Motion, laws friction effect

For the present we consider the case of very small frictional effects due to the beads i.e., the Stokes law radius a is small. We assume that the effects are so small that the motion of the surrounding medium is only very slightly disturbed by the movement of the polymer molecule relative to the medium. The frictional effects due to the polymer molecule are then comparatively easy to treat, for the velocity of the medium everywhere is approximately the same as though the polymer molecule were not present. The solvent streams through the molecule almost (but not entirely) unperturbed by it hence the term free-draining is appropriate for this case. The velocity difference we require in Eq. (11) is simply defined by the motion of the molecule on the one hand and the unperturbed flow of the medium on the other. 

To simulate the particle-particle collision, the hard-sphere model, which is based on the conservation law for linear momentum and angular momentum, is used. Two empirical parameters, a restitution coefficient of 0.9 and a friction coefficient of 0.3, are utilized in the simulation. In this study, collisions between spherical particles are assumed to be binary and quasi-instantaneous. The equations, which follow those of molecular dynamic simulation, are used to locate the minimum flight time of particles before any collision. Compared with the soft-sphere particle-particle collision model, the hard-sphere model accounts for the rotational particle motion in the collision dynamics calculation thus, only the translational motion equation is required to describe the fluid induced particle motion. In addition, the hard-sphere model also permits larger time steps in the calculation therefore, the simulation of a sequence of collisions can be more computationally effective. The details of this approach can be found in the literature (Hoomans et al., 1996 Crowe et al., 1998). 

These laws at first sight seem to go against our common experience. Indeed, they may seem to be incorrect when seen for the first time. Rather like Newton s laws of motion, the above statements strip away the interference of other effects such as gravity, friction, viscosity and geometry which dominate our everyday experience. They reveal the chemical reality of natural electronic forces between atoms. 

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