Pressure-free interface

A microfluidic chip has been developed for rapid screening of protein crystallization conditions (Hansen et al., 2002) using the free interface diffusion method. The chip is comprised of a multilayer, silicon elastomer and has 480 valves operated by pressure. The valves are formed at the intersection of two channels separated by a thin membrane. When pressure is applied to the top channel it collapses... 

If we assume that excess pressure, and the alveoli would collapse when the excess pressure fell below a certain value. This kind of instability is not common, since increases with increasing radius such that AP always increases with increasing radius. This behavior of crs is caused by a surface-active agent (phospholipids) in the liquid film. The concentration of the surface-active agent decreases in the interface between liquid and air when the surface of the film distends, and therefore both surface tension and excess pressure increase. The hysteresis of this process is controlled by the diffusion of matter between the free interface and interior of the liquid. 

When the explosion pressure waves reach the free interface of soils and air, they transport down from the free interface (Fig. 2.35b). Because of expansion waves and the pressure of product gases, the top soils above the explosives lift up (Fig. 2.35c). The tensile waves and shear waves are produced. These second stage producing waves transport radially to all directions have the maximum amplitudes, and induce the waves with maximum oscillations on the earth surface. 

Centrifugal field Pulse-free pumping No pressure-tight interfaces needed Low-pressure load on lids Standard operation in sample prep Robust liquid handling widely decoupled fi om viscosity and surface tension Intrinsic, buoyancy-based bubble removal Coriolis force manipulates flows Rotational symmetry... 

Surface tension variations affect the mobility of the fluid-fluid interface and cause Marangoni flow instabilities. Surfactant-laden flows exhibit surface tension variations at the gas-liquid or liquid-liquid contact line due to surfactant accumulation close to stagnation points [2,53]. For gas-liquid systems, these Marangoni effects can often be accounted for by assuming hardening of the gas bubble, i.e. by replacing the no-shear boundary condition that is normally associated with a gas-liquid (free) boundary with a no-slip boundary condition. It should be noted that such effects can drastically alter pressure drop in microfluidic networks and theoretical predictions based on no-shear at free interfaces must be used with care in practical applications [54]. 

For mild interfacial slope (i.e., wave lengths of the interfacial disturbances are large compared to the thickness of both layers), the local velocity profiles can be closely approximated based on the local values of the layer thickness and phases velocities. Also, under the shallow water assumption, the effect of the wave-induced flow in the perpendicular direction on the variation of the pressure gradient dP/dy can be neglected, whereby the pressure at each phase, P, P, varies only due to gravity. Hence, the average pressure at each phase, in terms of its pressure level at the free interface, y = h, is given by ... 

The disjoining pressure at the free interface pifi yielding the overall driving potential... 

Each of the constituent terms of Equation 11.1 represents a distinct force field. From left to right the terms represent the contributions of viscous forces, surface tension forces due to the curvature at the free interface (Laplace pressure), and the excess intermolecular forces (disjoining pressure) respectively [37, 38, 65, 67]. The viscous force in no way influences the stability as it merely controls the dynamics of the system. For tangentially immobile films, the prefactor of the viscous term 3 is replaced by 12 [38, 65]. The Laplace pressure arising from surface tension has a stabilizing influence, as already discussed. Thus, the only term that may induce an instability in the system is the one representing the excess intermolecular interactions [37,38,65]. 

An oil reservoir which exists at initial conditions with an overlying gas cap must by definition be at the bubble point pressure at the interface between the gas and the oil, the gas-oil-contact (GOC). Gas existing in an initial gas cap is called free gas, while the gas in solution in the oil is called dissolved or solution gas. 

The capillary pressure can be related to the height of the interface above the level at which the capillary pressure is zero (called the free water level) by using the hydrostatic pressure equation. Assuming the pressure at the free water level is PI ... 

This is consistent with the observation that the largest difference between the oil-water interface and the free water level (FWL) occurs in the narrowest capillaries, where the capillary pressure is greatest. In the tighter reservoir rocks, which contain the narrower capillaries, the difference between the oil-water interface and the FWL is larger. 

If a pressure measuring device were run inside the capillary, an oil gradient would be measured in the oil column. A pressure discontinuity would be apparent across the interface (the difference being the capillary pressure), and a water gradient would be measured below the interface. If the device also measured resistivity, a contact would be determined at this interface, and would be described as the oil-water contact (OWC). Note that if oil and water pressure measurements alone were used to construct a pressure-depth plot, and the gradient intercept technigue was used to determine an interface, it is the free water level which would be determined, not the OWC. 

Finally, it is worth remembering the sequence of events which occur during hydrocarbon accumulation. Initially, the pores in the structure are filled with water. As oil migrates into the structure, it displaces water downwards, and starts with the larger pore throats where lower pressures are required to curve the oil-water interface sufficiently for oil to enter the pore throats. As the process of accumulation continues the pressure difference between the oil and water phases increases above the free water level because of the density difference between the two fluids. As this happens the narrower pore throats begin to fill with oil and the smallest pore throats are the last to be filled. 

A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

A very important thermodynamic relationship is that giving the effect of surface curvature on the molar free energy of a substance. This is perhaps best understood in terms of the pressure drop AP across an interface, as given by Young and Laplace in Eq. II-7. From thermodynamics, the effect of a change in mechanical pressure at constant temperature on the molar h ee energy of a substance is... 

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