with respect to plain settling. However excess sludge was produced, which was not accounted for by the amount of suspended solids removed. This is probably due to incomplete dissolution of lime, which may be partially incorporated in the sludge.     

Understanding pH and Ionic Strength Effects on Aluminum Sulfate-Induced Microalgae Flocculation

The objective of this study was to understand the effect of pH and ionic strength of aluminum sulfate on the flocculation of microalgae. It was found that changing pH and ionic strength influenced algal flocculation by changing the zeta potential of cells, which was described by the classical theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO). For both algal species of Scenedesmus dimorphus and Nannochloropsis oculata, cells with lower total DLVO interaction energy had higher flocculation efficiency, indicating that the DLVO model was qualitatively accurate in predicting the flocculation of the two algae. However, the two algae responded differently to changing pH and ionic strength. The flocculation of N. oculata increased with increasing aluminum sulfate concentration and favored either low (pH 5) or high (pH 10) pH where cells had relatively low negative surface charges. For S. dimorphus, the highest flocculation was achieved at low ionic strength (1 μM) or moderate pH (pH 7.5) where cell surface charges were fully neutralized (zero zeta potential).     

Structural Effect and Composition of Anionic Copolymer on Protein Flocculation

Flocculation of lysozyme with anionic copolymers of acrylamide, acrylic acid, and sodium styrene sulfonate used as flocculants was performed in pursuit of high flocculation efficiency. Two major factors, pH and ionic strength, are used to investigate the relationship of the flocculation behavior of protein by copolymers and the functional group (–COOH, –NH₂, –SO₃H) compositions of these copolymers. The protein flocculation can be controlled by adjusting pH. In addition, the various copolymers exhibit differing effects on ionic strength induced protein flocculation. FT-Raman spectroscopy was applied to investigate the mechanism of interaction between protein and copolymer. An attempt was made to understand how the pH and ionic strength change the surface chemical characteristics of protein and copolymers, as well as the relationship between the structure of copolymer and the protein flocculation process.     

流体力学半径对估算胶体微球聚集速率常数的影响

胶体粒子聚集速率常数实验值远低于理论值一直是被普遍关注的问题.聚集速率常数的理论推导是基于粒子的几何半径来考虑的,但决定粒子扩散速率及聚集速率的应该是粒子的流体力学半径(大于几何半径),因而它是使聚集速率常数实验值低于理论值的因素之一.影响流体力学半径的因素很多,其中,带电粒子在溶液中因表面存在双电层,会明显增大流体力学半径,造成聚集速率减慢.而双电层的厚度又随溶液中离子强度的不同而改变.本工作在聚集速率的公式中引入了修正因子,即几何半径与其流体力学半径之比,以修正由于用几何半径代替流体力学半径带来的误差.其中几何半径和流体力学半径可以分别用扫描电镜(SEM)和动态光散射(DLS)来测定.以两种粒径的聚苯乙烯带电微球为例,考察了在不同离子强度下,该误差的大小.结果发现,对于半径为30 nm的微球,用流体力学半径计算的慢聚集速率常数比理论值偏低约8%.该误差随离子强度增加而减少.对于快聚集情况,流体力学半径对聚集速率基本没有影响.     

Towards predicting the stability of protein-stabilized emulsions

The protein concentration is known to determine the stability against coalescence during formation of emulsions. Recently, it was observed that the protein concentration also influences the stability of formed emulsions against flocculation as a result of changes in the ionic strength. In both cases, the stability was postulated to be the result of a complete (i.e. saturated) coverage of the interface. By combining the current views on emulsion stability against coalescence and flocculation with new experimental data, an empiric model is established to predict emulsion stability based on protein molecular properties such as exposed hydrophobicity and charge. It was shown that besides protein concentration, the adsorbed layer (i.e. maximum adsorbed amount and interfacial area) dominates emulsion stability against coalescence and flocculation. Surprisingly, the emulsion stability was also affected by the adsorption rate. From these observations, it was concluded that a completely covered interface indeed ensures the stability of an emulsion against coalescence and flocculation. The contribution of adsorption rate and adsorbed amount on the stability of emulsions was combined in a surface coverage model. For this model, the adsorbed amount was predicted from the protein radius, surface charge and ionic strength. Moreover, the adsorption rate, which depends on the protein charge and exposed hydrophobicity, was approximated by the relative exposed hydrophobicity (Q_H). The model in the current state already showed good correspondence with the experimental data, and was furthermore shown to be applicable to describe data obtained from literature.     

