Longitudinal gradient

Lateral gradients are much greater than longitudinal gradients, dC/dy dCldx. 

Figure 3.1. The differential element in a serpentine flow PEM fuel cell. In a small volume along the flow ehannels there are no longitudinal gradients, and the only compositional gradients are transverse to the membrane.

Thermal slip coefficient determines the tangential velocity of gas near a solid surface due to a longitudinal gradient of the surface temperature. 

Our discussion of strong flows is restricted to longitudinal gradients for the following reason. In the more familiar transverse situation ... 

Duling BR, Berne RM. 1970. Longitudinal gradients in periarteriolar oxygen tension a possible mechanism for the participation of oxygen in local regulation of blood flow. Circ Res 27(5) 669-678. 

In the case of longitudinal gradient, the viscosity increases very rapidly and goes to infinity at 3 = -5 for a coil with unlimited extensibility. Finite chain length limits the increase up to a limiting value L/a M. The rapid decrease... 

Twisted scrolls were also found by Yamaguchi and Muller [64] in thin tubes with longitudinal gradients of concentrations of the BZ initial reagents. They also observed the transition from a twisted scroll to a set of plane traveling waves. 

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