Diverging material flow

Specific aspects of dairy production are covered by the model proposed by Wouda et al. (2002). While the model is relatively simple with respect to its mathematical structure (single-period, domestic setting, two production levels), it contains aspects such as milk collection from production regions, divergent material flows occurring in the first stage of dairy processing and transshipment of the respective intermediates between plants. 

Figure 10.7 shows the extended RTN formulated for the benchmark problem. The production process includes diverging and converging material flows, flexible proportions of output goods (task Tj), cyclic material flows (recycling of output from task T3 into state Si), intermediate products which cannot be stored (state nodes S5, S9, S10, S12), and blending of products in task Ti 5. All processing tasks are operated batch-wise with lower and upper bounds on batch sizes. Batch sizes are... 

The reason for Ihis difference is to be found in the divergence of the whole material flow around an inverted internal cone, where flow only can take place on the outside of the insert. The kinetic energy of the powder is considerably increased over the situation with no insert. On the other hand, during flow in a cone in cone hopper, there is also flow on the inside of the internal cone, thereby causing less disturbance of the flow field. The increase in kinetic energy is considerably less than for an inverted cone, since part of the flow takes place inside the insert. 

A plastic material is one which displays a yield stress. As the shear rate is reduced the apparent viscosity progressively increases, diverging and never reaching a constant value. If a stress is applied to a plastic material no flow will be observed until the stress exceeds the yield stress. Expressions describing plastic materials must include at least two terms, a yield stress and a limiting high shear viscous term. Expressions usually describe shear stress in terms of shear rate ... 

The pressures developed in the deton reaction zone in condensed expls are of the order of 103 to 10 atm. Material at such pressures cannot in general be contained, so that the flow behind the front has a component radially outward. Gases, which develop much lower deton pressures (of the order of 10 atm), can be confined in a tube, and for them the one- dimensional approximation is good. The diverging flow is expected and is found experimentally to result in lower pressures and densities within the steady wave, and consequently in lower detonation velocities. 

Here Jix, Jiy, and J, z are the Cartesian coordinates of the vector J,. As the volume V and the product J, dA are scalars, the divergence is also a scalar quantity. A positive divergence means a source of component i, while a negative divergence indicates a sink, and at points of div J,- = 0, there is no accumulation and no removal of material. Transformation of the surface integral of a flow into a volume integral of a divergence is... 

The most efficient orientation fields are exten-sional. Using convergent and divergent flow one may control orientation of anisometric particles. Most of the work in this area has been done with fiber-filled materials but the effects are equally important for flow of neat semicrystafline polymer melts or liquid crystal polymers [Goettler and Shen, 1983 Goettler, 1984]. There is less information on the flow-induced orientation of platelets. In extensional flow, these particles are less susceptible to orientation. Two-stage orientation mechanism was observed in converging flow [Utracki, 1988]. 

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