Sinusoidal time-varying flow

Sinusoidal time-varying (STV) flow demonstrates differences between elastic and viscous properties, and it demonstrates viscoelastic behavior in more complex time-varying flow [14]. 

Cross-sectional view of the Miller-Schrag thin fluid layer (TFL) transducer, used to generate a precise sinusoidally time-varying shear flow for the oscillatory flow birefringence experiment (see Section 9.4.6). 

Kinds oi Inputs Since a tracer material balance is represented by a linear differential equation, the response to anv one kind of input is derivable from some other known input, either analytically or numerically. Although in practice some arbitrary variation of input concentration with time may be employed, five mathematically simple input signals supply most needs. Impulse and step are defined in the Glossaiy (Table 23-3). Square pulse is changed at time a, kept constant for an interval, then reduced to the original value. Ramp is changed at a constant rate for a period of interest. A sinusoid is a signal that varies sinusoidally with time. Sinusoidal concentrations are not easy to achieve, but such variations of flow rate and temperature are treated in the vast literature of automatic control and may have potential in tracer studies. 

Most mathematical models for particle and pollutant transport assume steady flow conditions. However, flow actually varies approximately sinusoidally over time, and breathing fluency ranges from 8 breaths/min for sedentary conditions to 50 breaths/min during sustained work and exercise. 

The first case considered is solute desorption during unconfined compression. We consider a two dimensional plane strain problem, see Fig. 1. A sinusoidal strain between 0 and 15 % is applied at 0.001 Hz, 0.01 Hz, 0.1 Hz and 1 Hz. To account for microscopic solute spreading due to fluid flow a dispersion parameter is introduced. Against the background of the release of newly synthesized matrix molecules the diffusion parameter is set to the value for chondroitin sulfate in dilute solution Dcs = 4 x 10 7 cm2 s-1 [4] The dispersion parameter Dd is varied in the range from 0 mm to 1 x 10 1 mm. The fluid volume fraction is set to v = 0.9, the bulk modulus k = 8.1 kPa, the shear modulus G = 8.9 kPa and the permeability K = lx 10-13m4 N-1 s-1 [14], The initial concentration is normalized to 1 and the evolution of the concentration is followed for a total time period of 4000 s. for the displacement and linear discontinuous. For displacement and fluid velocity a 9 noded quadrilateral is used, the pressure is taken linear discontinuous. 

Thus an approximately sinusoidal flow inside the mock-up could be obtained, with period in the 2 to 10 sec range and amplitude comprised between. 2 and. 5 times the average value. This average value, then, could be varied from 10 to 40 m3/h. 

Temperature modulated DSC uses the heat-flux DSC instrument design and configuration to measure the differential heat flow between a sample and an inert reference material as a function of time. However, in TMDSC a sinusoidal temperature modulation is superposed on the linear (constant) heating profile to yield a temperature programme in which the average sample temperature varies continuously in a sinusoidal manner ... 

As a result of the flow field accelerations and decelerations in pulsatile flows, a special type of boundary layer known as the Stokes layer develops. When the pressure gradient varies sinusoidally in time, as the pressure increases to its maximum, the flow increases, and as the pressure decreases, the flow does too. 

If steady shear flow of a viscoelastic liquid is abruptly halted, the normal stress differences a — azi and shear stress an (Fig, 1 -5). Also, for sinusoidally varying shear strains, each normal stress difference is a sinusoidal function of time, with oscillatory components at twice the frequency of the shear strain about a nonzero mean value. Some of these relations are given in Chapter 3. Other time-dependent experimental patterns of strain or stress history evoke various characteristic nonlinear phenomena. 

Suppose flow rate W2 is varied sinusoidally about a constant value, while the other inlet conditions are kept constant at their nominal values that is, wi(t) = x[(t) = 0. Because wiit) is sinusoidal, the output composition deviation x t) eventually becomes sinusoidal according to Eq. 5-26. However, there is a phase shift in the output relative to the input, as shown in Fig. 14.1, owing to the material holdup of the. tank. If the flow rate W2 oscillates very slowly relative to the residence time t(co 1/t), the phase shift is very small, aiyroaching 0°, whereas the normalized amplitude ratio(A/KA) is very nearly unity. For the case of a low-frequency input, the output is in phase with the input, tracking the sinusoidal input as if the process model were G s) = K. 

The rectification process in terms of input voltage and output current is demonstrated in Figure 18.23. Whereas voltage varies sinusoidally with time (Figure 18.23a), maximum current flow for reverse bias voltage is extremely small in comparison to... 

There are numerous transient shear flows in which y(t) varies in a specific way with time. One of the most frequently used experiments is when y(t) varies sinusoidally with time ... 

Some variation in thickness is always present in continuously extruded products. It may be too small to be of concern for the product application or it may not be measured or measurable with instrumentation in use. However, the result is always thickness that is varying in time periodically or continually (very long period of change.) For periodic variation, the thickness variation will have a wave shape, which may be irregular or regular (e.g., a simple sinusoidal wave shape.) Also, the period of the wave shape or disturbance may be regular or irregular (random.) Observation and analysis of these characteristics of the wave shape can be used to trace the source of the flow disturbances. 

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