Shear fields Couette

When a fluid is subject to a simultaneous Couette shear field and a concentration or temperature gradient, the shear field, being a tensorial quantity, cannot affect vector quantities such as mass or heat currents (Curie s principle). However, when... 

Fig. 1. Transition temperature as a function of by various methods (from ref. 3). Methods (1) shear modulus vs. temperature (2) recoverable strain as a function of temperature (3) recoverable strain as a fimction of time (4) yield stress and (S) stress relaxation. Methods (1) - (5) used a Couette shear field. Method (6) measured stress relaxation using a Pochettino shear field.

Fig. 17. Stress relaxation of the 310,000 polymer, j = 1.26 sec l, Couette shear field.

We wish to study the effects of planar Couette flow on a system that is in the NPT (fully flexible box) ensemble. In this section, we consider the effects of the external field alone on the dynamics of the cell. The intrinsic cell dynamics arising out of the internal stress is assumed implicitly. The constant NPT ensemble can be employed in simulations of crystalline materials, so as to perform dynamics consistent with the cell geometry. In this section, we assume that the shear field is applied to anisotropic systems such as liquid crystals, or crystalline polytetrafluoroethylene. For an anisotropic solid, we assume that the shear field is oriented in such a way that different weakly interacting planes of atoms in the solid slide past each other. The methodology presented is quite general hence it is straightforward to apply for simulations of shear flow in liquids in a cubic box, as well. 

Figure 13 Minimum imaging under cell representations where cases A and B are equivalent. The box in B is skewed owing to the planar Couette hear field, and resetting it to representation A is consistent with the dynamics, h is the matrix representing the box size and shape, y is the shear rate, and t denotes time.

Williams and Janssen (20) studied the behavior of droplets in a simple shear flow in the presence of a protein emulsifier. The effect of two structurally diverse protein emulsifiers, P-lactoglobulin and P-casein, upon the breakup behavior of a single aqueous droplet in a Couette flow field has been studied over a wide range of protein concentrations. It was found that P-casein and low concentrations of P-lactoglobulin cause the droplets to be at least as stable as expected from conventional theories based on the equilibrium interfacial tension. In such cases the presence of the emulsifier at the deforming interface is thought to enhance the interfacial elasticity. This effect can be characterized by... 

Fig. 9. (a) Diagrammatic representation of a couette shear cell, (b) The resultant geometry of the shear field, where the x-axis is the flow direction, they-axis is the shear gradient and the z-axis is the vorticity direction. Note that the incident radiation is also along the y-axis, and the measured scattering intensity is in the flow-vorticity plane. 

Casamitjana [15] discussed and predicted experimental data, using latex particles placed in couette flow system. A population balance was considered with the introduction of two parameters called effective probabdity for collision to count aggregation and break up coefficient for shear fragmentation. Both parameters were investigated under different shear fields and volume fraction of the particles. 

If each of the three epsilons are zero we recover the boundary conditions of planar Couette (shear) flow. For y = 0, there are three basic elongation flow fields defined as follows if one of the epsilons is also zero, the flow field is referred to as planar elongation flow if one of the epsilons is negative while the other two are positive and equal, the flow field is referred to as biaxial stretching flow and if one of the epsilons is positive while the other two are negative and equal, the flow field is referred to as uniaxial stretching flow. 

One characteristic of shear banded flow is the presence of fluctuations in the flow field. Such fluctuations also occur in some glassy colloidal materials at colloid volume fractions close to the glass transition. One such system is the soft gel formed by crowded monodisperse multiarm (122) star 1,4-polybutadienes in decane. Using NMR velocimetry Holmes et al. [23] found evidence for fluctuations in the flow behavior across the gap of a wide gap concentric cylindrical Couette device, in association with a degree of apparent slip at the inner wall. The timescale of these fluctuations appeared to be rapid (with respect to the measurement time per shear rate in the flow curve), in the order of tens to hundreds of milliseconds. As a result, the velocity distributions, measured at different points across the cell, exhibited bimodal behavior, as apparent in Figure 2.8.13. These workers interpreted their data... 

Common geometries used to make viscosity measurements over a range of shear rates are Couette, concentric cylinder, or cup and bob systems. The gap between the two cylinders is usually small so that a constant shear rate can be assumed at all points in the gap. When the liquid is in laminar flow, any small element of the liquid moves along lines of constant velocity known as streamlines. The translational velocity of the element is the same as that of the streamline at its centre. There is of course a velocity difference across the element equal to the shear rate and this shearing action means that there is a rotational or vorticity component to the flow field which is numerically equal to the shear rate/2. The geometry is shown in Figure 1.7. 

It is also possible to calculate the shear viscosities and the twist viscosities by applying the SLLOD equations of motion for planar Couette flow, Eq. (3.9). If we have a velocity field in the x-direction that varies linearly in the z-direction the velocity gradient becomes Vu=ye ej, see Fig. 3. Introducing a director based coordinate system (Cj, C2, 63) where the director points in the e3-direction and the angle between the director and the stream lines is equal to 0, gives the following expression for the strain rate in the director based coordinate system. 

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