Nanomechanical response and creep behavior of electroless deposited copper films under nanoindentation test

Effect of particle size distribution on the collection efficiency of Brownian particles

“…With the consideration of this random Brownian force as shown in the Langevin-type trajectory equation of Eqs. (10) and (11), it can be found that the simulation results obtained by the present method fit fairly well with the Pannu's data at 5 × 10 −4 σ 3 × 10 −3 .…”

“…For a chosen value of N R , our previous simulation results of η s /η s 0 vs σ already found that the values of η s /η s 0 increase with the increase of σ , and the values of Brownian particles are higher than those of non-Brownian particles [10]. Experimental results of Chiang and Tien [23] and Pannu's data [7] for measuring the collection efficiencies of colloidal particles of specific sized in terms of σ in a packed bed are adopted here to compare with the predictions by using the present simulation method as follows.…”

“…The shadow area is shown to increase as the position of deposition moves away from the front stagnation point of the collector, and also increases as the relative size ratio increases. Our previous simulation results also indicated that the Brownian particles can always cause a bigger shadow area at a smaller deposition angle than the non-Brownian particles, and the particle's Brownian motion behavior can accelerate the formation of dendrites on the front part of the spherical collector and therefore promotes the collection efficiency [10].…”

“…With the aid of this Langevin-type equation and the concept of the control window [6,7], a stochastic simulation method describing the deposition behavior of Brownian particles was successfully established by Ramarao et al [8] and Chang et al [9]. By applying this dynamics method, we successfully established a stochastic procedure to simulate the initial deposition rates of Brownian particles onto a spherical collector [10] and in the constricted tube model [11]. The results obtained by those papers showed that the height of the primary maximum and the depth of the secondary minimum in the total interaction energy curve of DLVO theory [12] play important roles in determining the collection efficiency of Brownian particles at low Reynolds numbers.…”

“…This dimensionless parameter N R determines the contributions to the particle collection by the interception mechanism [17] and by the DLVO interaction forces [9,11]. In studying the morphology of particle deposits onto a spherical collector, Wang et al [6] and Chang et al [10] found that the extent of the multilayers formatted by those deposited particles is determined by the value of N R . In their studies, the particle deposition morphology was examined by tracking the trajectories of individual particles as they move toward the collector.…”