Influence of the ionic strength in the heterocoagulation process between bare and surfactant-coated latexes

A novel and useful process of heterocoagulation between bare and surfactant-coated latexes is studied. Basically, this process consists of the heterocoagulation of two identical latexes, i.e. of the same size and with charges of the same sign, but distinguished by the degree of coverage by a nonionic surfactant (Triton X-100). The different critical coagulation concentrations (ccc) of this type of sample permitted us to analyze the influence of the ionic strength in the heterocoagulation process between both colloidal samples. Different ratios (2:1, 1:1 and 1:2) of the bare and surfactant-coated latexes were used during the experiments. In all cases, the heterocoagulation rate constants were lower than the homocoagulation rate constant in diffusion conditions; however, for an ionic strength higher than the ccc of both systems, similar values were found for the rate constants. Received: 18 January 1999 Accepted in revised form: 14 April 1999     

Adsorption of polyelectrolytes on colloidal latex particles, electrostatic interactions and stability behaviour

The stabilization and flocculation behaviour of colloidal latex particles covered with cationic polyelectrolytes (PE) is studied with photon correlation spectroscopy and zetapotential measurements. Diffusion coefficients, flocculation rate constants and zetapotentials have been determined as a function of adsorbed amount of cationic poly-(diallyl-dimethyl-ammoniumchloride) (PDADMAC) of different molar masses and of statistic copolymers of DADMAC and N-methyl-N-vinyl-acetamide (NMVA) of various compositions in water and at high ionic strength. Flocculation by van der Waals attraction can be observed if the zetapotential is low. This occurs, if the surface charge is screened by the oppositely charged cations. Furthermore, in the case of adsorption of high molecular polycations mosaic flocculation occurs if the adsorbed amount is low. At high ionic strength, flocculation takes place if the adsorbed amount is below the adsorption plateau. If the adsorption plateau is reached the suspensions become stabilized. In water the charge reversal at full coverage leads to electrosteric stabilization both with low and high molar mass polycations. At high ionic strength only polycations with high molar mass are able to stabilize the suspension. If a certain molar mass of the polycation is exceeded, steric stabilization of the suspension occurs due to the formation of long adsorbed PE tails and their osmotic repulsion. The layer thicknesses are determined as a function of the molar mass. Received: 4 July 2000/Accepted: 18 August 2000     

Synthesis of a new flocculant based on poly(acrylamide-co-(N-octyl-4-vinylpyridinium bromide)) [AM5/VP5C8Br]-application for the turbidity removal from clay suspension

The interactions between poly(acrylamide-co-(N-octyl-4-vinylpyridinium bromide)) [AM5/VP5C8Br] cationic polyelectrolyte, and clay particles in dilute aqueous suspensions are studied in the aim of adsorption and flocculation. The extents of both phenomena are significantly influenced by the ionic strength of the medium. The adsorption of the clay particles on the copolymer chains occurs initially by the hydrophobic interaction. As flocculation mechanisms, the hydrophobic interaction between copolymer chains and the clay particles appears to be principal. In this work, we have prepared a copolymer which has been characterized by conductivity, viscosity, ¹H NMR, and FT-IR spectroscopies. The copolymer dosage and pH are two of the most important experimental parameters in the coagulation/flocculation operations used for study and optimization of the wastewater treatment operations. Under optimized conditions, 97% efficiency of the turbidity elimination, with a very low flocculant concentration of 3?ppm have been achieved in order to produce drinking water with standard limits around the world (< 1 NTU). The conclusion drawn on the basis of these results is that wastewater treatment using this new copolymer [AM5/VP5C8Br] has proved to be a good flocculant in overseeing of wastewater turbidity problems.     

Flocculation of dilute titanium dioxide suspensions by graft cationic polyelectrolytes

The flocculation of a dilute titanium dioxide (TiO₂) suspension using homopolymers and graft copolymers of acrylamide (AM) and diallyldimethylammonium chloride (DADMAC) was investigated. The graft copolymers produced by γ-irradiating the mixtures of polyacrylamide (PAM) and polyDADMAC gave better flocculating performance than homopolymers, reflecting the higher fractions of large particles and bigger floc size. A kinetic delay in the onset of flocculation was observed after adding the copolymers in the dose range 5–30 [mg polymer]/ [g TiO₂]. Increasing dosage resulted in a longer delay period. No significant flocculation was observed when the dose was above 50 [mg polymer]/[g TiO₂]. This delay was interpreted in terms of the re-conformation of polymer chains driven by charge neutralization, between the positively charged polymer branches and the negative particle surface. Depending on the dosage used, the flocculation behavior of the graft copolymer has been suggested to be equilibrium and non-equilibrium flocculation. It was also observed that re-conformation is not affected by the ion strength of the media, but a strong shear force significantly reduces the chain reconformation time. Received: 9 April 1998 Accepted in revised form: 28 August 1998     

Interfacial biocatalysis on charged and immobilized substrates: the roles of enzyme and substrate surface charge

