Anionic surfactants by Stache H.W. (ed.)

By Stache H.W. (ed.)

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Such an expansion with a factor α of particleÀparticle distances gives rise to the system volume V 5 54rp3d3α3. The volumetric fraction φV is related to the system volume as φV 5 NVp/V, in which Vp is the volume of a spherocylinder particle, expressed as Vp 5 πd3(3rp 2 1)/12. 4A. 3. 4 Aggregation for spherolong axis direction cylinder particles. 5B. Capturing such clusters in simulations requires a simulation region with suitable dimensions. As in the previous case of a spherocylinder particle system, a nearly close-packed configuration is first arranged.

92), but the weighting constants are different from Eq. 93) and are expressed in Eq. 69). The basic equations for fα(r 1 cαΔt,t 1 Δt) are the same as Eq. 91), and the above-mentioned simulation procedure is also directly applicable to the D3Q19 model. This page intentionally left blank 2 Outline of Methodology of Simulations In order to develop a simulation program, it is necessary to have an overview of the general methodology, which should include the assignment of the initial configuration and velocities, the treatment of boundary conditions, and techniques for reducing computation time.

3. Calculate the total number of particles N. 4. Evaluate the expansion ratio α from Eq. 1) or Eq. 2) to give rise to the desired volumetric fraction φV. 5. Expand particleÀparticle distances equally by the factor α. 5 Initial conditions for disk-like particles. 6. Perturb the particle positions by small distances using random numbers in order to destroy the regularity of the initial configuration; otherwise, all particleÀparticle interactions may be zero and therefore the particles may not move with time.

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