Effect of the shear stress

The effect of the shear stress on the surface of the liquid layer will be small if ... 

If the effects of the shear stress are small, this can be approximated by ... 

Consider laminar film condensation on a vertical plate when the vapor is flow ing parallel to the surface in a downward direction at velocity, V. Assume that a turbulent boundary layer is formed in the vapor along the outer surface of the laminar liquid film. Determine a criterion that will indicate when the effect of the shear stress at the outer edge of the condensed liquid film on the heat transfer rate is less than 59c. Assume that pv [Pg.602]

As for the effects of the shear stress, it was shown by a Synchrotron radiation X-ray diffraction study that transformations from metastable to more stable forms, especially to Form V, were accelerated by high shear stress (110). Figure 25 shows the time variation of relative intensities of X-ray diffraction peaks of CB crystals formed after cooling from 50°C to 18°C at a rate of 3°C/min. In the case of no shear. Form III appeared at first after the temperature reached at 18°C, and then Form IV crystallized at the expense of Form III. On the other hand, applying the shear stress at 1440 s caused accelerated transformation from Form III to Form V, without the occurrence of Form IV. The same result was observed with lower shear rates (19), and the persistence time of Form III was reduced as the shear rate was increased. Mazaanti et al also observed that the orientation of CB crystals are aligned with the shear flow (110). These results indicated that temperature and shear treatments are the tools for tailoring the desired polymorphic structures of fats. 

As mentioned above, when the transverse dimensions of the beam are of the same order of magnitude as the length, the simple beam theory must be corrected to introduce the effects of the shear stresses, deformations, and rotary inertia. The theory becomes inadequate for the high frequency modes and for highly anisotropic materials, where large errors can be produced by neglecting shear deformations. This problem was addressed by Timoshenko et al. (7) for the elastic case starting from the balance equations of the respective moments and transverse forces on a beam element. Here the main lines of Timoshenko et al. s approach are followed to solve the viscoelastic counterpart problem. 

The detrimental effect of the shear stress component and thus of the associated biaxiality ratio A2 is illustrated also in Figures 7.7—7.9. Figure 7.7 shows fatigue data obtained from in-phase bending—torsion tests on glass/epoxy filament-wound... 

Chimg et al. demonstrated the effect of the shear stress working from the spinneret wall to the outermost surface of the spinning dope [58]. The hollow fibers were spun with no air gap so that the surface morphology could be frozen in the coagulation bath immediately after the fibers extruded from the spinneret. Then, the AFM image of the outer surface of polysulfone (PSf) hollow fibers was obtained. 

Qi, Li Feke, DL. Manas-Zloczower Effect of the shear stress on the Carbon Black Dispersion in Liquid Medium. Powder Technology, 1997, Vol. 92,>fo 1,17-24. 

Calculating the shear stress at the wall, were obtained values which confirm the rapport of the two shear stresses, (Table 3.84). Superposing the effect of the shear stress at the eapillary wall on the changes produeed in the entrance zone, there results a series of phenomena, whieh determine the characteristies of the extruded polymer. 

Fig. 17. Effect of mean shear stress on the fatigue strength of EN25 for life of 10 cycles (92). To convert MPa to psi, multiply by 145.

Composite materials typically have a low matrix Young s modulus in comparison to the fiber modulus and even in comparison to the overall laminae moduli. Because the matrix material is the bonding agent between laminae, the shearing effect on the entire laminate is built up by summation of the contributions of each interlaminar zone of matrix material. This summation effect cannot be ignored because laminates can have 100 or more layersi The point is that the composite material shear moduli and G are much lower relative to the direct modulus than for isotropic materials. Thus, the effect of transverse shearing stresses. 

The effect of driving shear stresses on the dislocations are studied by superimposing a corresponding homogeneous shear strain on the whole model before relaxation. By repeating these calculations with increasing shear strains, the Peierls barrier is determined from the superimposed strain at which the dislocation starts moving. 

The viscosity of the polymer or mix also controls the level of the shear stresses developed in the nip region. The level of temperature in the rubber mass, by its effect on viscosity, will also influence the level of shear stresses developed. 

Cross-flow filtration systems utilize high liquid axial velocities to generate shear at the liquid-membrane interface. Shear is necessary to maintain acceptable permeate fluxes, especially with concentrated catalyst slurries. The degree of catalyst deposition on the filter membrane or membrane fouling is a function of the shear stress at the surface and particle convection with the permeate flow.16 Membrane surface fouling also depends on many application-specific variables, such as particle size in the retentate, viscosity of the permeate, axial velocity, and the transmembrane pressure. All of these variables can influence the degree of deposition of particles within the filter membrane, and thus decrease the effective pore size of the membrane. 

The following measurements were made on the inner cylinder of a coaxial cylinders viscometer having inner and outer diameters of 24 mm and 26 mm, and an effective cylinder length of 35 mm. Using these data, determine the values of the shear stress, shear rate and apparent viscosity of the sample. 

