Peristaltic Transport of a Herschel-Bulkley Fluid in a Non-Uniform Channel with Wall Effects
669 Abstract—The present study considers the peristaltic transport of a Herschel-Bulkley fluid in a two-dimensional channel of non-uniform cross section with wall properties. Using long wavelength approximation with low Reynolds number and dynamic boundary conditions, analytical expressions have been obtained stream function and time average velocity. The effects of pertinent parameters on these flow variables have been studied in both converging and diverging channel. It is observed that time average velocity increases with rigidity and stiffness in the wall.
Impact of Permeable Lining of the Wall on the Peristaltic Flow of Herschel Bulkley Fluid
The peristaltic motion is modeled for the Herschel Bulkley fluid, considered to flow in a nonuniform inclined channel. The channel wall is supposed to be lined with a non-erodible porous material. The flow is considered to be moving in a wave frame of reference moving with same velocity as of the sinusoidal wave. Low Reynolds number and long wave length assumptions are made to solve the model. Analytical solution is obtained for the pressure difference and also for the frictional force. Graphs are plotted, using Mathematica software, for both the results of pressure difference and frictional force against time average velocity. We observe that increasing the porous thickening, increases the pressure difference while, it decreases the frictional force. It is seen that the behavior of the pressure difference is opposite to the behavior of the frictional force for all the parameters considered.
CATARACT: A HISTORICAL PERSPECTIVE.
The earliest extant description of a surgical operation for the cure of cataract is that of Celsus, toho practiced medicine in Rome at the beginning of the Christian era. In his text De Meclicina he described in detail his method of couching, by which he inserted a bronze needle into the eye at the equator on the lateral side of ihe globe and depressed the cataract downward into the lower part of the vitreous where the surgeon hoped it would remain out of the way of vision. The same method had been employed by the Greeks and Hindus for at least several hundred years earlier and ivas to continue as the only operation available until the middle of the eighteenth century when Daviel of Paris described extraction of the lens through the cornea. The early couchers worked on the premise that the crystallin humor we know as the lens was the receptor for vision, and that in certain conditions of disease a suffusion flowed doivn in front of the crystallin humor where it solidified and formed a dense curtain. The purpose of couching was to press the hardened corrupt humor out of the way of the lens. That cataract was opaque material within the lens itself was not recognized until after the middle of ihe seventeenth century. Until then ihe surgeons were not even aware that it was the lens they were dislocating.