Tilted open channel

When a viscoelastic fluid flows down a tilted, open channel, the free surface bulges slightly as indicated in Figive 6.4.4. This curvature is across the streamlines of the flow thus, as with parallel pressure slot and axial annular flow, we expect the bulge to be proportional 

Side and cross-sectional views of flow of a viscoelastic fluid down a semicircular tube. The bulge h(,xi) is an indication of negative N2. After Tanner (1970). 

Chatmel bulge is perhaps the simplest and most direct measurement of the second nmmal stress difference. If h is positive, a convex surface N2 is negative. Since Tanner s first experiments with the tilted trough in 1970 and the discovery of the pressure hole error (Broadbent et al., 1968), nearly all studies have shown N2 to be small and negative. 

Because N2 is relatively small and Tw is limited by 6 15°, the channel bulge is small. However, photographing the reflection of a graduated straight edge allowed Keentok et al. (1980) to measure h 10/xm. They report N2 data on five fluids at several concentrations with an accuracy 0.1 Pa. The results indicate -N2/N 0.1 independent of shear rate. The technique is limited to lower viscosities ( 0.1 Pa-s), lower shear stresses ( 20 Pa), and room temperature. 

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Figure 13. Left An array of hair cells. Right The movement of a hair cell s cilia bundle (left panel) opens ion channels at the tips of the cilia. When the bundle tilts to the right (middle panel), tip links from the higher cilia pull up the gates of the ion channels on adjoining, shorter cilia. This (still middle panel) close-up shows how a tip link between two cilia opens an ion channel on the shorter cilium. Even more highly magnified in the right panel, the open channel allows ions into the cell. This illustration is by Jennifer Jordan, RCW Communications, Inc. (adapted from a sketch by James Hudspeth, HHMI, University of Texas Southwestern Medical Center at Dallas).

The C-terminal transmembrane helix, the inner helix, faces the central pore while the N-terminal helix, the outer helix, faces the lipid membrane. The four inner helices of the molecule are tilted and kinked so that the subunits open like petals of a flower towards the outside of the cell (Figure 12.10). The open petals house the region of the polypeptide chain between the two transmembrane helices. This segment of about 30 residues contains an additional helix, the pore helix, and loop regions which form the outer part of the ion channel. One of these loop regions with its counterparts from the three other subunits forms the narrow selectivity filter that is responsible for ion selectivity. The central and inner parts of the ion channel are lined by residues from the four inner helices. 

Figure 13.18. Opening of the Acetylcholine Channel Pore. Large hydrophobic side chains (L) occlude the pore of the closed form of the acetylcholine receptor channel. Channel opening is probably mediated by the tilting of helices that line the pore. Large residues move away from the pore and small ones (S) take their place. [After N. Unwin. Neuron 3 (1989) 665.]...

In order to study into more details the mechanisms involved in the process of opening and closing of the potassium channel a complete analysis of the Hodgkin and Huxley rate constants as a function of potential, was done. The results are shown in fig. 3a. At pH 9.6 both the backward, 3 (E), and the forward rate constant, a (E), are shifted to the right and slightly tilted in the upward direction. 

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