Couette method

In the cone and plate rheometer, a cone-shaped bob is placed against a flat plate so that the fluid to be studied may be placed into the gap between the lower face of the cone and the upper face of the plate. Again, in the Searle method, the cone is rotated while in the Couette method the plate turns. In each case, the torque on the cone is measured. Figure 6.5 shows a Searle-type cone and plate arrangement. For this arrangement the shear stress is given by ... 

Joos data on distearoyl lecithin (DSL)-cholesterol mixed films (35) coincide with data from our DPL-cholesterol system in the sense that cholesterol reduced the viscosity of the lecithin film, and the surface viscosity decreased with increasing cholesterol concentrations. However, the comparison and interpretation of surface viscosity data require caution (2,6). For example, in Joos experiments the lipid was distearoyl lecithin (DSL), the subphase was distilled water, phospholipid and cholesterol were premixed, and viscosity was measured by the rotational surface Couette method. By the torsion oscillation method, at all film pressures... 

The ex vivo flow-through couette method provides a very convenient model for assessing the effect of drugs on the thrombogenic process. By directly monitoring the accumulation of radioisotope in the couette device, a direct measure of the kinetics of thrombus accumulation can be obtained. An example of the deposition of platelets on the rod surface after the administration of systemic heparin is shown in Figure 10 (4). In this experiment... 

Couette Flow Simulation. MD typically simulate systems at thermodynamic equilibrium. For the simulation of systems undergoing flow various methods of nonequilibrium MD have been developed (Ifl iZ.). In all of these methods the viscosity Is calculated directly from the constitutive equation. 

The nonequilibrium MD method we employed ( ) is the reservoir method (iff.) which simulates plane Couette flow. The effective viscosity Is calculated from the constitutive relation... 

The shear stress Is uniform throughout the main liquid slab for Couette flow ( ). Therefore, two Independent methods for the calculation of the shear stress are available It can be calculated either from the y component of the force exerted by the particles of the liquid slab upon each reservoir or from the volume average of the shear stress developed Inside the liquid slab from the Irving-Kirkwood formula (JA). For reasons explained In Reference (5) the simpler version of this formula can be used In both our systems although this version does not apply In general to structured systems. The Irvlng-Klrkwood expression for the xy component of the stress tensor used In our simulation Is... 

It was of interest to compare the results obtained with the FRAP technique with those obtained with classical surface rheological techniques. Our detailed knowledge of properties of solutions of /3-lg containing Tween 20 made this an ideal system on which to compare the methods. Firstly, surface shear viscosity measurements were performed on the Tween 20//3-lg system [47] using a Couette-type torsion-wire surface rheometer as described previously [3,48]. All the experiments were carried out at a macroscopic n-tetradecane-water interface at a fixed protein concentration of O.Olmg/ml. In the absence of Tween 20, the surface shear... 

A plot of yapp against 1 / h will then be a straight line with slope 2Vs. This method has been used to measure the slip velocity for polyethylene melts in a sliding plate (plane Couette) rheometer by Hatzikiriakos and Dealy (1991). Analogous methods have been applied to shearing flows of melts in capillaries and in plate-and-plate rheometers (Mooney 1931 Henson and Mackay 1995 Wang and Drda 1996). 

The treatment of applying periodic boundary conditions discussed here is markedly different from that traditionally employed in simulations of planar Couette flow. The PBC method that is commonly used is called the Lees-Edwards boundary condition. In its simplified form applied to cubic boxes, it represents a translation of the image boxes in the y direction, at a rate equal to y. Further details on this method can be found elsewhere. In contrast to the method involving the dynamical evolution of h presented here, the Lees-Edwards method is much harder to develop and implement for noncubic simulation cells. Also, in simulations involving charged particles, the Coulom-bic interaction is handled in both real and recipro l spaces. The reciprocal space vectors k of the simulation cell represented by h can be written " " as follows ... 

Let us start with the case of pure phases, when surfactant is missing and the fluid-liquid interfaces are mobile. Under these conditions, the interaction of an emulsion droplet with a planar solid wall was investigated by Ryskin and Leal, and numerical solutions were obtained. A new formulation of the same problem was proposed by Liron and Barta. The case of a small droplet moving in the restricted space between two parallel solid surfaces was solved by Shapira and Haber. ° These authors used the Lorentz reflection method to obtain analytical solutions for the drag force and the shape of a small droplet moving in Couette flow or with constant translational velocity. 

Although the full Navier Stokes equations are nonlinear, we have studied a number of problems in Chap. 3 in which the flow was either unidirectional so that the nonlinear terms u Vu were identically equal to zero or else appeared only in an equation for the crossstream pressure gradient, which was decoupled from the primary linear flow equation, as in the ID analog of circular Couette flow. This class of flow problems is unusual in the sense that exact solutions could be obtained by use of standard methods of analysis for linear PDEs. In virtually all circumstances besides the special class of flows described in Chap. 3, we must utilize the original, nonlinear Navier Stokes equations. In such cases, the analytic methods of the preceding chapter do not apply because they rely explicitly on the so-called superposition principle, according to which a sum of solutions of linear equations is still a solution. In fact, no generally applicable analytic method exists for the exact solution of nonlinear PDEs. 

Two common methods for measuring viscosity are the cup and bob (Couette) and the tube flow (Poiseuille) viscometers. 

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