Dynamics of wetting

We consider a fluid of a uniform density, p, moving with velocity u(r, t). The conservation of mass or continuity equation implies 

For a thin, incompressible film (thin compared with the variations in the profile in the x and y directions), we assume that in the Navier-Stokes equations, V is only z dependent thus. 

In addition, we assume that since the film is thin, the pressure is constant in the z direction. Thus the only components of Vp are in the x and y directions. Finally, we consider steady-state solutions of the Navier-Stokes equation dv/dt = 0. Writing v = u(z), these equations are 

Since we take p to be independent of z within the lubrication approximation, Vz = 0. The pressure drop across a curved interface located at z = h(Xyy) is given by the Laplace condition (see Chapter 2)  

The characteristic velocity of the fluid is of the order yfri 10 cm/s, while the contact line velocity is much smaller since it depends on the curvature which is small typically U cm/s. 

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Since drying occurs simultaneously with wetting, the effect of diy-ing can substantially modify the expected impacd of a given process variable and this should not be overlooked. In addition, simultaneously drying often implies that the dynamics of wetting are far more important than the extent. 

C. Redon, F. Brochard-Wyart, F. Rondelez. Dynamics of wetting. Phys Rev Lett 66 715-718, 1991. 

P., Dynamics of wetting local contact angles, J. Fluid. Mecdi. 212 (1990) 55-63. 

F. Heslot, A. M. Cazabat, and P. Levinson, Dynamics of wetting of tiny drops Ellipsometric study of the late stages of spreading, Phys. Rev. Lett. 62, 1286-1289 (1989). 

An upper limit on the capillary number required for snap-off arises from the dynamics of wetting fluid flow into the constriction. The capillary number must be below the upper limit for a long enough time that sufficient wetting fluid can flow back into the constriction to form a lamella (40). If the volume of wetting fluid is too small, the lamella cannot form. 

Marangoni interfacial stresses which slow the dynamics of wetting. Additional variables which influence adhesion tension include (1) impurity profile and particle habit/morphology typically controlled in the particle formation stage such as crystallization, (2) temperature of granulation, and (3) technique of grinding, which is an additional source of impurity as well. 

J. E Joanny, Dynamics of wetting Interface profile of a spreading liquid. J. Mec. Theor. Appl. Special Issue, 249-71 (1986). 

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