Spreading dynamics

The results obtained for three tips with different channel diameters (2 / o = 220 nm, 500 nm, and 760 nm) are reported in Fig. 12.13c, where the width w is plotted as a function of the velocity v. 

To interpret the experimental power law, we consider that the spreading d3mamics is governed by the Cox-Voinov equation resulting from the equilibrium between capillary and viscous forces  

Additional experiments have been performed to study the influence of tip and substrate surface properties on line width. It 

This study shows that NADIS is a unique tool to study liquid behavior at small scales. A nonconventional spreading regime has been evidenced in the submicron range and down to a milliseconds time scale, conditions that are difficult to investigate with other methods. 

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Spreading dynamics plays a key role in numerous applications. However, controlling the dewetting of liquids may be potentially more important for some industrial uses. 

This result demonstrates that the self-spreading dynamics are controllable by tuning the bilayer-substrate interactions. The above-mentioned electrolyte dependence is an example of this fact. Considering that there are many parameters that alter the bilayer-substrate interaction, a diverse approach can be proposed. For example, Nissen et al. investigated the spreading dynamics on the substrate coated with polymetic materials [48]. They found that insertion of a hydrophilic and inert polymer layer under the self-spreading lipid bilayer strongly attenuated the bilayer-substrate interaction. 

Of course, other physical and chemical conditions also affect the self-spreading dynamics. Figure 13.9 shows the dependences of P on the temperature and lipid... 

This fact strongly suggests that it is not sufficient to consider only the bilayer-substrate interaction for a comprehensive understanding of the self-spreading dynamics. 

In addition to the spreading dynamics, the stacking structure of the self-spreading lipid bilayer is also controllable via the NaCl concentration [54, 55]. Further experimental and theoretical investigations regarding the control of self-spreading are required before we will be able to easily control the self-spreading behavior in microfluidic devices. 

Confirmation of certain conditions usually needs to be demonstrated for natural attenuation to be deemed acceptable as a remedial option. This demonstration may involve showing the contaminant plume to be stable and contained, shrinking, or to be intrinsically remediated at the same rate as its spreading (Figure 10.11). When the plume is essentially being remediated at the same rate that it is spreading, dynamic equilibrium conditions exist. 

Trokhymchuk A, Henderson D, Nikolov A, Wasan D (2005) In-layer structuring of like-charged macroions in a thin film. Ind Eng Chem Res 44 1175-1180 Von Bahr M, Tiberg F, Zhmud BV (1999) Spreading dynamics of surfactant solutions. Langmuir 15 7069-7075... 

The 3D results for PFPE Zdol, (Figs. 1.37 and 1.38), provide more insight into the layer coupling. For the weaker endgroup interactions (Fig. 1.37), the 3D picture appears similar to Figure 1.35 (PFPE Z), except for the slower spreading dynamics. However, a difference manifests in the spacing of the individual layer... 

J. A. Nieminen and T. Ala-Nissila, Spreading dynamics of polymer microdroplets A molecular-dynamics study, Phys. Rev. E 49, 4228-4236 (1994). 

Wetting and Spreading Dynamics, edited by Victor Starov, Manuel G. Velarde, and Clayton Radke... 

A potential model structure requiring multiple-Fields could e.g. come from the need to model the spread dynamics of corporate bonds separately from the underlying default-free bond dynamics. 

The non-slip boundary condition is discussed in an excellent paper by Huh and Scriven They take note of the fact that, previous workers seem not to have been well informed by fluid mechanics , in aUuding to the essentially surface chemical analyses of spreading dynamics. Another point they address is that except for very smooth surfaces and non-adsorbing hquids the advancing or receding of the contact line proceeds in a slip-stick and discontinuous fashion a fact which is the focus of attention in current analyses of contact angle hysteresis using the theory of random fluctuations... 

Future work will hopefully help to clarify the relationship between paper surface morphology and spreading dynamics. 

Starov V, Velarde M, Radke C (2007) Wetting and spreading dynamics. In Surfactant science series 138. Taylor and Francis, p 515... 

Thus, assuming the film in this region to be thin such that the lubrication approximation holds, the spreading dynamics of the drop in the limit L/L quasi-steady limit with respect to a moving coordinate frame translating at a constant dimensionless speed given by Ca are governed by the Bretherton [9] equation ... 

It is now possible to insert this dynamic contact angle condition back into the spreading relationship in Eq. 15 to obtain an explicit power law for the spreading dynamics of a drop lying on a horizontal substrate [7]. If the drop can be assumed to be thin, then the axisymmetric Laplace-Young equation in the lubrication limit reads... 

Let us concentrate on the spreading dynamics of this liquid film which appears directly connected to the air entrainment phenomenon, restricting here to the most interesting non-wetting domain (90° < < 180°). The situation that needs be... 

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