Interfacial Flow

Thus, the enhancement of heat transfer may be connected to the decrease in the surface tension value at low surfactant concentration. In such a system of coordinates, the effect of the surface tension on excess heat transfer (/z — /zw)/ (/ max — w) may be presented as the linear fit of the value C/Cq. On the other hand, the decrease in heat transfer at higher surfactant concentration may be related to the increased viscosity. Unfortunately, we did not find surfactant viscosity data in the other studies. However, we can assume that the effect of viscosity on heat transfer at surfactant boiling becomes negligible at low concentration of surfactant only. The surface tension of a rapidly extending interface in surfactant solution may be different from the static value, because the surfactant component cannot diffuse to the absorber layer promptly. This may result in an interfacial flow driven by the surface tension gradi-... 

Many polymers exhibit neither a measurable stick-slip transition nor flow oscillation. For example, commercial polystyrene (PS), polypropylene (PP), and low density polyethylene (LDPE) usually do not undergo a flow discontinuity transition nor oscillating flow. This does not mean that their extrudate would remain smooth. The often observed spiral-like extrudate distortion of PS, LDPE and PP, among other polymer melts, normally arises from a secondary (vortex) flow in the barrel due to a sharp die entry and is unrelated to interfacial slip. Section 11 discusses this type of extrudate distortion in some detail. Here we focus on the question of why polymers such as PS often do not exhibit interfacial flow instabilities and flow discontinuity. The answer is contained in the celebrated formula Eqs. (3) or (5). For a polymer to show an observable wall slip on a length scale of 1 mm requires a viscosity ratio q/q equal to 105 or larger. In other words, there should be a sufficient level of bulk chain entanglement at the critical stress for an interfacial breakdown (i.e., disentanglement transition between adsorbed and unbound chains). The above-mentioned commercial polymers do not meet this criterion. 

Simulation of free-surface and interfacial flows is a topic with many practical applications, e.g., the formation of droplet clouds or sprays from liquid jets,... 

Rudman, M., Volume-tracking methods for interfacial flow calculations. Int. J. Num. Methods Fluids 24,671 (1997). 

Rudman, M. (1997) Volume-Tracking Methods for Interfacial Flow Calculations, International Journal for Numerical Methods in Fluids, Vol. 24(7), pp. 671-691. 

Colloidal filtration is selected as the dip-coating mechanism for the first trials in the development path. This means that cake filtration should occur when the suspension comes into contact with the substrate. So the particle size in the suspension should not be much smaller than 1 pm (approximately 4 times less than the mean pore size in the substrate) otherwise too much penetration and clogging of the substrate occurs prior to cake build-up. This would give rise to an extra high interfacial flow resistance during application of the MF membrane. 

McKenna SP (1997) The influence of surface films on interfacial flow dynamics. MS thesis, Massachusetts Institute of Technology/Woods Hole Oceanographic Institution, Cambridge, MA... 

See Ref. 1 in Chap. 3. Typical papers from Annual Reviews include A. Leonard, Computing three-dimensional incompressible flows with vortex elements, Annu. Rev. Fluid Mech. 17, 523-59 (1985) M. Y. Hussaini and T. A. Zang, Spectral methods in fluid dynamics, Annu. Rev. Fluid Mech. 19, 339-67 (1987) R. Glowinski and O. Pironneau, Finite element methods forNavier-Stokes equations, Annu. Rev. Fluid Mech. 24, 167-204 (1992) R. Scardovelli and S. Zaleski, Dierect numerical simulation of free-surface and interfacial flow, Annu. Rev. Fluid Mech. 31, 567-603 (1999). 

Therefore the emphasis is placed here on the accurate computations of interfacial flows in complex geometries as the complex geometries are ubiquitous in microfluidic applications. For this purpose, the FV/FT method that is designed to compute multiphase flows in complex geometries is first validated against the FD/FT method that can simulate flows only in simple... 

The front-tracking method has been developed by Trgyyvason and coworkers and been successfully used for computational modeling of interfacial flows... 

R. Scardovelli, S. Zaleski, Direct Numerical Simulation of Free-Surface and Interfacial Flow, Annu. Rev. Fluid Mech, 31 (1999). 

M. Muradoglu and G. Tiyggvason, A Front-Tracking Method for Computation of Interfacial Flows with Soluble Surfactants, J. Comput Phys., 227 (4), 2238-2262 (2008). 

Surface active agents (surfactant) are either present as impurities that are difficult to remove from a system or they are deliberately added to fluid mixtures to manipulate interfacial flows. It has been well known that the presence of surfactant in a fluid mixture can critically alter the motion and deformation of bubbles moving through a continuous liquid phase. Probably, the best-known example is the retardation effect of surfactant on the buoyancy-driven motion of small bubbles. Numerous experimental studies have shown that the terminal velocity of a contaminated spherical bubble is significantly smaller than the classical Hadamard-Rybczynski prediction... 

Surfactants are either present as impurities that are difficult to remove from the system or are added deliberately to the bulk fluid to manipulate the interfacial flows [24]. Surfactants may also be created at the interface as a result of chemical reaction between the drop fluid and solutes in the bulk fluid [25, 26]. Surfactants usually reduce the surface tension by creating a buffer layer between the bulk fluid and droplet at the interface. Non-uniform distribution of surfactant concentration creates Marangoni stress at the interface and thus can critically alter the interfacial flows. Surfactants are widely used in numerous important scientific and engineering applications. In particular, surfactants can be used to manipulate drops and bubbles in microchannels [2, 25], and to synthesize micron or submicron size monodispersed drops and bubbles for microfluidic applications [27]. 

It is a challenging task to model the effects of interfacial flows with soluble surfactants since surfactants are advected and diffused both at the interface and in the bulk fluid by the motion of fluid and by molecular mechanism, respectively. Therefore the evolution equations of the surfactant concentrations at the interface and in the bulk fluid must be solved coupled with the flow equations. The surfactant concentration at the interface alters the interfacial tension and thus alters the flow field in a complicated way. This interaction between the surfactant and the flow field is highly nonlinear and poses a computational challenge. 

After the static test mentioned above, the method is now tested for the impact and spreading of a glycerin droplet on a wax substrate and the computational results are compared with the experimental data of Sikalo et al. [32], The details of the experimental setup, material properties and computational model can be found in Refs. [33, 51]. The computed and experimental spread factor and contact line are plotted in Figs. 19a and b, respectively. These figures show that the present front-tracking method is a viable tool for simulation of interfacial flows involving moving contact lines. 

Mesoscopic roughness at the solid-liquid interface can greatly modify both interfacial flow and static wetting properties leading to two behaviors, either a decrease [45,64,102] or an increase [63,103] of surface slippage with roughness. 

Wasan and his research group focused on the field of interfacial rheology during the past three decades [15]. They developed novel instruments, such as oscillatory deep-channel interfacial viscometer [20,21,28] and biconical bob oscillatory interfacial rheometer [29] for interfacial shear measurement and the maximum bubble-pressure method [15,29,30] and the controlled drop tensiometer [1,31] for interfacial dilatational measurement, to resolve complex interfacial flow behavior in dynamic stress conditions [1,15,27,32-35]. Their research has clearly demonstrated the importance of interfacial rheology in the coalescence process of emulsions and foams. In connection with the maximum bubble-pressure method, it has been used in the BLM system to access the properties of lipid bilayers formed from a variety of surfactants [17,28,36]. 

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