Resistance hydrodynamic

An alternative point of view assumes that each repeat unit of the polymer chain offers hydrodynamic resistance to the flow such that f-the friction factor per repeat unit-is applicable to each of the n units. This situation is called the free-draining coil. The free-draining coil is the model upon which the Debye viscosity equation is based in Chap. 2. Accordingly, we use Eq. (2.53) to give the contribution of a single polymer chain to the rate of energy dissipation ... 

Davies et al. (D9) have recently measured the rates of absorption of various gases into turbulently stirred water both with carefully cleaned surfaces and with surfaces covered with varying amounts of surfactants. That hydrodynamic resistances, rather than monolayer resistances, are predominant in their work is consistent with the high sensitivity of kL to very small amounts of surface contamination and also with the observation that a limit to the reduction in kL is found (D7, D9). This is in agreement with the results of Lindland and Terjesen (L9), who found that after a small concentration of surfactant had been used further additions caused but little change in terminal velocity (L9). 

Dorfman, L.A., Hydrodynamic Resistance and the Heat Loss of Rotating Solids, Olivier and Boyd, London, 1963, pp. 95-97. 

John C. Berg, Andreas Acrivos, and Michel Boudart, Evaporation Convection H. M. Tsuchiya, A. G, Fredrickson, and R. Aiis, Dynamics of Microbial Cell Populations Samuel Sideman, Direct Contact Heat Transfer between Immiscible Liquids Howard Brenner, Hydrodynamic Resistance of Particles at Small Reynolds Numbers... 

In chemical micro process technology with porous catalyst layers attached to the channel walls, convection through the porous medium can often be neglected. When the reactor geometry allows the flow to bypass the porous medium it will follow the path of smaller hydrodynamic resistance and will not penetrate the pore space. Thus, in micro reactors with channels coated with a catalyst medium, the flow velocity inside the medium is usually zero and heat and mass transfer occur by diffusion alone. 

Hydrodynamic Resistance of Particles at Small Reynolds Numbers... 

Unfortunately, the thin lamella resists instantaneous fluid exchange. According to the simple Reynolds parallel-film model QA,15) adopted below, this hydrodynamic resistance is inversely 3... 

For Ca < 0.1 in Figure 7 the critical capillary pressure is also independent of the initial film thickness. In this case, the hydrodynamic resistance to fluid filling or draining is small enough that the film reaches the periodic steady state in less than half a pore length. Figure 7 confirms the trend observed by Khatib, Hirasaki and Falls that P falls with increasing flow rate (5). c... 

In this section we illustrate how the proposed theory for single, surfactant-laden bubbles in a cylindrical tube can be extended to predict the hydrodynamic resistance of bubble trains flowing in porous media. Some of the basic ideas are known (7, 23), so the present discussion is brief. 

In the bypass position, the carrier solution flows through the bypass loop and across the ISFET. The sample is injected into the sampling valve and is introduced into the carrier solution. The bypass loop has a high hydrodynamic resistance and thus the solution proceeds to the detector. The reference electrode is always immersed only in the carrier solution and is electrically connected with the ISFET through the solutioa The apparatus is regularly calibrated by K, Ca and pH standard solutions. 

Model simulating the hydrodynamic properties of a chain macromolecule consisting of a sequence of beads, each of which offers hydrodynamic resistance to the flow of the surrounding medium and is connected to the next bead by a rigid rod which does not. The mutual orientation of the rods is random. 

Hydrodynamic and frictional effects may be described by a Cartesian mobility tensor which is generally a function of all of the system coordinates. In models of systems of beads (i.e., localized centers of hydrodynamic resistance) with hydrodynamic interactions, is normally taken to be of the form... 

In this section, we use the Cartesian force of Section VI to derive several equivalent expressions for the stress tensor of a constrained system of pointlike particles in a flow field with a macroscopic velocity gradient Vv. The excess stress of any system of interacting beads (i.e., point centers of hydrodynamic resistance) in a Newtonian solvent, beyond the Newtonian contribution that would be present at the applied deformation rate in the absence of the beads, is given by the Kramers-Kirkwood expression [1,4,18]... 

Problems encountered with filtration ate that membrane fouhng can occur, which causes a decline in flux with time under constant operating conditions. Furthermore, concentration polarization, the effect that the increased concentration of components on the membrane surface reduces the flux due to the additional hydrodynamic resistance, is observed. This effect can be minimized in cross-flow filtration, by applying high flux rates across the membrane surface (Wang et al, 1979 Lee, 1989). 

Fio. 9. Experimental measurements of CAST soot hydrodynamic resistance factor as a function of Peclet number and aggregate mobility diameter. The continuous lines are plotted using the scaling relation form Eqs. (8) and (9). 

Fig. 24. Experimental determination of the change of (p x during oxidation. At the soot mass load of 1 g/m2 the soot cake starts to vanish and its hydrodynamic resistance starts to increase rapidly.

El perin IT, Smol skii BM, Leventhal LI (1967) Decreasing the hydrodynamic resistence of pipelines Int Chem Eng 7 276... 

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