Droplet collision calculated

The first maj or extension of the stochastic particle method was made by O Rourke 5501 who developed a new method for calculating droplet collisions and coalescences. Consistent with the stochastic particle method, collisions are calculated by a statistical, rather than a deterministic, approach. The probability distributions governing the number and nature of the collisions between two droplets are sampled stochastically. This method was initially applied to diesel sprays13171... 

Droplet collision is a phenomenon inherent in the dense region of a spray. Droplet collisions may lead to local agglomeration that affects the droplet size distribution. There have been considerable efforts in modeling droplet-droplet collisions and coalescence,12291 but the models are still not generally applicable. 1576] Moreover, the calculations in the dense region of a metal spray is much more complicated than in a diesel spray because the physical phenomena and mechanisms in the dense region are not well understood. 

In order to obtain a correlation, the outflow of the effervescent spray was simulated by a numerical model based on the Navier-Stokes equations and the particle tracking method. The external gas flow was considered turbulent. In droplet phase modeling, Lagrangian approach was followed. Droplet primary and secondary breakup were considered in their model. Secondary breakup consisted of cascade atomization, droplet collision, and coalescence. The droplet mean diameter under different operating conditions and liquid properties were calculated for the spray SMD using the curve fitting technique [43] ... 

M. Ruger, S. Hohmann, M. Sommerfeld, G. Kohnen, Euler/Lagrange calculations of turbulent sprays the effect of droplet collisions and coalescence. Atomization and Sprays 10(1) (2000)... 

The same apparatus was used to measure the kinetics of emulsion crystallization under shear. McClements and co-workers (20) showed that supercooled liquid n-hexadecane droplets crystallize more rapidly when a population of solid n-hexa-decane droplets are present. They hypothesized that a collision between a solid and liquid droplet could be sufficient to act as a nucleation event in the liquid. The frequency of collisions increases with the intensity of applied shear field, and hence shearing should increase the crystallization rate. A 50 50 mixture of solid and liquid n-hexadecane emulsion droplets was stored at 6 -0.01 °C in a water bath (i.e., between the melting points and freezing points of emulsified n-hexadecane). A constant shear rate (0-200 s ) was applied to the emulsion in the shear cell, and ultrasonic velocities were determined as a function of time. The change in speed of sound was used to calculate the percentage solids in the system (Fig. 7). Surprisingly, there was no clear effect of increased shear rate. This could either be because increase in collision rate was relatively modest for the small particles used (in the order of 30% at the fastest rate) or because the time the interacting droplets remain in proximity is not affected by the applied shear. 

Calculations for larger drops are complicated by phenomena such as shape deformation, wake oscillations, and eddy shedding, making theoretical estimates of E difficult. The overall process of rain formation is further complicated by the fact that drops on collision trajectories may not coalesce but bounce off each other. The principal barrier to coalescence is the cushion of air between the two drops that must be drained before they can come into contact. An empirical coalescence efficiency Ec suggested by Whelpdale and List (1971) to address droplet bounce-off is... 

In a generic W/O microemulsion (L2 phase), the monomeric surfactant and water in the continuous oil phase are in equilibrium with spherical droplets however, the monomeric concentrations are very low (often neglected in calculations). Depending on temperature and volume fraction, the droplets are in equilibrium with clusters of droplets, mainly because of sticlQ collisions. Such is the constitution of the original equilibrium system that is perturbed by the electric field. 

To determine the charge, the electrophoretic mobility, i.e., the mobiHly of the charged particles in the electric held, is determined. From this the so-called potential can be calculated, which is a parameter for the stabilization by means of electrostatic forces. The tnec/uinira/ stability of the emulsifying film is also of considerable importance. On the one hand, it must be sufficiently rigid to stabilize the interface, but on the other hand must also be sufficiently flexible that collision of emulsion droplets does not lead to rupture of the emulsifying film and to resulting coalescence. 

To estimate colloidal forces acting between the droplets during the collision, x, z coordinates of the initial (x, Zj) and final (xf, Zf) positions of the mobile droplet before and after the collision are needed. When several pairs of x, z coordinates are plotted on a graph a speeifie seattering pattern will appear. This pattern can be analyzed by eompar-ing the experimental final positions with the ones ealeulated from a theory (2,3), which covers hydrodynamic interactions between the droplets and between the mobile droplet and the wall as well as all external forees aeting on the mobile drop, e.g., those described by DLVO theory. Thus, in the calculations, we assume the existenee of a certain force described by a certain function of the droplet-droplet separation. The final position of the droplet is then calculated and compared with the experimental results. The best match between experimental and theoretical final droplet positions yields the optimum set of parameters or the optimum force-distance profile. 

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