Resistive force theory

They could not use the oar principle because the oars would not slip by the water on the return stroke. Not only would rowing be harder, but it would also not go anywhere. Thus, bacteria have devised a flagellum that rotates at its base like a miniature propeller (Bonner and Horn, 2000). Viscous fluid resistive force theory shows how this rotational motion can be translated into the forward motion of the microbe. 

Hydrodynamic Friction of a Filament Resistive Force Theory... 

Dynamic equations for the elastic filament need a proper account of the frictional forces with the surrounding fluid. Within resistive force theory, they are proportional to the local velocities of the filaments. Furthermore, inthelow Reynolds number limit they have to balance the bending and stretching forces introduced in Eqs. (9.5) and (9.9). Using the two friction coefficients per unit length, Yy and Yj., one thus arrives at the highly nonlinear dynamic equations ... 

Here, the filament is modeled by a bead-spring configuration that additionally resists bending like a worm-like chain (81). TTius, each bead in the filament experiences a force caused by stretching and bending as described in Eq. (9.12). This offers an approach to treat hydrodynamic friction of the filament with the surrounding fluid beyond resistive force theory. Each bead moving under the influence of a force initiates a flow field that influences the motion of other beads and vice versa, so a complicated many-body problem arises. At low Reynolds number the flow field ( , t) around the spheres is described by the Stokes equations and the incompressibiUty condition ... 

Substituting the resistance force into equation 51 and expressing F and V in terms of d, the basic equation of sedimentation theory is obtained ... 

Resistance functions have been evaluated in numerical compu-tations15831 for low Reynolds number flows past spherical particles, droplets and bubbles in cylindrical tubes. The undisturbed fluid may be at rest or subject to a pressure-driven flow. A spectral boundary element method was employed to calculate the resistance force for torque-free bodies in three cases (a) rigid solids, (b) fluid droplets with viscosity ratio of unity, and (c) bubbles with viscosity ratio of zero. A lubrication theory was developed to predict the limiting resistance of bodies near contact with the cylinder walls. Compact algebraic expressions were derived to accurately represent the numerical data over the entire range of particle positions in a tube for all particle diameters ranging from nearly zero up to almost the tube diameter. The resistance functions formulated are consistent with known analytical results and are presented in a form suitable for further studies of particle migration in cylindrical vessels. 

There is nothing in the free electron theory to explain the existence of the resisting force or the relaxation time. It is usually described as coming from collisions between the electrons and the atoms, and thus cannot properly be explained unless we take the atoms into account specifically. We can see something about the mechanism of the collisions, however, by considering the motion of the electrons in a momentum space, similar to that of Chap. IV, Sec. 1, in which px, pvt pM are plotted as variables, and each electron is represented by a point. As we saw in that... 

From a mechanistic perspective, what transpires in the context of all of these strengthening mechanisms when viewed from the microstructural level is the creation of obstacles to dislocation motion. These obstacles provide an additional resisting force above and beyond the intrinsic lattice friction (i.e. Peierls stress) and are revealed macroscopically through a larger flow stress than would be observed in the absence of such mechanisms. Our aim in this section is to examine how such disorder offers obstacles to the motion of dislocations, to review the phenomenology of particular mechanisms, and then to uncover the ways in which they can be understood on the basis of dislocation theory. 

The resistance to nucleation is associated with the surface energy of forming small clusters. Once beyond a critical size, the growth proceeds with the considerable driving force due to the supersaturation or subcooling. It is the definition of this critical nucleus size that has consumed much theoretical and experimental research. We present a brief description of the classic nucleation theory along with some examples of crystal nucleation and growth studies. 

The separation of two surfaces in contact is resisted by adhesive forces. As the nonnal force is decreased, the contact regions pass from conditions of compressive to tensile stress. As revealed by JKR theory, surface tension alone is sufficient to ensure that there is a finite contact area between the two at zero nonnal force. One contribution to adhesion is the work that must be done to increase surface area during separation. If the surfaces have undergone plastic defonnation, the contact area will be even greater at zero nonnal force than predicted by JKR theory. In reality, continued plastic defonnation can occur during separation and also contributes to adhesive work. 

HARRIOTT 25 suggested that, as a result of the effects of interfaeial tension, the layers of fluid in the immediate vicinity of the interface would frequently be unaffected by the mixing process postulated in the penetration theory. There would then be a thin laminar layer unaffected by the mixing process and offering a constant resistance to mass transfer. The overall resistance may be calculated in a manner similar to that used in the previous section where the total resistance to transfer was made up of two components—a Him resistance in one phase and a penetration model resistance in the other. It is necessary in equation 10.132 to put the Henry s law constant equal to unity and the diffusivity Df in the film equal to that in the remainder of the fluid D. The driving force is then CAi — CAo in place of C Ao — JPCAo, and the mass transfer rate at time t is given for a film thickness L by ... 

These relations between the various coefficients are valid provided that the transfer rate is linearly related to the driving force and that the equilibrium relationship is a straight line. They are therefore applicable for the two-film theory, and for any instant of time for the penetration and film-penetration theories. In general, application to time-averaged coefficients obtained from the penetration and film-penetration theories is not permissible because the condition at the interface will be time-dependent unless all of the resistance lies in one of the phases. 

The liquid state is a condensed state, so each molecule is always interacting with a group of neighbours although diffusing quite rapidly. As a result, although momentum through a shear plane still occurs, it is a small contribution when compared to the frictional resistance of the molecules in adjacent layers. It is the nature of this frictional resistance that we must now address and it will become clear that it arises from the intermolecular forces. The theories of the viscosity of liquids are still in an unfinished state but the physical ideas have been laid down. The first... 

One of the limitations of this model is that the confinement of water molecules within clusters precludes its use within the context of water transport simulation because cluster-connective hydration structure is absent. Furthermore, water activity and contractile modulus are macroscopic based concepts whose application at the nanoscopic level is dubious. P is represented by a function borrowed from macroscopic elastic theory that contains E, and there is no microstructure-specific model for the resistance to deformation that can be applied to Nation so that one is forced to use experimental tensile moduli by default. 

OXYGEN, OXIDES 0X0 ANIONS Vancomycin-resistant enterococci, d-ALANYL-d-ALANINE LIGASE VAN DER WAALS FORCES VANT HOFF RELATIONSHIP COLLISION THEORY ARRHENIUS LAW TRANSITION-STATE THEORY TEMPERATURE DEPENDENCE VANT HOFF S LAWS VARIANCE... 

Variable one of any number of factors that change and may influence an observation or experimental outcome Viscosity the resistance to flow Vitalism theory that a vital force associated with life was associated with all organic substances... 

English theory of gyroscopic projectile flight was modified to take into account the variation of air resistance and the moment of this force with the "yaw or obliqueness of a projectile in flight (Refs 1 8c 2)... 

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