Non-Newtonian Flow
`and Heat Transfer
`
`A. H. P. Skelland
`
`of Chemical Engineering
`Professor
`The University of Notre Dame
`
`JohnWiley & Sons,
`
`Inc.
`
`New York
`
`London
`
`Sydney
`
`SNF Holding Company et al v BASF Corporation,
`
`IPR20
`
`5e-0106030
`
`EXHIBIT
`
`I zon
`
`

`
`Copyright @ I%7 by John Wiley & Sons,
`
`Inc.
`
`All Rights Reserved
`This book or any part thereof must not
`the
`reproduced in any form without
`written permission of the publisher.
`
`be
`
`Library of Congress Catalog Card Number: 6625230
`Printed in the United States of America
`
`Page 2 of 3
`
`r
`

`
`50 Determination of Flow Properties
`
`this serves to
`
`depicted in Figure L4 are time effects,
`Since the phenomena
`distinguish them from phenomena caused by effective slip.
`Thixotropic
`or Theapectie
`qualitatively
`tube
`effects
`are detected
`in
`as described in Chapter 5 with the aid of Figures 5.3 and 5.4.
`viscometers
`The effects of
`increasing tube diameter for
`fixed tube length for
`thixo-
`tropic fluids are similar
`those resulting from effective
`slip in a
`time-
`to
`independent fluid. The two phenomena may be distinguished, however,
`by
`the tube length at
`fixed diameter. Separate curves of D AP/4L
`varying
`versus 8VfD will still be obtained for
`the thixotropic fluid but not for
`the
`time-independent
`fluid with effective slip.
`
`a
`
`a
`
`DETERMINATIONOF VISCOELASTIC FLOW PROPERTIES
`
`I
`
`-r,,,
`
`In Chapter
`in addition to shear stresses, normal
`it was noted that
`a viscotlastic fluid which is
`stresses are generated
`subject
`to steady
`in
`shearing motion.
`[Reiner (42) has discussed
`physical
`reasons
`for
`these
`normal stresses.} The normal stresses y
`and 7., were considered in
`Chapter I
`between two flat plates
`for an element of such a
`fluid located
`which are parallel
`to the plane through the z-z-axes. The relative shearing
`motion between the plates is
`in direction x.
`in addition to the
`required,
`Measurement of
`these normal stresses is
`shearing stresses,
`characterization of
`fluid. A
`a viscoelastic
`for complete
`and comprehensive survey of
`the methods avail-
`very extensive, detailed,
`able for measuring and calculating these normal stresses has been pre-
`review article by White and Metzner
`(53), which should be
`sented in a
`read by anyone faced with this problem. As noted by White and Metzner,
`procedures for measuring normal stresses are
`most of
`the established
`confmed to shear rates below the ranges of engineering interest, which they
`follows.
`define as
`Under laminar flow conditions,
`exemplified by molten
`polymers:
`In various common mixers:
`In boundary layers and turbulent
`now in ducts:
`1000 to 500,000 sec
`In roll and knire coating devices:
`x 10"sec-I
`up to 5
`probably up to to 102or
`In lubricating applications:
`106 sec-I
`The dangers of extrapolation are such that new measuring devices operat-
`rate are needed with some urgency.
`in the above ranges of shear
`ing
`to formulate the normal stresses r,
`7,,, and 7,
`is customary
`It
`isotropic or hydrostatic pressure
`p and corresponding
`the sums of an
`
`100 to 10,000 sec-1
`
`10
`
`to 5000 see
`
`I
`
`2
`
`as
`
`Page 3 of 3