Steady-state aspect ratio

Figure 4. The steady-state aspect ratio (length/width) of the channel versus the nondimensional parameter v /kD. Results are valid only for a limited range of Damkohler number. Aquifer widths of 3, 5, and 7 meters were used.

During a steady-state capillary flow, several shear-induced effects emerge on blend morphology [4-6]. It is, for instance, frequently observed that TLCP domains form a fibrillar structure. The higher the shear rate, the higher the aspect ratio of the TLCP fibrils [7]. It is even possible that fibers coalesce to form platelet or interlayers. 

In fact, the fiber contribution to the shear viscosity of a fiber suspension at steady state is modest, at most. The reason is that, without Brownian motion, the fibers quickly rotate in a shear flow until they come to the flow direction in this orientation they contribute little to the viscosity. Of course, the finite aspect ratio of a fiber causes it to occasionally flip through an angle of n in its Jeffery orbit, during which it dissipates energy and contributes more substantially to the viscosity. The contribution of these rotations to the shear viscosity is proportional to the ensemble- or time-averaged quantity (u u ), where is the component of fiber orientation in the flow direction and Uy is the component in the shear gradient direction. Figure 6-21 shows as a function of vL for rods of aspect... 

Since at steady state the angular distribution of fiber orientations is predicted to be symmetric about the flow direction in a shearing flow, Eq. (6-50) implies that the normal stresses (e.g., a oc [u uy) will be identically zero. However, nonzero positive values of N have frequently been reported for fiber suspensions (Zimsak et al. 1994). Figure 6-24 shows normalized as discussed below, as a function of shear rate for various suspensions of high fiber aspect ratio. These normal stress differences are linear in the shear rate and can be quite large, as high as 0.4 times the shear stress, which is dominated by the contribution of the solvent medium, cr Fig- 6-24, the N] data are normalized... 

Field-flow fractionation experiments are mainly performed in a thin ribbonlike channel with tapered inlet and outlet ends (see Fig. 1). This simple geometry is advantageous for the exact and simple calculation of separation characteristics in FFF Theories of infinite parallel plates are often used to describe the behavior of analytes because the cross-sectional aspect ratio of the channel is usually large and, thus, the end effects can be neglected. This means that the flow velocity and concentration profiles are not dependent on the coordinate y. It has been shown that, under suitable conditions, the analytes move along the channel as steady-state zones. Then, equilibrium concentration profiles of analytes can be easily calculated. 

An important aspect to note here is the nse of f3, which is the bioavaUabihty term for the effect compartment. Here, f3 is nsed to initiahze the effect compartment to the basehne valne of the biomarker being modeled, which is why it is set to the ratio of ksyn/kdeg. Prior to therapy, the biomarker is presumed to be at some steady-state value, which should be equivalent to the ratio of formation to degradation. f3 is used in conjunction with a special dose item for this compartment to initialize the effect compartment. 

A very interesting series of studies of the influence of end effects in the rotating concentric cylinder problem has been published by Mullin and co-workers T. Mullin, Mutations of steady cellular flows in the Taylor experiment,J. Fluid Mech. 121, 207-18 (1982) T. B. Benjamin and T. Mullin, Notes on the multiplicity of flows in the Taylor experiment, J. Fluid Mech. 121, 219-30 (1982) K. A. Cliff and T. Mullin, A numerical and expwerimental study of anomalous modes in the Taylor experiment, J. Fluid Mech. 153, 243-58 (1985) G. Pfister, H. Schmidt, K. A. Cliffe and T. Mullin, Bifurcation phenomena in Taylor-Couette flow in a very short annulus, J. Fluid Mech. 191, 1-18 (1988) K. A. Cliffe, 1.1. Kobine, and T. Mullin, The role of anomalous modes in Taylor-Couette flow, Proc. R. Soc. London Ser. A 439, 341-57 (1992) T. Mullin, Y. Toya, and S. I. Tavener, Symmetry breaking and multiplicity of states in small aspect ratio Taylor-Couette flow, Phys. Fluids 14, 2778-87 (2002). 

The aspect ratio effect is seen in Fig. 29. Given a localized source of species (e.g. radicals), the spatial distribution of these species at steady state will depend on the reactor aspect ratio. Low aspect ratio reactors (tall, small radius) yield a distribution that peaks on axis, while large aspect ratio systems (short, large radius) yield a dis-... 

Spreading (constriction) resistance is an important thermal parameter that depends on several factors such as (1) geometry (singly or doubly connected areas, shape, aspect ratio), (2) domain (half-space, flux tube), (3) boundary condition (Dirchlet, Neumann, Robin), and (4) time (steady-state, transient). The results are presented in the form of infinite series and integrals that can be computed quickly and accurately by means of computer algebra systems. Accurate correlation equations are also provided. 

The theory makes it possible to compute the drop aspect ratio, p = a /a, a parameter that can be directly measured in either transient or steady-state flows. Following the derivation by Hinch and Acrivos [1980] the flow-induced changes to the drop aspect ratio were assumed to be proportional to the first normal stress difference coefficient of the matrix fluid. The coalescence was assumed to follow the Silberberg and Kuhn [1954] mechanism. These assumptions substituted into Eq 7.110 gave a simple dependence for the aspect ratio ... 

Predictive model for the morphology variation during simple shear flow under steady state uniform shear field was developed. The model considers the balance between the rate of breakup and the rate of drop coalescence. The theory makes it possible to compute the drop aspect ratio, p a parameter that was directly measured for PS/PMMA =1 9 blends. 

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