Backflow flow/viscosity

From now on, the permeation in (16) is neglected as it is several orders of magnitude smaller than the advection due to the radial component of the velocity vr (now playing the role of vz in the planar case). As far as the velocity perturbation is concerned, our aim is to describe its principal effect-the radial motion of smectic layers, i.e., instead of diffusion (permeation) we now have advective transport. In this spirit we make several simplifications to keep the model tractable. The backflow-flow generation due to director reorientation-is neglected, as well as the effect of anisotropic viscosity (third and fourth line of (19)). Thereby (19) is reduced to the Navier-Stokes equation for the velocity perturbation, which upon linearization takes the form... 

Hiac ABS-2 automatic bottle sampler is a pressure sampling device used for batch analysis of volatile or viscous fluids. The ABS-2 delivers liquid to the sensor at flow rates of 10 to 200 ml min T A check valve in the sample introduction line eliminates backflow and minimizes sample cross contamination, and an automatic drain mechanism allows unattended sample analysis of multiple runs. The sampler has a built-in pressure/vacuum chamber that subjects samples to pressures up to 60 psi, accommodating viscosities up to 80 centistokes. In addition, vacuum levels of 23 psi are used to degas samples which contain entrained air. 

Here, the electroosmotic flow is proportional to the proton current density jp with a drag coefficient n (wx). D Arcy flow as the mechanism of water backflow proceeds in the direction of the negative gradient of liquid pressure, which (for A P% = 0) is equal to the gradient of capillary pressure. The density of water, cw, and the viscosity, /1, are assumed to be independent of w. The transport coefficient of D Arcy flow is the hydraulic permeability K wx). 

The coefficients of friction for the director have the dimensions of viscosity and are particular combinations of Leslie coefficients, ji = aj,- (I2, Ji = 3 + 2-It is significant that only two coefficients of viscosity enter the equation for motion of the director. One (72) describes the director coupling to fluid motion. Eor example, if the director tumes rapidly under the influence of the magnetic held, then, due to friction, this rotation drags the liquid and creates flow. It is the backflow effect that will be described in more details in Section 11.2.5. The other coefficient (Yi) describes rather a slow director motion in an immobile liquid. Therefore, the kinetics of all optical effects caused by pure realignment of the director is determined by the same coefficient yj. However a description of flow demands for all the five viscosity coefficients. 

An externally applied torque on the director can only be transmitted to the surfaces of a vessel without shear, if the director rotation is homogeneous throughout the sample as assumed in Sect. 8.1.2 for the rotational viscosity. Otherwise this transmission occurs partially by shear stresses. The resulting shear flow is called backflow. As there is usually a fixed director orientation at the surfaces of the sample container, a director rotation in the bulk of the sample by application of a routing magnetic field leads to an inhomogeneous rotation of the director and to a backflow [42]. 

The dynamics of the splay and bend distortions inevitably involve the flow processes coupled with the director rotation. Such a backflow effect usually renormalizes the viscosity coefficients. Only a pure twist distortion is not accompanied by the flow. In the latter case, and for the infinite anchoring energy, the equation of motion of the director (angle variation) expresses the balance between the torques due to the elastic and viscous forces and the external field (and... 

Backflow effects may accompany the transient process of the director reorientation [64,65]. The process is opposite to the flow orientation of the director known from rheological experiments. Disregarding the back-flow, we can use the same equations for the splay (with A",) and bend (K33) small-angle distortions. The backflow effects renormalize the rotational viscosity of a nematic ... 

As the transmission curve of a liquid crystal display during the switching process depends on all the Leslie coefficients due to backflow effects, it is possible to determine the coefficients from the transmission curve. In analogy to light scattering, the coefficients are obtained with different accuracies [38, 39]. The investigation of torsional shear flow in a liquid crystal [31-35] allows the determination of quantities from which some Leslie coefficients can be determined, if one shear viscosity coefficient is known. 

The simulations of a tethered polymer in a Poiseuille flow [74] yield a series of morphological transitions from sphere to deformed sphere to trumpet to stem and flower to rod, similar to theoretically predicted structures [129-131]. The crossovers between the various regimes occur at flow rates close to the theoretical estimates for a similar system. Moreover, the simulations in [74] show that backflow effects lead to an effective increase in viscosity, which is attributed to the fluctuations of the free polymer end rather than its shape. 

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