A first-passage algorithm for the hydrodynamic friction and diffusion-limited reaction rate of macromolecules A first-passage scheme is devised to determine the overall rate constant of suspensions under the non-diffusion-limited condition. The original first-passage scheme developed for diffusion-limited processes is modified to account for the finite incorporation rate at the inclusion surface by using a concept of the nonzero survival probability of the diffusing entity at entity-inclusion encounters. This nonzero survival probability is obtained from solving a relevant boundary value problem. The new first-passage scheme is validated by an excellent agreement between overall rate constant results from the present development and from an accurate boundary collocation calculation for the three common spherical arrays ͓J. Chem. Phys. 109, 4985 ͑1998͔͒, namely simple cubic, body-centered cubic, and face-centered cubic arrays, for a wide range of P and f. Here, P is a dimensionless quantity characterizing the relative rate of diffusion versus surface incorporation, and f is the volume fraction of the inclusion. The scheme is further applied to random spherical suspensions and to investigate the effect of inclusion coagulation on overall rate constants. It is found that randomness in inclusion arrangement tends to lower the overall rate constant for f up to the near close-packing value of the regular arrays because of the inclusion screening effect. This screening effect turns stronger for regular arrays when f is near and above the close-packing value of the regular arrays, and consequently the overall rate constant of the random array exceeds that of the regular array. Inclusion coagulation too induces the inclusion screening effect, and leads to lower overall rate constants.
The determination of minimum coating thickness for covering substrate holes through particle deposition is achieved with a combined, three-dimensional, on-lattice model, in which both deterministic and non-deterministic driving forces are taken into account. The relative importance of deterministic forces to non-deterministic forces is quantified by a dimensionless parameter, Peclet number. The minimum covering thickness normalized with the characteristic hole size (h c/H w) is investigated subject to variation in Peclet number (Pe) and normalized size (D p/L) of the depositing particle, normalized hole size (H w/L), and degree of post-contact restructuring allowed (N r). It is found that there exists a scaling relationship between the normalized minimum covering thickness and the normalized hole size as h c/H w∼(H w/L) E with E=0.53, 0.54, 0.96, and 1.42 for Pe of 1000, 10, 0.5, and 0.1, respectively. The magnitude of the scaling exponent implies that the hole covering ability of diffusive particle movement varies more than that of ballistic particle movement over variation in hole size. It is also found that h c/H w increases with increasing H w/L and D p/L. At low Pe (<1), h c/H w increases with increasing Pe for smaller holes, but decreases with increasing Pe for larger holes. For larger Pe, h c/H w decreases with increasing Pe, implying that ballistic particle movement is more efficient in covering holes. Post-contact surface restructuring deteriorates the hole covering efficiency of particle deposition for ballistic movement dominated situations (large Pe). But for low Pe situations, there exists an optimal surface restructuring extent, at which h c/H w is a minimum.
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