Hydrodynamics of Thin Films

Woods, W.P. The Hydrodynamics of Thin Films Flowing over a Rotating Disk. Ph.D. Thesis, University of Newcastle-upon-Tyne, U.K. 1995. 

Woods, W.P. (1995). The hydrodynamics of thin films fbwing over a rotating disc. PhD Dissertation, Newcastle University, Newcastle upon Tyne, UK. 

In polymer processing, we frequently encounter creeping viscous flow in slowly tapering, relatively narrow, gaps as did the ancient Egyptians so depicted in Fig. 2.5. These flows are usually solved by the well-known lubrication approximation, which originates with the famous work by Osborne Reynolds, in which he laid the foundations of hydrodynamic lubrication.14 The theoretical analysis of lubrication deals with the hydrodynamic behavior of thin films from a fraction of a mil (10 in) to a few mils thick. High pressures of the... 

D. E. Tambe and M. M. Sharma, Hydrodynamics of thin liquid-films bounded by viscoelastic interfaces, J. Colloid Interface Sci. 147, 137-151 (1991) Factors controlling the stability of colloid-stabilized emulsions. 1. An experimental investigation, J. Colloid Interface Sci. 157, 244-253 (1993) Factors controlling the stability of colloid-stabilized emulsions. 2. A model for the rheological properties of colloid-laden interfaces, J. Colloid Interface Sci. 162, 1-10 (1994) Factors controlling the stability of colloid-stabilized emulsions. 3. Measurement of the rheological properties of colloid-laden interfaces, J. Colloid Interface Sci. 171, 456-462 (1995). 

Dissipative particle dynamics can be employed also for simulating hydrodynamic instabilities. Dzwinel and Yuen (1999) present the algorithm applied for simulation of thin film falling down the inclined plane. In other studies, such as Clark et al. (2000), Dzwinel and Yuen (2001), and Boryczko et al. (2000), more challenging problems are attacked for example, droplet breakup and mixing in complex fluids. 

In fact, Equation 5.281 describes an interface as a two-dimensional Newtonian fluid. On the other hand, a number of non-Newtonian interfacial rheological models have been described in the literature. Tambe and Sharma modeled the hydrodynamics of thin liquid films bounded by viscoelastic interfaces, which obey a generalized Maxwell model for the interfacial stress tensor. These authors also presented a constitutive equation to describe the rheological properties of fluid interfaces containing colloidal particles. A new constitutive equation for the total stress was proposed by Horozov et al. ° and Danov et al. who applied a local approach to the interfacial dilatation of adsorption layers. 

Maldarelli, Ch. and Jain, R.K., The hydrodynamic stability of thin films, in Thin Liquid Films, Ivanov, I.B., Ed., Marcel Dekker, New York, 1988, p. 497. 

Danov, K.D. et al., Bancroft rule and hydrodynamic stability of thin films and emulsions, in Proc. First World Congress on Emulsion, 19-22 Oct., Paris, 1993, p. 125. 

These assumptions result in the one-dimensional velocity and pressure profiles V = V(Y) and P - P(Y), where Y is the coordinate measured along the normal to the film surface. The corresponding hydrodynamic equations of thin films express the balance of viscous and gravity forces [41,441] ... 

I. B. Ivanov, Physicochemical Hydrodynamics of Thin Liquid Films, thesis, Sofia, 1977. 

A detailed treatise on the fundamentals and applications of thin films, i.e., lamella plus smface film, is found in Ivanov (147). The two major forces involved in the lamella behavior are thermodynamic (disjoining forces) and hydro-dynamic. Further in-depth studies on the thermodynamics are presented in de Feijter (148) and Hirasaki (149) and on the hydrodynamics in Maldarelli and Jain (150). Because of the complexity of this topic, which is not within the scope of this chapter, the following discussions will be limited to the understanding that this research brought about concem-... 

Danov, K.D., Velev, O.D., Ivanov, I.B., and Borwankar, R.P., Bancroft rule and hydrodynamic stability of thin films and emulsions, in First World Congress on Emulsion, October 19-22, Paris, France, 1993, p. 125. Kunieda, H., Evans, D.F., Solans, C., and Yoshida, Colloids Surf., 47, 35, 1990. 

DE Tambe, MM Sharma. Hydrodynamics of thin liquid films bounded by viscoelastic interfaces. J Colloid Interface Sci 147 137-151, 1991. 

In addition to measuring the equilibrium thickness of thin films, the method is widely used to analyze film stability and drainage [810, 811, 813]. In many practical applications, a system is far away from equilibrium and highly dynamic. One example is a flotation cell in which particles and bubbles are mixed. The attachment of a particle to a bubble is limited by the hydrodynamic interaction rather than equilibrium surface forces [695]. When a particle and a bubble approach each other, the liquid in between needs to have time to flow out of the closing gap [728]. This process of film drainage is also studied with the thin film balance. 

In 1981, a novel flotation device known as the air-sparged hydrocyclone, shown in Figure 3, was developed (16). In this equipment, a thin film and swid flotation is accompHshed in a centrifugal field, where air sparges through a porous wall. Because of the enhanced hydrodynamic condition, separation of fine hydrophobic particles can be readily accompHshed. Also, retention times can be reduced to a matter of seconds. Thus, this device provides up to 200 times the throughput of conventional flotation cells at similar yields and product quaHties. 

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