Flow field orientation

The fact that stiffer chains are more difficult to unfold and that in addition to the entropic characteristic of the rigidity (x), the energetic characteristic should also be considered, was not taken into consideration in the analysis. In general, two factors must be kept in mind in studying the process of the formation of the LC phase in a flow field orientation and deformation. The first factor is related to the orientation of asymmetric molecular formations in flow and it is favorable for chains with elevated rigidity. The second is due to unfolding of the chains, is related to their chemical structure, and is more easily realized for flexible molecules. 

The stack orientation, and so the flow field orientation, may be either vertical or horizontal. In the latter case, either anode or cathode may be facing up (Figure 6-15). Again, this may have some effect on liquid water removal, particularly after shutdown and cooling. 

C. Characteristically, these nematic melts show the persistence of orientational order under the influence of elongational flow fields which result in low melt viscosities under typical fiber formation conditions even at high molecular weights. 

Molecules of nematic Hquid crystals also are aligned in flow fields which results in a viscosity that is lower than that of the isotropic Hquid the rod-shaped molecules easily stream past one another when oriented. Flow may be impeded if an electric or magnetic field is appHed to counter the flow orientation the viscosity then becomes an anisotropic property. 

This apparent time dependent cell disruption is caused because of the statistically random distribution of the orientation of the cells within a flow field and the random changes in that distribution as a function of time, the latter is caused as the cells spin in the flow field in response to the forces that act on them. In the present discussion this is referred to as apparent time dependency in order to distinguish it from true time-dependent disruption arising from anelastic behaviour of the cell walls. Anelastic behaviour, or time-dependent elasticity, is thought to arise from a restructuring of the fabric of the cell wall material at a molecular level. Anelasticity is stress induced and requires energy which is dissipated as heat, and if it is excessive it can weaken the structure and cause its breakage. 

External fields have been widely used to align block copolymer microdomains. This approach relies on the ability to couple an external applied bias field to some molecular or supermolecular feature, and thus achieve directional control over the microdomains. External fields, such as an electric field [61-63], mechanical flow field [53-55], and temperature gradient [60], have been utilized to control the long-range orientation of block copolymers in the bulk state. 

Theoretical predictions relating to the orientation and deformation of fluid particles in shear and hyperbolic flow fields are restricted to low Reynolds numbers and small deformations (B7, C8, T3, TIO). The fluid particle may be considered initially spherical with radius ciq. If the surrounding fluid is initially at rest, but at time t = 0, the fluid is impulsively given a constant velocity gradient G, the particle undergoes damped shape oscillations, finally deforming into an ellipsoid (C8, TIO) with axes in the ratio where... 

Autoclave processing is a process in which individual prepreg plies are laid up in a prescribed orientation to form a laminate (Fig. 5.9). The process involves consolidation of the laminate, which generally results in a three-dimensional flow field. Similar to the IP process the fiber bed is not stationary in the AP process hence, its movement has to be specifically considered when the appropriate conservation equation for this process are developed. If it is assumed that the resin has a relatively constant density (i.e., the excess resin is squeezed out before the gel point is reached) then the appropriate conservation of mass equation for this consolidating system is Equation 5.12. 

We assume the system under consideration to be a single domain. Then the orientational state of the system can be specified by the order parameter tensor S defined by Eq. (63), The time evolution of S is governed by the kinetic equation, Eq. (64), along with Eqs. (62) and (65). This kinetic equation tells us that the orientational state in the rodlike polymer system in an external flow field is determined by the term F related to the mean-field potential Vscf and by the term G arising from the external flow field. These two terms control the orientation state in a complex manner as explained below. 

The stress tensor plays a prominent role in the Navier-Stokes and the energy equations, which are at the core of all fluid-flow analyses. The purpose of the stress tensor is to define uniquely the stress state at any (every) point in a flow field. It takes nine quantities (i.e., the entries in the tensor) to represent the stress state. It is also be important to extract from the stress tensor the three quantities needed to represent the stress vector on a given surface with a particular orientation in the flow. By relating the stress tensor to the strain-rate tensor, it is possible to describe the stress state in terms of the velocity field and the fluid viscosity. 

Developing the stress-strain-rate relationships is greatly facilitated in the principal coordinate directions. Since isotropy requires that the constitutive relationships be independent of coordinate orientation, the principal-direction relationships can be transformed to any other coordinate directions. At every point in a flow field the strain-rate and stress state... 

If the mixing device generates a simple shear flow, as shown in Fig. 3.23, the maximum separation forces that act on the particles as they travel on their streamline occur when they are oriented in a 45° position as they continuously rotate during flow. However, if the flow field generated by the mixing device is a pure elongational flow, such as shown in Fig. 3.24, the particles will always be oriented at 0° the position of maximum force. 

From the previous Section it is expected that the application of the flow field will primarily affect the last two order parameters, i.e. the orientation and conformation of the chain. In the discussion of the nucleation dynamics, it is helpful to separate the contributions from the kinetic and thermodynamic processes. The first represents the fundamental timescale to form a nucleus, the prefactor, and the second describes the driving force for the phase transition based on the position of the system in the phase diagram. 

A rep < 1, Des < 1, the nucleation dynamics is stochastic in nature as a critical fluctuation in one, or more, order parameters is required for the development of a nucleus. For DeYep > 1, Des < 1 the chains become more uniformly oriented in the flow direction but the conformation remains unaffected. Hence a thermally activated fluctuation in the conformation can be sufficient for the development of a nucleus. For a number of polymers, for example PET and PEEK, the Kuhn length is larger than the distance between two entanglements. For this class of polymers, the nucleation dynamics is very similar to the phase transition observed in liquid crystalline polymers under quiescent [8], and flow conditions [21]. In fast flows, Derep > 1, Des > 1, A > A (T), one reaches the condition where the chains are fully oriented and the chain conformation becomes similar to that of the crystalline state. Critical fluctuations in the orientation and conformation of the chain are therefore no longer needed, as these requirements are fulfilled, in a more deterministic manner, by the applied flow field. Hence, an increase of the parameters Deiep, Des and A results into a shift of the nucleation dynamics from a stochastic to a more deterministic process, resulting into an increase of the nucleation rate. 

Consider an arbitrarily oriented surface element in a homogeneous simple shear flow field vx = yyxy [Fig. 7.1a]. The surface element at time to is confined between two position vectors pi and p2. The area of the surface element is... 

---