Cell wall Poiseuille flow

Figure 9-16. Pressure drops across a hypothetical xylem cell that is 1 mm long, 40 pm in inside diameter, and has an axial flow rate of 1 mm s-1 (a) artificially surrounded by a plasma membrane, (b) artificially having a cell wall 1 pm thick across each end, and (c) realistically consisting of a hollow tube in which Poiseuille flow occurs. Allows are placed at the main barriers to flow in each case. See text for calculation details.

In contrast, a dPIdx of only -0.02 MPa m-1 is needed for the same Jv in the xylem element with a 20-pm radius. Thus, the dPIdx for Poiseuille flow through the small interstices of a cell wall is over 107 times greater than that for the same flux density through the lumen of the xylem element. Because of the tremendous pressure gradients required to force water through the small interstices available for solution conduction in the cell wall, fluid cannot flow rapidly enough up a tree in its cell walls — as has been suggested — to account for the observed rates of water movement. 

Water is conducted to and across the leaves in the xylem. It then moves to the individual leaf cells by flowing partly apoplastically in the cell walls and partly symplastically (only short distances are involved, because the xylem ramifies extensively in a leaf). The water potential is usually about the same in the vacuole, the cytosol, and the cell wall of a particular mesophyll cell (see values in Table 9-3). If this were not the case, water would redistribute by flowing energetically downhill toward lower water potentials. The water in the cell wall pores is in contact with air, where evaporation can take place, leading to a flow along the cell wall interstices to replace the lost water. This flow can be approximately described by Poiseuille s law (Eq. 9.11), which indicates that a (very small) hydrostatic pressure decrease exists across such cell walls. 

The steady gas flow in a long macroscopic channel with impermeable walls is basically a Poiseuille flow with the constant velocity determined by the pressure gradient. However, the velocity of the flow in the fuel cell channel varies since there is mass and momentum transfer through the channel/backing layer interface. 

We next calculate the stationary level and observed particle velocity in a cylindrical capillary of radius assuming Aq/a < 1. The electroosmotic effect gives rise to a velocity across the cross section of the tube toward the electrode of the same polarity as the charge on the cell wall. The liquid velocity across the tube according to the description above, is the vector sum of the electroosmotic velocity and the reverse Poiseuille flow ... 

It follows that at the channel center y = h, the observed particle velocity obs — E special case when the particles and the cell walls have the same potential so that = - , the observed velocity at the cell center is f Mg. Again this is equivalent to the maximum velocity in Poiseuille flow in a two-dimensional channel being equal to three halves the mean velocity. 

In spiral, rectangular channels, cells and particles experience Dean drag forces in addition to inertial lift forces. The first conclusive research to analyze flow in curved channels was done by Dean in 1927 [10]. He showed that in curved channels/pipes, the plane Poiseuille flow is disturbed by the presence of centrifugal force (Fcf), and in this condition, the maximum point of velocity distribution shifts from the center of the channel toward the concave wall of the channel (Fig. 2a). This shift causes a sharp velocity gradient to develop near the concave wall between the point of maximum velocity and the outer concave channel wall where the velocity is zero. This causes decrease in the centrifugal force on the fluid near the concave wall which leads to... 

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