Hydrodynamic force measurement

For the no-slip boundary condition,/slip = 1. Otherwise when there is slip,/gUp 1, we have 

Slip increases the rate of drainage of the fluid confined between the surfaces. For h L, /slip 1 indicating that the liquid flow is unaffected by slip for surface separations much greater than the slip length. When h L, /np 0 is given as 

the hydrodynamic force for the slip flow case is smaller in magnitude than that for the no-slip case. 

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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... 

Hydrodynamic force measurements boundary slip of water on hydrophilic surfaces and electrokinetic effects, Phys. 

The slip length also depends on the shear rate imposed on the fluid particle. Thompson and Troian [8] have reported the molecular dynamics simulation of Couette flow at different shear rates. At lower shear rate, the velocity profile follows the no-slip boundary condition. The slip length increases with increase in shear rate. The critical shear rate for slip is very high for simple liquids, i.e., 10 s for water, indicating that slip flow can be achieved experimentally in very small devices at very high speeds. Experiments performed with the SEA and AFM have also showed shear dependence slip in the hydrodynamic force measurements. 

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). 

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. 

We report here, for the first time, that hydrodynamic forces can dramatically Increase the rate of desorption in polymer systems which are otherwise irreversibly adsorbed under no-flow conditions. Indeed, at high enough shear stresses, complete removal of the polymer is possible. The technique of ellipsometry is well suited for this problem as simultaneous measurements of both film thickness and adsorbance are possible during the flow process. 

Two similar techniques to probe hydrodynamic behaviour have been recently developed by Horn et al. [33] and Gee and co-workers [34-37]. The measurements by Horn et al. employ interferometry to measure the shape of a mercury drop at the end of a microcapillary as it approaches a flat interface. The capillaries are much larger than those used in an LSFA, where the drop profile is recorded under hydrodynamic forces. The work by Gee [34-37] is similar but uses hydrocarbon drops and determines the separation using imaging ellipsometry/reflectometry. This method is useful for systems... 

Other methods have appeared more recently for measuring forces between macroscopic surfaces or between a (large) colloidal particle and a surface, immersed in a liquid. These include the total internal reflection microscope in 1990 (TIRM) and the atomic force microscope in 1991(AFM). With TIRM, incredibly weak forces can be measured (-10 N), whilst with AFM forces - 10 N can be determined. With the development of optical tweezers, we now have the ability to measure forces directly between two colloidal particles. Using these latest techniques, not only may interaction forces between surfaces be measured but, by performing dynamic measurements, the hydrodynamic forces can also be examined. We are now at a stage surely undreamt of by Theo Overbeek 50 or so years ago when he made his own measurements. It is surely fitting that he has lived to witness all this, and that he has reached an age almost commensurate with that of the Faraday Society/Division itself ... 

As two bubbles approach at any reasonable rate, there must arise a hydrodynamic repulsive force, due to the need to expel water molecules from the film between bubbles. In water, coalescence is observed. Thus, there must exist an attractive force that overcomes the hydrodynamic repulsion. The attractive van der Waals force calculated between two bubbles in water is found to be orders of magnitude smaller than the hydrodynamic repulsion present at reasonable approach rates. As bubbles are highly hydrophobic (/air-water = 72mjm 2) it is reasonable to assume that the "hydrophobic force" is present, and acts to produce coalescence. Available force measurements are found to give an attraction of sufficient magnitude to overcome the hydrodynamic repulsion. This implies that for salts and sugars to reduce bubble coalescence, the attractive hydrophobic force is reduced in their... 

The adhesion of these cells to the tumor vessel wall occurs when the force between the adhesion molecules on the surfaces of endothelium and effector cell is greater than the hydrodynamic force exerted by blood flow. The deformability of these cells also plays an important role in this process, since it can alter the surface area of contact (Sasaki et al., 1989 Melder and Jain, 1992). Measurement of forces exerted by various adhesion molecules as well as cell deformability in vitro and in vivo is an active area of research in many laboratories, including our own (Ohkubo et al., 1991 Munn et al., 1994). 

The FIA system used is shown in Fig. 6.8, showing the sample injection by means of the hydrodynamic forces, the principle being explained in Fig. 6.8 (cf. Section 5.1.3). The carrier stream contains iodate and dissolved starch in diluted sulfuric acid. In the acidic solution the sulfite of the sample reacts with iodate leading to the formation of free iodine that with the starch forms a strongly colored blue complex which is measured spectrophotometrically at 600 nm. Since the formation of the end product is a very complex reaction which proceeds in several steps depending on the concentration of iodine, a linear calibration curve cannot be expected. 

Though relations of the form (109) and (110) are merely special cases of the more general symbolic operator relations (81) and (82), they may also be regarded as phenomenological equations in their own right. The polyadic resistance coefficients appearing therein can, at least in principle, be determined experimentally from appropriate measurements of the hydrodynamic forces and torques for an appropriate number of orientations of the particle relative to the principal axes of dilatation of the fluid motion. 

Oliver (02) observed that a sphere settling slowly near the wall of a tube in an otherwise stagnant fluid moved inwardly, towards the tube axis. Karnis (K4a, K5b), in a series of more detailed measurements, made simitar observations and followed the motion of the sphere all the way to the tube axis. It is on the basis of these observations that F, iP) is concluded to be negative. This conclusion accords with Oseen s (04) theoretical finding [also summarized in Berker (B4, p. 328)1 that, when small inertial effects are considered, a sphere moving parallel to a plane wall in a semi-infinite fluid experiences a repulsive hydrodynamic force, due to the sourcelike behavior of the flow at points distant from the sphere not lying within the wake [cf. Lamb (L5, p. 613)]. 

The rationalization of their data at intermediate velocities in terms of interfacial effects is a valient attempt at understanding dynamic contact angles in terms of surface interactions. However, the dynamic angle was measured by optical methods which, as in the case of flow in capillary tubes, gives 0 values considerably away fi-om the line of intersection and it is problematical whether they are governed by hydrodynamic forces or by surface forces. 

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