For convenience and simplicity, polymers have generally been considered to be isotropic in which the principle force is shear stress. While such assumptions are acceptable for polymers at low shear rates, they fail to account for stresses perpendicular to the plane of the shear stress, which are encountered at high shear rates. For example, an extrudate such as the formation of a pipe or filament expands when it emerges from the die in what is called the Barus or Weissenberg effect or die swell. This behavior is not explained by simple flow theories. 

However, if the answer to this first question is yes there is an effect of fluid shear stresses on the process, then there needs to have a second question asked. Is it at the micro-or macroscale that the process participants are involved And, of course, it may be both. 

The rotational speed, which only appeared as a parameter in the linear Eqs. 7.1 and 7.4, forms now an independent dimensionless parameter in the form of the Deborah number n . While the dimensionless pressure generation and dimensionless energy only depend on the kinematic parameter of flow for Newtonian liquids, the dimensionless revolution speed appears as an additional influencing variable for shear thinning. This is plausible if we consider that the rotational speed is a measure of the shear stresses on the material, and thus influences the effective viscosity of the material. It is also to be expected that the interaction will assume a non-linear form since the flow curve is already non-linear. 

Qualitatively, the same effect has been observed in ternary solutions of p- PODZ, PA-6 and sulfuric acid [104]. At room temperature the quiescent system displays phase separation above 14% of total polymer concentration. Above the critical concentration shearing of initially biphasic solutions led to transparent one-phase systems. After cessation of the shear stress the biphasic morphologies recovered. 

An empirical method to cope with the effect of molecular-weight distribution was proposed by Van der Vegt (1964). Fie determined viscosities of several grades of polypropylenes with different Mw and MMD as a function of the shear stress ash- A plot °f V/Vo vs. the product tvdv = t1wQ proved to give practically coinciding curves. This generalised curve has been reproduced in Fig. 15.21. 

Newtonian shear flow of polymer melts is a stable process. This means that small disturbances in the flow conditions, caused by external effects, are readily suppressed. As the rate of shear increases, however, the elastic response of the melt becomes more pronounced relative to the viscous response. In other words, components of the stress tensor in directions different from the direction of the shear stress become more important. As a result, small disturbances are not so readily compensated and may even be magnified. 

The first correction is for entrance and end effects and was suggested by Bagley (1957). Due to these effects, in the calculation of the shear stress at the wall one has to use an effective flow length Le(p. 

Mammalian cell culture processes must be tightly controlled to attain acceptable cell density and maximize product titer. Slight deviations in pH, temperature, nutrient, or catabolite concentrations can cause irreparable damage to the cells. This section covers the effects of pH, shear stress, catabolite, and carbon dioxide accumulation on cell growth and product formation, and discusses the importance of controlling glucose and glutamine concentrations... 

A study of the flow of a polyhedral foam in a regime of slip at the tube walls has been conducted [39]. It has been established that the rise in the dynamic viscosity of the foaming solution leads to diminishing the flow rate but to a much lesser extent at t0 = 1.25 Pa. Thus, a two fold increase in viscosity causes a 1.3 times decrease in the flow rate, while a 6 times increase in the dynamic viscosity only a 2.23 times decrease. This is probably related to the expanding of the effective thickness of the liquid layer 8 (ca. 3 times). The transition from plug flow (slip regime) to shear flow occurs at To = 9-10 Pa. This value of the shear stress is much smaller than the one obtained from Princen s formula for a two-dimensional foam (Eq. (8.18)) at a given expansion ratio and correlates well with To calculated from Eq. (8.24) and the experimental data of Thondavald and Lemlich [23],... 

Now the differential viscosity. In the following we assume that the shear rate is high, so that the effect of the yield stress is unimportant. When you squeeze a tube of toothpaste, you increase the pressure inside. We have estimated the force exerted by clenching a personal weighing scale ... 

Curve 1 in Fig. 1 under low rotor r.p.m. corresponds to the case when the rate of the stress buildup under the effect of deformation is commensurate with the rate of their relaxation. The development of time-delayed elastic deformations determines the final rate of attainment of the steady-state regime of viscous flow, under which the stationary value of the shear stress is recorded. Starting with the moment of time t, the stress will increase and the period of the viscous-plastic state comes to an end. 

The distribution of particle orientations near a capillary wall is restricted by the presence of such a rigid body (the wall) which introduces a preferred direction in an otherwise isotropic medium. As a consequence the rate of shear near the wall may not be a function of the shearing stress alone and there may be an effective velocity of slip at the wall. This complication however is usually ignored in routine work. 

For aqueous solutions, say, at 25°C the lower limit of the critical Reynolds number will not be reached as long as V/Rt is well below 30. Thus for all practical purposes this complication will not arise in routine viscosity measurements. On the other hand if the non-Newtonian viscosity measurements are extended to a very high range of the shearing stress, it is desirable to check the possibility of this effect. 

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