Hydrodynamic friction

Describe the reasons for hydrodynamic friction. What is the physical significance of the friction factor What are its units ... 

There have been several other theoretical studies by different authors [144, 145,156,163] where the frequency-dependent friction was modeled by using the modified version of the generalized hydrodynamic expression [23, 165]. These theories failed to reproduce the experimental results at certain limits. Barbara and coworkers attributed this failure of the G-H theory to the nonavailability of a reliable frequency-dependent friction and called for the use of a friction better than the hydrodynamic friction. 

This is Stokes5 law of hydrodynamic friction. Equating the two expressions leads to... 

This discrepancy can be due to a breakdown in the hydrodynamics friction law, Eq. (11.45), i.e., Stokes law, and/or a breakdown of the basic assumptions of Kramers theory. As we will see in the following section, a problem with Kramers theory is that the Langevin equation does not provide a sufficiently accurate description of the dynamics associated with the reaction coordinate. 

We have observed similar effects in the TREPR spectra of the polymeric radical of poly(adamantyl methacrylate) (PAMA, spectrum not shown). Earge ester side chains such as the adamantyl and fluorinated alkyl groups experience a larger amount of hydrodynamic friction than do smaller side chains such as methyl and ethyl groups. ... 

Here, shows the hydrodynamic friction-resistance coeffi-... 

According to the stochastic theory (Sec. 3.1.3), the hydrodynamic friction should influence mainly the pre-exponential factor of the rate constant. However, ions studied differ considerably in the standard potential difference which con-... 

Fig. 21). The negatively charged DLPE monolayer accelerates the transfer of the former ion and reduces appreciably the transfer of the latter ion. The effect is reversed in the case of a positively charged DLPE monolayer. The authors concluded that the ion permeability is primarily determined by the hydrodynamic friction and the double layer effect arising from the sign and density of the surface charge of adsorbed phospholipid molecules. 

Figure 4. Schematic of the effect of viscosity and sliding speed on hydrodynamic friction. W is the normal load (44).

In the previous sections a model of the frequency-dependent collisional friction has been derived. Because the zero-frequency friction for a spherical particle in a dense fluid is well modeled by the Stokes-Einstein result, even for particles of similar size as the bath particles, there has been considerable interest in generalizing the hydrodynamic approach used to derive this result into the frequency domain in order to derive a frequency-dependent friction that takes into account collective bath motions. The theory of Zwanzig and Bixon, corrected by Metiu, Oxtoby, and Freed, has been invoked to explain deviation from the Kramers theory for unimolec-ular chemical reactions. The hydrodynamic friction can be used as input in the Grote-Hynes theory [Eq. (2.35)] to determine the reactive frequency and hence the barrier crossing rate of the molecular reaction. However, the use of sharp boundary conditions leads to an unphysical nonzero high-frequency limit to Ib(s). which compromises its utility. 

It should be noted, however, that for molecular species of geometries other than spheres, different approximations are needed to describe the hydrodynamic frictional coefficient, / [8]. Since there is a relationship between rg and the effective molecular size and shape of the molecular species, it is clear that diffusion coefficients are sensitive to the structural properties and aggregation modes of these species. Therefore, the diffusion coefficient can be used to probe binding phenomena and intermolecular interactions [10, 11]. 

A recent study showed that under low-load conditions and with ultra-smooth surfaces, lyophilic friction modifiers can influence hydrodynamic friction by inducing... 

Introducing the hydrodynamic friction coefficients f = /iwcw /p = /pwcw, we may express the ionic velocities in the form... 

The weaker dependence is completely unexpected and contradicts the common view that hydrodynamic friction force drives CST and chain fracture. Nguyen and Kausch [108] ascribed (10) to the intramolecular friction (so-called internal viscosity ) between chain segments in the coiled part in FTF. Unlike the internal viscosity depends on strain rate and could reach much higher values than... 

In this case, perhaps unexpectedly, the TRIBO 2000-1 material shows both a higher hydrodynamic friction and a deviation with increasing velocity when compared with TRIBO 2000 and EKasic D. 

If the electric field is applied in a solution, there is force acting on a charged object, which will accelerate the charged object. Hydrodynamic friction is counteracting the force of the electric field. The hydrodynamic friction is proportional to the velocity, and the friction coefficient according to Einstein s equation can be determined from the diffusion coefficient [23]. Eventually both forces will be balanced and the object/molecule will move with a constant velocity. This steady state is reached very quickly on the time scale of the PEG NMR experiment, which is on the order of tens of milliseconds. Therefore it is justified to assume this force balance for the entire experiment and to calculate from the force balance the effective number of charges per molecule or complex [22]. 

---