An enzyme charge ladder was used to examine the role of electrostatic interactions involved in biocatalysis at the solid-liquid interface. The reactive substrate consisted of an immobilized bovine serum albumin (BSA) multilayer prepared using a layer-by-layer technique. The zeta potential of the BSA substrate and each enzyme variant was measured to determine the absolute charge in solution. Enzyme adsorption and the rate of substrate surface hydrolysis were monitored for the enzyme charge ladder series to provide information regarding the strength of the enzyme-substrate interaction and the rate of interfacial biocatalysis. First, each variant of the charge ladder was examined at pH 8 for various solution ionic strengths. We found that for positively charged variants the adsorption increased with the magnitude of the charge until the surface became saturated. For higher ionic strength solutions, a greater positive enzyme charge was required to induce adsorption. Interestingly, the maximum catalytic rate was not achieved at enzyme saturation but at an invariable intermediate level of adsorption for each ionic strength value. Furthermore, the maximum achievable reaction rate for the charge ladder was larger for higher ionic strength values. We propose that diffusion plays an important role in interfacial biocatalysis, and for strong enzyme-substrate interaction, the rate of diffusion is reduced, leading to a decrease in the overall reaction rate. We investigated the effect of substrate charge by varying the solution pH from 6.1 to 8.7 and by examining multiple ionic strength values for each pH. The same intermediate level of adsorption was found to maximize the overall reaction rate. However, the ionic strength response of the maximum achievable rate was clearly dependent on the pH of the experiment. We propose that this observation is not a direct effect of pH but is caused by the change in substrate surface charge induced by changing the pH. To prove this hypothesis, BSA substrates were chemically modified to reduce the magnitude of the negative charge at pH 8. Chemical modification was accomplished by the amidation of aspartic and glutamic acids to asparagine and glutamine. The ionic strength response of the chemically modified substrate was considerably different than that for the native BSA substrate at an identical pH, consistent with the trend based on substrate surface charge. Consequently, for substrates with a low net surface charge, the maximum achievable catalytic rate of the charge ladder was relatively independent of the solution ionic strength over the range examined; however, at high net substrate surface charge, the maximum rate showed a considerable ionic strength dependence.     

Sorption of Metal Ions on Clay Minerals

The mechanism of Co uptake from aqueous solution onto hectorite (a magnesian smectite) and its impact on the stability of this clay mineral were investigated as a function of Co concentration (TotCo = 20 to 200 μM, 0.3 M NaNO(3)) and ionic strength (0.3 and 0.01 M NaNO(3), TotCo = 100 μM) by combining kinetics measurements and Co K-edge extended X-ray absorption fine structure (EXAFS) spectroscopy. The morphology of the sorbent phase was characterized by atomic force microscopy (AFM) and consists of lath-type particles bounded by large basal planes and layer edges. At low ionic strength (0.01 M NaNO(3)), important Co uptake occurred within the first 5 min of reaction, consistent with Co adsorption on exchange sites of hectorite basal planes. Thereafter, the sorption rate dramatically decreased. In contrast, at high ionic strength (0.3 M NaNO(3)), Co uptake rate was much slower within the first 5 min and afterward higher than at 0.01 M NaNO(3), consistent with Co adsorption on specific surface sites located on the edges of hectorite. Time-dependent isotherms for Co uptake at high ionic strength indicated the existence of several sorption mechanisms having distinct equilibration times. The dissolution of hectorite was monitored before and after Co addition. A congruent dissolution regime was observed prior to Co addition. Just after Co addition, an excess release of Mg relatively to congruent dissolution rates occurred at both high and low ionic strengths. At high ionic strength, this excess release nearly equaled the amount of sorbed Co. The dissolution rate of hectorite then decreased at longer Co sorption times. EXAFS spectra of hectorite reacted with Co at high and low ionic strengths and for reaction times longer than 6 h, exhibited similar features, suggesting that the local structural environments of Co atoms are similar. Spectral simulations revealed the occurrence of approximately 2 Mg and approximately 2 Si neighboring cations at interatomic distances characteristic of edge-sharing linkages between Co and Mg octahedra and corner-sharing linkages between Co octahedra and Si tetrahedra, respectively. This local structure is characteristic of inner sphere mononuclear surface complexes at layer edges of hectorite platelets. The occurrence of these complexes even at low ionic strength apparently conflicts with kinetics results, as exchangeable divalent cations are known to form outer sphere surface complexes. To clarify this issue, the amount of Co adsorbed on exchange sites was calculated from the solute Co concentration, assuming that cation exchange was always at equilibrium. These calculations showed that sorbed Co was transferred within 48 h from exchange sites to edge sorption sites. Copyright 1999 Academic Press.     

