No abstract

No abstract

Reactors or crystallizers synthesizing valuable particles can be formally described by combining the laws of continuum transport theory with a population balance equation governing evolution of the "dispersed" (suspended) particle population. Early examples necessarily focused on highly idealized device configurations and populations described locally using only one particle state variable, i.e., "size" (length or volume). However, in almost every application of current/future importance, a multivariate description is required, for which the existing literature offers little guidance. We describe here our recent research on an instructive bivariate prototype of physical interest (coagulating, sintering nanoparticles of prescribed composition, etc.) that will, hopefully, motivate a broader attack on important multivariate population balance problems, including those describing continuous molecular mixtures. We illustrate the use of both physically based bivariate "mixed" moment and Monte Carlo simulation methods amenable to future generalization. Multivariate extensions, improved and fully coupled rate laws, and consideration of interacting (coexisting) populations will be required to deal with future sol reaction engineering problems using similar strategies/techniques.

We have modeled platelet aggregation in a linear shear flow by accounting for two body collision hydrodynamics, platelet activation and receptor biology. Considering platelets and their aggregates as unequal-sized spheres with DLVO interactions (psi(platelet) = -15 mV, Hamaker constant = 10(-19) J), detailed hydrodynamics provided the flow field around the colliding platelets. Trajectory calculations were performed to obtain the far upstream cross-sectional area and the particle flux through this area provided the collision frequency. Only a fraction of platelets brought together by a shearing fluid flow were held together if successfully bound by fibrinogen cross-bridging GPIIb/IIIa receptors on the platelet surfaces. This fraction was calculated by modeling receptor-mediated aggregation using the formalism of Bell (Bell, G. I. 1979. A theoretical model for adhesion between cells mediated by multivalent ligands. Cell Biophys. 1:133-147) where the forward rate of bond formation dictated aggregation during collision and was estimated from the diffusional limited rate of lateral association of receptors multiplied by an effectiveness factor, eta, to give an apparent rate. For a value of eta = 0.0178, we calculated the overall efficiency (including both receptor binding and hydrodynamics effects) for equal-sized platelets with 50,000 receptors/platelet to be 0.206 for G = 41.9 s(-1), 0.05 for G = 335 s(-1), and 0.0086 for G = 1920 s(-1), values which are in agreement with efficiencies determined from initial platelet singlet consumption rates in flow through a tube. From our analysis, we predict that bond formation proceeds at a rate of approximately 0.1925 bonds/microm2 per ms, which is approximately 50-fold slower than the diffusion limited rate of association. This value of eta is also consistent with a colloidal stability of unactivated platelets at low shear rates. Fibrinogen was calculated to mediate aggregation quite efficiently at low shear rates but not at high shear rates. Although secondary collisions (an orbitlike trajectory) form only a small fraction of the total number of collisions, they become important at high shear rates (>750 s(-1)), as these are the only collisions that provide enough time to result in successful aggregate formation mediated by fibrinogen. The overall method provides a hydrodynamic and receptor correction of the Smoluchowski collision kernel and gives a first estimate of eta for the fibrinogen-GPIIb/IIIa cross-bridging of platelets. We also predict that secondary collisions extend the shear rate range at which fibrinogen can mediate successful aggregation.

No abstract

No abstract

No abstract

Activated neutrophils aggregate in a shear field via bonding of L-selectin to P-selectin glycoprotein ligand-1 (PSGL-1) followed by a more stable bonding of LFA-1 (CD11a/CD18) to intercellular adhesion molecule 3 (ICAM-3) and Mac-1 (CD11b/CD18) to an unknown counter receptor. Assuming that the Mac-1 counter receptor is ICAM-3-like in strength and number, rate processes were deconvoluted from neutrophil homoaggregation data for shear rates (G) of 100-3000 s-1 with a two-body hydrodynamic collision model (. Biophys. J. 73:2819-2835). For integrin-mediated aggregation (characteristic bond strength of 5 microdynes) in the absence of L-selectin contributions, an average forward rate of kf = 1.57 x 10(-12) cm2/s predicted the measured efficiencies for G = 100-800 s-1. For a selectin bond formation rate constant equal to the integrin bond formation rate constant, the colloidal stability of unactivated neutrophils was satisfied for a reverse rate of the L-selectin-PGSL bond corresponding to an average bond half-life of 10 ms at a characteristic bond strength of 1 microdyne. Colliding neutrophils initially bridged by at least one L-selectin-PSGL-1 bond were calculated to rotate from 8 to 50 times at G = 400 to 3000 s-1, respectively, before obtaining mechanical stability in sheared fluid of either 0.75 or 1.75 cP viscosity. Thus for G > 400 s-1, the interaction time needed for the rotating aggregates to become stable was relatively constant at 52.5 +/- 8.5 ms, largely independent of shear rate or shear stress. Aggregation data and the colloidal stability criterion can provide a consistent set of forward and reverse rate constants and characteristic bond strengths for a known time-dependent stoichiometry of receptors on cells interacting in a shear flow field.