Kenneth A. Kline

Theory of Simple Deformable Directed Fluids

The governing equations are given for a fluid with deforming microstructure by postulating an energy balance, an entropy production inequality, and a principle of material frame indifference. A canonical form of the energy equation is derived which serves as a guide to define a simple deformable directed fluid. A theory for such fluids is developed.

A spin-vorticity relation for unidirectional plane flows of micropolar fluids

Abstract The field equations of micropolar fluid theory are applied to consider transient unidirectional plane flows. The relative angular velocity is introduced and maximum and minimum principles of parabolic partial differential equations are utilized to establish a spin-vorticity relation which is valid for very general boundary and initial conditions on spin.

Nonsteady Flows of Fluids with Microstructure

The theory of nonsteady flows of fluids with microstructure is summarized. For parallel flows a decomposition of velocity and microstructure spin fields is given and used to reduce the governing equations to two uncoupled parabolic partial differential equations. These equations are solved for the suddenly accelerated plane wall problem. The effects of fluid microstructure on the velocity field, boundary‐layer thickness, and resultant shear stress are examined.

A theory of mixtures with microstructure

ZusammenfassungEine Theorie der Mischungen von Flüssigkeiten mit Mikrostruktur wird von einem Energiepostulat hergeleitet, wobei das Prinzip der Indifferenz des Bezugssystems benutzt wird. Es werden Definitionen für die Wärmeproduktion der Mischung, innere Energie, Wärmeströmung und Spannungen gegeben, welche mit denjenigenTruesdells übereinstimmen.

A Thermodynamical Theory of Fluid Suspensions

A development is given of a thermodynamical theory of fluid suspensions of deformable particles. Assuming particles are spherical when undeformed and become ellipsoidal when sheared, linear constitutive equations are extracted from the general theory and restrictions on the material coefficients which appear in these linear constitutive equations are deduced by thermodynamical considerations. Applying this linear theory to steady shear flow of solutions for which particle interactions are negligible, it is found, solely by use of the thermodynamical restrictions on material coefficients, that the theory qualitatively predicts observed behavior in steady shear flow of dilute solutions of random coiling macromolecules, such as solutions of polyisobutylene. In particular, the resulting expressions for apparent viscosity t21/K and normal stress difference t11 − t22 are exactly those known to characterize experimental results for K≤103sec−1. For low shear rates K, the predicted value for the second normal stre...

The relationship of pressure gradient to blood velocity based on a continuum theory of blood

Abstract We discuss a continuum theory which treats blood as a fluid suspension. This theory allows one to account for the presence of red cells in blood flow and is used in the paper to develop a theoretical relationship of pressure gradient to blood velocity. Non-dimensional hydraulic resistance and inductance are calculated as functions of the volume concentration of cells. These results are compared with Womersleys theory and experimentally determined values.

On continuum theories of suspensions of deformable particles

ZusammenfassungDas vonAllen, DeSilva undKline [1] vorgeschlagene Kontinuumsmodell richtungsorientierter Flüssigkeiten wird auf die TheorieEricksens [2, 3] undHands [4] zurückgeführt. Es wird die Suspension fester Drehkörper in Flüssigkeiten und solche sphärischer Partikel unter elastischer Verformung behandelt.

Nonlinear constitutive equations for directed viscoelastic materials with memory

ZusammenfassungEs werden die nichtlinearen Konstitutionsgleichungenfür ein richtungsorientiertes viskoelastisches Material mit Gedächtnis entwickelt. Die Beziehungen zwischen dieser Theorie und derjenigen der klassischen Elastizität und Viskoelastizität und einige andere Arbeiten auf dem Gebiete der Theorie der richtungsorientierten Medien werden besprochen.

On thermodynamics of directed continuous media

ZusammenfassungDie Thermodynamik der richtungsorientierten Medien wird mit Hilfe der Clausius-Duhem-Ungleichheit und des Prinzips der materiellen Objektivität untersucht. Ein besonderer Fall der Materialsymmetrie wird diskutiert.

Rectilinear shear flow of fluid with interacting deformable substructure

ZusammenfassungDie Grundgleichungen für eine lineare Theorie der Flüssigkeiten mit starker Konzentration suspendierter Partikel werden auf das Problem der geradlinigen Strömung mit Flüssigkeitsreibung zwischen zwei Platten angewandt. Es werden die Geschwindigkeit, die Partikeldeformation und die Spannungen bestimmt.