Fabrication of colloidal doublets by a salting out-quenching-fusing technique

It is well-known that high ionic strength promotes colloid aggregation. Here we show that, by controlling this aggregation process, we can produce high yields of homodoublet and heterodoublet polymer colloids. The aggregation process is started by increasing the ionic strength to roughly 250 mM KCl. After approximately the rapid flocculation time, we quench the "reaction" by mixing in a large quantity of deionized water, which dilutes the ionic strength and prevents further aggregation. At this point, the suspension consists primarily of singlet and doublet particles. Through heating above the glass transition temperature of the polymers, the doublets are fused together and remain intact even after sonication. It is also shown that heterodoublets can include a silica particle together with a polymer colloid. The salting out-quenching-fusing technique is a rapid, easy-to-perform, repeatable process for fabricating colloidal doublets from polymers and other materials.     

Removal of Tannic Acid Stabilizes CuO Nanoparticles from Aqueous Media by PAFC: Effect of Process Conditions and Water Chemistry

The increased utilization of CuO nanoparticles (CuO NPs) in various fields has raised concerns about their discharge into water containing a wide range of organic ligands. Moreover, the adsorption of these ligands can stabilize the CuO NPs in drinking water treatment plants. Thus, their removal from potable water is important to mitigate the risk to humans. The present study explored the efficacy of the coagulation–sedimentation (C/S) process for the removal of tannic acid (TA)-stabilized CuO NPs using polyaluminum ferric chloride (PAFC) as a coagulant. Moreover, the influence of process conditions (stirring speed) and water chemistry (i.e., pH and ionic strength (IS)) were also investigated to determine their impact on removal. The results showed that stirring speed in the reaction phase significantly affected the removal due to increased flocculation compared with stirring speed in the mixing phase. In addition, pH and IS affect the colloidal stability and removal efficiency of CuO NPs. A relatively better removal performance (<99%) of CuO NPs was found at lower coagulant dosage in the pH range 6–8. The addition of organic ligands reversed the surface charge potential and enhanced the colloidal stability of CuO NPs, resulting in the destabilization of TA-CuO NPs, thereby reducing the optimum PAFC dosage for removal. By contrast, the IS above the critical coagulation concentration decreased the removal efficiency due to inhibition of the ionic activity of PAFC hydrolysate in the aqueous environment. Fourier transform infrared findings of TA-CuO NPs composite flocs suggest that the primary removal mechanism might be mediated via the combined effect of neutralization, complexation as well as adsorption.     

Kinetics of polyelectrolyte adsorption onto polystyrene latex particle studied using electrophoresis: effects of molecular weight and ionic strength

The kinetics of the adsorption of a cationic polymer flocculant onto negatively charged polystyrene latex (PSL) particles were measured by means of electrophoresis as a function of the molecular weight of the polyelectrolyte and the ionic strength of the solution. In the experiment, the dispersion of bare PSL particles was mixed with a polyelectrolyte solution by means of end-over-end rotation in which the mixing intensity was evaluated in terms of the collision frequency between the colloidal particles. The rate of electrophoretic mobility of a PSL particle, which remained as a singlet, was measured against the mixing steps, which was equivalent to the time elapsed after the onset of flocculation. The shape of the kinetic curves is typical: a linear increase for a short period followed by a plateau, implying the saturation of the colloidal surface by the adsorbed polyelectrolyte. In the case of low ionic strength, the plateau value was dependent on the molecular weight of the polyelectrolyte. That is, a lower plateau value was detected when the molecular weight of the polyelectrolyte was smaller and its concentration was lower. However, the amount of adsorption was kinetically controlled only for the case of higher molecular weight. In the case of high ionic strength, the plateau value of electrophoresis was constant, regardless of the polyelectrolyte concentration and molecular weight. These data will ultimately be useful in further analysis of the flocculation behavior of colloidal particles with a polyelectrolyte.     

Effect of floc structure on the rate of shear coagulation

We derived a mathematical expression for the temporal evolution of the number of particles due to shear coagulation, covering the later stage by expanding the initial stage approximation to take into account the formation of floc structure. In the derivation, it is assumed that flocculation proceeds through binary collisions between identical fractal flocs. The capture efficiency between flocs is calculated on the basis of trajectory analysis, which is determined by viscous hydrodynamic interaction between flocs and van der Waals attractive forces between two primary particles located at colliding points of flocs. The validity of the derived equation was tested by a coagulation experiment using polystyrene sulfate latex particles under conditions of rapid coagulation. The experiment was carried out in a laminar Couette flow generated in the gap between two concentric cylinders. Careful and direct observation of flocculation under microscopy provided the data on the fractal dimension as well as the temporal evolution of number concentration of flocs. The measured rate of coagulation gradually increases in accordance with the formation of the fractal structure of flocs. This behavior agreed very well with the prediction based on the derived equation.