Response to Flow

The configurational response to flow depends upon which of the normal modes interact frictionally with the flow field. In simple shear the distribution envelope in the flow direction alone is altered, and only the N normal modes associated with the flow direction are active. The polymer contribution to the shear relaxation modulus for a system with v chains per unit volume is  

The validity of Eqs.(4.10)(4.12) probably extends well beyond the Rouse model itself [characterized by the specific set of rt values in Eq. (4.5)1 and it seems likely that they will apply, at least for small disturbances, whenever the elements supporting the stress are joined by sufficiently flexible connectors and configurational relaxation is driven by simple Brownian diffusion. One might speculate further that these same forms would apply even in concentrated systems, with Eq.(4.10) expressed in a somewhat more general form because of intermolecular interactions  

13) NT is the total number of internal degrees of freedom per unit volume which relax by simple diffusion (NT — 3vN for dilute solutions), and t, is the relaxation time of the ith normal mode (/ = 1,2,3NT) for small disturbances. Equation (4.13), together with a stipulation that all relaxation times have the same temperature coefficient, provides, in fact, the molecular basis of time-temperature superposition in linear viscoelasticity. It also reduces to the expression for the equilibrium shear modulus in the kinetic theory of rubber elasticity when tj = oo for some of the modes. 

Zimm 100) has extended the Rouse model to allow for intramolecular hydro-dynamic interaction, i.e., changes in medium velocity near each bead caused by the flow disturbance from other beads on the same chain. The Oseen approximation, evaluated with the beads located at their mean equilibrium positions, was used to estimate the velocity disturbances. The intensity of the disturbance depends on the parameter h  

Note that h is proportional to n1/2 in 0-solvents, and thus to N112. For 0 = 0 the flow disturbance is zero, the chain is said to be free draining, and the original Rouse model is recovered. For hP, flow in the coil interior is presumed to be substantially reduced, the chain is frequently said to behave as an impenetrable coil, and the Zimm model is obtained. Equations (4.10-4.12) continue to apply for all values of h, although the distribution of relaxation times depends on h. Some results for the two limiting cases and large N are  

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The behavior of the animal in response to flow is important, not just the flows themselves. An animal searching for the source of an odor moves in the direction of increasing stimulus intensity and stays within the boundaries of the plume. If an animal needs to sample odor in turbulence frequently, it may have to reduce speed, to untenable levels in the case of moths or birds, or to an energetically... 

These two types of detector1 have very different responses to flow Ichanges, as just suggested. Consider an extreme case where the flow in... 

Modulation of the rotation frequency about gives a response of the velocity component normal to the electrode, which can be obtained by a series expansion in the dimensionless variable pScl/3 where p = (w/fl0). This leads to an expression for the variation of the concentration, or concentration gradient, at the interface, and hence, by way of consideration of the equivalent circuit of the interface, to an expression for the modulated potential or current in response to flow modulation. 

Both these models find their basis in network theories. The stress, as a response to flow, is assiimed to find its origin in the existence of a temporary network of junctions that may be destroyed by both time and strain effects. Though the physics of time effects might be complex, it is supposed to be correctly described by a generalized Maxwell model. This enables the recovery of a representative discrete time spectrum which can be easily calculated from experiments in linear viscoelasticity. 

Al borate PC/ABS silane improved adhesion and orientation change due to response to flow 43... 

When a polymer chain stretches, entropy tends to return the coil to its equilibrium configuration, leading to an elastic restoring force. Thus, elastic stresses are generated as the polymer chain stretches and relaxes in response to flow. A liquid exhibiting both elastic and viscous stresses is viscoelastic. We note that the ratio of a viscosity r/ to an elastic modulus G yields a characteristic relaxation time X rj/G characterizing the memory of a fluid of its past deformation history or the timescale for a stretched polymer chain to relax toward equilibrium. 

Be sure the feed is rqrresentative and does not change during the test. Normal bulk measurements such as pH, temperature, viscosity, and concentration may not be sufficient, since the menibrane may inferact with the stream fai unforeseen ways. Periodically returning to the starting conditions with a clean membrane to see that flux, retention, and response to flow are unchanged is a wise precaution. Save the permeate and use it to redilute a concentrated sample. 

In a subsequent publication the authors concentrated on the transient rheology/ morphology response to flow [262]. For affine deformation at k > 2Kcnt the authors... 

The fully implicit BI method was used by Anderson [45, 46] to simulate the steady state current response to flow rate within a channel flow cell. Subsequently, this was implemented by Fisher and Compton [47] to evaluate the time-dependent convective-diffusion problem... 

Figure 5 Sensor response to flow on/flow off cycles with a Cytosensor chamber loaded with acetyl cholinesterase coated beads. The flow medium contains 8 mM acetylcholine.

Ando, J. et al.. Wall shear stress rather than shear rate regulates cytoplasmic Ca+-F responses to flow in vascular endothelial cells, Biochem. Biophys. Res. Commun., 190,716,1993. 

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