The effectiveness of high molecular weight PEI species 1n producing rapid flocculation at small doses is attributed to the formation. At large doses of high molecular weight species, redispersion of macroflocs occurred, caused by excessive adsorption of cationic molecules. The first step is adsorption of colloidal material suspended in wastewater by microorganisms and biological absorption of dissolved organic matter.
From the above scheme, the degree of flocculation can be determined by a measurement of the relative concentrations of (PS) and (PS); i.e., other theoretical (9) and experimental results (6, l 0) suggest that the overall aggregation efficiency varies from the first power to the second power of the aggregate. The rate of reduction of electrostatic repulsion depends on the molarity and valence of the counterions in the.
In the case of hydrophobic particles, when the electrokinetic potential difference in the double layer of the particles falls below a. Using pH variations in the isoelectric range, they illustrated the electrostatic nature of the attraction between the bacterial cells and the added material. Optimal destabilization occurs when only part of the available adsorption sites on the surface of the colloidal particles are covered.
The degree of subordination depends on the nature of the polymer (charge density, configuration, concentration) and the colloid (charge density).
5 is a plot of polymer density p(6) as a function of distance 6 from the surface for five values of traction. This computer simulation describes virtually complete absorption of polymer segments on the surface for segment absorption energies greater than 1 kT, and only limited expectation for long polymer loops extending into solution. Roe (16) extended the computer simulation of the three-dimensional random walk adsorption model to include end effects, which had previously been considered unimportant.
6 Average Length of Loops LL Versus Normalized Adsorption Energy Es s /kT for Flexible and Rigid Molecules of and 5000 Segments. 7, the average length of the desorbed sequences at the polymer chain ends L is plotted as a function of the normalized. Numerous additional statistical-mechanical treatments of the configuration of polymer molecules adsorbed on solid surfaces have been published by Rubin (17).
8 illustrates the maximum normal distance to an adsorbing surface for different size molecules as a function of normalized adsorption energy when the excluded volume effect is taken into account. McCrackin determined that the fraction of adsorbed segments is reduced by a factor of about 2 for molecules up to 300 segments.
J_OO~-J FLEXIBLE STIFF
In addition, the fraction of segments in contact with the surface at adsorption energies greater than zero was estimated to lie between 0. Further revisions of the Silberberg model included adsorbed and bulk phase polymer concentrations, polymer flexibility parameters, and polymer-solvent interaction energy parameters. Silberberg's revisions provided a more realistic picture of the adsorption process, allowing a closer correlation of theoretical predictions with experimental results.
9 depicts the combined effect of solvent-polymer interaction energy (E ) and polymer concentration. C) on the average LL loop length as a function of normalized segment–surface interaction energy (E/kT). 10 illustrates that there are far fewer segments on the surface than would be expected on the previous basis.
C. STIRRING MOTOR
The volume flow rate of the flocculated suspension was recorded as the refiltration rate Q, and that of an untreated suspension as Q • The cell concentration was 2. The flocs that had sedimented on the surface of the Nucleopore filter were examined in an Autoscan scanning electron microscope . In the Zimm chart, the molecular weight is defined as the reciprocal of the intersection of the zero concentration line, the zero angle line, and the ordinate axis.
Substitution of the value 1/h in equation (4-5) makes it possible to calculate the proportion of surface coverage 8 for a specified PEl dose. 7 summarizes the effect of the PEl molecular weight on the fraction of surface coverage. Nevertheless, it provides an estimate of the number of monolayers of surface coverage at each polymer dose.
The ability of the high molecular weight species PEl 350 and PEl 600 to improve the refiltration rate is in sharp contrast to. Although the measurement of total electrophoretic mobility and the subsequent determination of zeta potential is ideally suited for the following systems. In the operation of the Coulter counter (Figure 5. 2), a vacuum supply (P) is used to draw a sample of the cell suspension through a small opening (A) in the wall of a non-conductive tube (B).
The resistance R of an aperture segment with a particle equivalent to the resistance of two parallel resistors is given by . In the case of aggregates, however, this latter simplification cannot be justified due to the porosity of the aggregate itself. This elongation of the aggregate as it passes through the orifice produces a pulse that has both height and width.
The shape of the curve relating the calculated porosity f to the number of cells per aggregate B indicates an exponential shape relationship. 65 ensures the preservation of the volume of the entire suspended matter in the non-flocculated and flocculated state. In equation (5-11), the LlR Coulter counter response to aggregate passage is a function of two unknowns: d, the equivalent spherical diameter of the aggregate, and B, the number of cells per aggregate.
Consequently, as aggregate porosity increases, the response of the Coulter counter decreases. The following paragraphs discuss the proposed modification to the initial Coulter counter data analysis to compensate for the effects of aggregate porosity.
CHANNEL
Changing the frequency of the voltage pulse during the recovery of the electronic circuit did not shift the recorded channel. Using monodisperse polystyrene latex particles, the logarithm of the Coulter counter/PHA/MCA system can be determined for various orifice diameters, current settings, and amplification factors. Another, Rayleigh-Gans-type treatment derived by Benoit et al. 22) evaluates the scattering properties of aggregates whose component particles have refractive indices close to the dispersion medium.
For these particles, the scattered light will be the superposition of the waves from different parts of the same particle, resulting in interference between scattering centers. In the general case, the phase and intensity of the waves will have complicated relationships to each other; an exact solution is only available for the homogeneous sphere. This condition is met for particles smaller than the wavelength of light in media chosen so that the relative refractive index (particle/medium) is less than about 1.
P('i'), the ratio of the intensity scattered through an angle 'i' to that which would be observed if the particles had the same molecular weight but infinite dimensions compared to A, is given by. De bye (25) calculated the reduction factors with respect to the scattering intensity using the average sum of the contributions from the submolecules. These equations relate the amount and direction of scattered light to the size and shape characteristics of molecules, allowing for interference between waves scattered by a particle.
Using this method, Oster (26) successfully estimated the shape and length of the tobacco mosaic virus. Overall, the Rayleigh-Cans treatment of the scattering of large particles as a collection of independent dipole oscillators must satisfy the condition Za.(m-1) << 1, where a. 65 ~m) compared to the wavelength of incident light, this simplified picture may not apply. However, Koch (2 7) has pointed out that the Rayleigh-Gans method can give fairly accurate results. results if only the total amount of scattered light is to be calculated.
The reason for this is simply that the main effect of the phase shift is to change the direction in which the scattered light waves interfere more strongly without affecting the total amount of interference. In the analysis of Benoit et al. 22 ), primary particles within an aggregate scatter light that immediately interferes with it. The intensity of light scattered at an angle '¥ by an aggregate of k randomly oriented monodisperse spheres in the incident light beam can be expressed as.
