Hydrodynamics forces

If, however, the reservoir pressure drops below the bubble point, then gas will be liberated in the reservoir. This liberated gas may flow either towards the producing wells under the hydrodynamic force imposed by the lower pressure at the well, or it may migrate... 

The cleaning process proceeds by one of three primary mechanisms solubilization, emulsification, and roll-up [229]. In solubilization the oily phase partitions into surfactant micelles that desorb from the solid surface and diffuse into the bulk. As mentioned above, there is a body of theoretical work on solubilization [146, 147] and numerous experimental studies by a variety of spectroscopic techniques [143-145,230]. Emulsification involves the formation and removal of an emulsion at the oil-water interface the removal step may involve hydrodynamic as well as surface chemical forces. Emulsion formation is covered in Chapter XIV. In roll-up the surfactant reduces the contact angle of the liquid soil or the surface free energy of a solid particle aiding its detachment and subsequent removal by hydrodynamic forces. Adam and Stevenson s beautiful photographs illustrate roll-up of lanoline on wood fibers [231]. In order to achieve roll-up, one requires the surface free energies for soil detachment illustrated in Fig. XIII-14 to obey... 

Horn R G ef a/1996 The effect of surface and hydrodynamic forces on the shape of a fluid drop approaching a soiid surface J. Rhys. Condens. Matters 9483-90... 

The surface mean diameter is the diameter of a sphere of the same surface area-to-volume ratio as the actual particle, which is usually not a perfect sphere. The surface mean diameter, which is sometimes referred to as the Sauter mean diameter, is the most useful particle size correlation, because hydrodynamic forces in the fluid bed act on the outside surface of the particle. The surface mean diameter is directly obtained from automated laser light diffraction devices, which are commonly used to measure particle sizes from 0.5 to 600 p.m. X-ray diffraction is commonly used to measure smaller particles (see Size TffiASURETffiNT OF PARTICLES). 

Equations 3 to 7 indicate the method by which terminal velocity may be calculated. Erom a hydrodynamic force balance that considers gravity, buoyancy, and drag, but neglects interparticle forces, the single particle terminal velocity is... 

The ends of the knives can be square, beveled, or rounded. If the end is square and parallel to the web, if the upstream face is perpendicular to the web, and if there is a fixed gap between the end of the knife and the web, then the wet coverage is exacfly one-half the gap. On the other hand, if there is a low angle in a converging section of the knife or of the blade, leading up to a tight gap, as there is for many knives and for all bent blades, then strong hydrodynamic forces build up and tend to lift the knife or blade away from the web. This forces more fluid under the knife or blade, so that the coated thickness is greater than half the gap. 

The solids concentration ultimately will reach a level at which particle descent is restrained not only by hydrodynamic forces but also partially by mechanical support from the particles below therefore. 

Short-time Brownian motion was simulated and compared with experiments [108]. The structural evolution and dynamics [109] and the translational and bond-orientational order [110] were simulated with Brownian dynamics (BD) for dense binary colloidal mixtures. The short-time dynamics was investigated through the velocity autocorrelation function [111] and an algebraic decay of velocity fluctuation in a confined liquid was found [112]. Dissipative particle dynamics [113] is an attempt to bridge the gap between atomistic and mesoscopic simulation. Colloidal adsorption was simulated with BD [114]. The hydrodynamic forces, usually friction forces, are found to be able to enhance the self-diffusion of colloidal particles [115]. A novel MC approach to the dynamics of fluids was proposed in Ref. 116. Spinodal decomposition [117] in binary fluids was simulated. BD simulations for hard spherocylinders in the isotropic [118] and in the nematic phase [119] were done. A two-site Yukawa system [120] was studied with... 

The hydrodynamic forces are usually described by a linear relation between drag resistance and relative fluid velocity ... 

Due to the gradual decay of the hydrodynamic interaction (Eq. 27), the extra velocity component at bead i results from the motion of all the remaining beads and it is presumed that vj depends linearly on the hydrodynamic forces acting on these beads ... 

The electroviscous effect present with solid particles suspended in ionic liquids, to increase the viscosity over that of the bulk liquid. The primary effect caused by the shear field distorting the electrical double layer surrounding the solid particles in suspension. The secondary effect results from the overlap of the electrical double layers of neighboring particles. The tertiary effect arises from changes in size and shape of the particles caused by the shear field. The primary electroviscous effect has been the subject of much study and has been shown to depend on (a) the size of the Debye length of the electrical double layer compared to the size of the suspended particle (b) the potential at the slipping plane between the particle and the bulk fluid (c) the Peclet number, i.e., diffusive to hydrodynamic forces (d) the Hartmarm number, i.e. electrical to hydrodynamic forces and (e) variations in the Stern layer around the particle (Garcia-Salinas et al. 2000). 

Bonaccurso, E., Kappl, M., Butt, H. )., Hydrodynamic force measurements boundary slip of water on hydrophilic surfaces and electrokinetic effects, Phys. Rev. Lett. 88 (2002) 76103-76106. 

Potential Analysis Method for Hydrodynamic Force Measurement... 

From the theoretical calculations of the hydrodynamic force, we can estimate the distance dependences of the interaction coefficients in the x- and y-directions. According to ref [29], the interaction coefficients P /y and Py/y are calculated from the following approximated equations, assuming that the two particles are spherical in shape with the same diameter. 

We introduced the technique for measuring the weak interaction forces acting between two particles using the photon force measurement method. Compared with the previous typically used methods, such as cross-correlation analysis, this technique makes it possible to evaluate the interaction forces without a priori information, such as media viscosity, particle mass and size. In this chapter, we focused especially on the hydrodynamic force as the interaction between particles and measured the interaction force by the potential analysis method when changing the distance between particles. As a result, when the particles were dose to each other, the two-dimensional plots of the kinetic potentials for each particle were distorted in the diagonal direction due to the increase in the interaction force. From the results, we evaluated the interaction coeffidents and confirmed that the dependence of the... 

Bartlett, P., Henderson, S. I. and Mitchell, S. J. (2001) Measurement of the hydrodynamic forces between two polymer-coated spheres. Philos. Trans. R. Soc. London, Ser.A, 359, 883-895. 

The hydrodynamic forces acting on the suspended colloids determine the rate of cake buildup and therefore the fluid loss rate. A simple model has been proposed in literature [907] that predicts a power law relationship between the filtration rate and the shear stress at the cake surface. The model shows that the cake formed will be inhomogeneous with smaller and smaller particles being deposited as the filtration proceeds. An equilibrium cake thickness is achieved when no particles small enough to be deposited are available in the suspension. The cake thickness as a function of time can be computed from the model. 

The rate of separation of the fragments depends on the functions A r), C(r), Fc> and the fragmentation number, while the rate of rotation depends only on the function B(r). Further, it is apparent that the separation between the fragments increases only when the hydrodynamic force exceeds the binding physicochemical force. The pair of fragments rotates as a material element in an apparent flow with an effective velocity gradient tensor... 

Hydrodynamic Forces Necessary To Release Non-Brownian Particles Attached to a Surface... 

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