Relative Importance of the Effects of Seed and Feed Stage ...

More documents

Recommendations

Info

366 Krishnan et al. F LO ¼ y 1 þ y 2 2 F HI ¼ y 3 þ y 4 2 m f ¼ F HI F LO 2 h ¼ y 1 þ y 2 þ y 3 þ y 4 4 The experimental error is calculated as follows: E LO ¼ y 2 þ y 3 2 E HI ¼ y 1 þ y 4 2 m e ¼ E HI E LO 2 error ¼ absðm e Þ ð6Þ ð7Þ ð8Þ The calculation of the first order effect involves all four experimental data. The averaging reduces the influence of an error in any datum. The coefficients m s and m f can be directly compared to determine the relative importance of each independent variable. For a measured effect to be significant, it has to be greater than the experimental error. The error also includes the deviation of the experimental effect from the simple model assumed (Eq. 4). RESULTS Effect of Agitation on Coagulum Formation Shear-induced coagulation in latexes has been studied by several researchers (Ali and Zollars, 1987, 1988; Husband and Adams, 1992; Kusters et al., 1997; Lowry et al., 1984, 1986; Matejicek et al., 1988; Utracki, 1973; Zollars and Ali, 1986). Smoluchowski’s expression for orthokinetic (shear-induced) flocculation is normally used to describe the rate of shear-induced aggregation. The collision frequency in the absence of interparticle forces, for uniform particles approaching each other along rectilinear paths, was predicted by Smoluchowski to be (16/3)N 2 p a3 g where N p is the number of particles per unit volume, a is the particle radius, and g is the shear rate (von Smoluchowski, 1917). If each collision results in
Seed and Feed Stage Agitations of BMA and NMA 367 aggregation, this also gives the rate of shear-induced aggregation. However, the surfactant molecules on the surface of the latex particles provide stability to the particles, by electrostatic or steric repulsion, and only those collisions with force sufficient to overcome the repulsive force barrier will be effective. Husband and Adams (1992) have studied the orthokinetic flocculation of carboxylated latex particles and have found that a certain minimum shear rate was required to initiate aggregation. The minimum shear rate could be predicted by equating the electrostatic repulsive force between a pair of particles and the hydrodynamic shear force opposing it. Thus, in the presence of repulsive interparticle forces, the rate of decrease in the number concentration of particles is given by: dN p dt ¼ 16 3 N2 p a3 g W where W is a stability factor. When the colliding particles coalesce and form spherical aggregates, Eq. 10 can be expressed in a pseudo-first order form (Koh et al., 1984): dN p dt ¼ 4f gN p pW ð9Þ ð10Þ where f=4pa 3 N p /3 is the particle volume fraction, which remains constant during a batch flocculation process. Integration of Eq. 10 with respect to time gives ln N p N p;0 ¼ 4f g pW t ð11Þ where N p,0 is the number of particles at t =0. If c is the fraction of particles coagulated at time t, then or, lnð1 cÞ ¼ 4f g pW t ð12Þ c 4f g pW t ð13Þ for c less than ca. 10%. Thus, the amount of coagulum is expected to be proportional to f, the volume fraction of the particles in the suspension, g, the shear rate, the time t for which the latex is sheared, and inversely proportional to the stability factor, W. Based on the assumptions of homogeneous isotropic turbulent flow in a stirred vessel, a frequent assumption is that the average shear rate, g avg ,
Page 1 and 2: POLYMER REACTION ENGINEERING Vol. 1
Page 3 and 4: Seed and Feed Stage Agitations of B
Page 7: Seed and Feed Stage Agitations of B

Relative Importance of the Effects of Seed and Feed Stage ...

Create successful ePaper yourself

Delete template?

Save as template?