Young-Laplace law

Let us start with the action of Young-Laplace law (Equation 9.6), which determines the equilibrium configuration of the fluids (liquid and liquid-like phases) and the driving force of mass transfer that cause the spontaneous formation of equilibrium configurations. 

This is the law of Young and Laplace. The quantity in parentheses is known as the mean curvature of the surface. The Young-Laplace law says that the pressure is... 

In the context of foams and emulsions, the Young-Laplace law is often applied across the thin film separating two bubbles or droplets. Such a film has two interfaces the continuous phase participates in both. Because of the thinness of the film, we can approximate the two interfaces as locally parallel. Labeling the bubbles/droplets i and , their pressure difference Ap,. is... 

Given the truncated sphere of Figure 12.7, the Young-Laplace law can be used to obtain an approximate relation between the imposed force and the resulting deformation. For each bubble, the body force F must be balanced by a force with magnitude Ap nrj) applied by the fluid in the thin film, where ry V2R6 is the radius of the facet and 8 = 8(F) is the dilference between the sphere radius and the distance from the bubble center to the center of the facet. The radius of the... 

Young s law for capillary pressure see capillary pressure, Young and Laplace Z-average 1.7.63... 

The difference in curvature radii creates a pressure drop in ceil capillaries in accordance with Laplace-Young s law... 

Wenzel s relation has been confirmed in terms of the first two laws of thermodynamics. Huh and Mason, in 1976, used a perturbation method for solving the Young-Laplace equation while applying Wenzel s equation to the surface texture. Their results can be reduced to Wenzel s equation for random roughness of small amplitude. They assume that hysteresis was caused by nonisotropic equilibrium positions of the three-phase contact line, and its movement was predicted to occur in jumps. On the other hand, in 1966, Timmons and Zisman attributed hysteresis to microporosity of solids, because they found that hysteresis was dependent on the size of the liquid molecules or associated cluster of molecules (like water behaves as an associated cluster of six molecules). 

In the last part of this section, we show that the profile determined in the previous subsection from the Laplace equation and Young s law indeed corresponds to a minimum in the free energy. A convenient method of proving this fact is that of functional differentiation. This derivation [11] of Young s law and Laplace s law in the presence of gravity is closely related to the derivation first outlined by Gibbs [4] and later given by Johnson [8] (see also Ref. 9). 

We have thus shown that the profile r(z) that minimizes the free energy in Eq. (22) has to obey the Laplace equation with Young s law as a boundary condition. 

Gauthier and colleagues have pointed out that polymer-water interfacial tension and capillary pressure at the air-water interface are expressions of the same physical phenomenon and can be described by the Young and Laplace laws for surface energy [5]. The fact that there are two minimum film formation temperatures, one wet and one "dry," may be an indication that the receding polymer-water interface and evaporating interstitial water are both driving the film formation (see Section 3.4). 

The equation of Young and Laplace describes one of the fundamental laws in interface science If an interface between two fluids is curved, there is a pressure difference across it provided the system is in equilibrium. The Young-Laplace equation relates the pressure difference between the two phases AP and the curvature of the interface. In the absence of gravitation, or if the objects are so small that gravitation is negligible, the Young-Laplace equation is... 

Classical laws of capillarity are important down to the 2-4 nm range.5 The Laplace-Young law is fundamental. This law states that the interface of any... 

It may be added here that the four basic laws of capillarity, i.e., the equations of Gibbs [(10.2)], Laplace [(10.7)], Kelvin [(10.9)] and Young [(10.10)], all describe manifestations of the same phenomenon the system tries to minimize its interfacial free energy. (Another manifestation is found in the Hamaker equations see Section 12.2.1.) These laws describe equilibrium situations. Moreover, dynamic surface phenomena are of great importance. 

The aim of this book is to show that there is a great deal of science in ice cream, and in particular to demonstrate the link between the microscopic structure and the macroscopic properties. It is naturally biased towards physics, physical chemistry and materials science as these are the areas in which I trained. The book is aimed at schools and universities, and a scientific background is required to understand the more technical sections. I have attempted to make it readable by 16-18-year-olds, and many sections are suitable for adaptation by GCSE science teachers. I have unashamedly made reference to the giants of chemistry and physics such as Newton, Einstein, Boyle, Gibbs, Kelvin, Laplace and Young where the laws and equations that bear their names are relevant. I hope that as a result teachers reading this book will find in ice cream useful illustrations of a number of scientific principles. Some... 

The breakthrough pressure ( b) through a pore of cylindrical cross-section can be related to the membrane pore size and to the interfadal tension at the liquid-liquid interface, according to the Laplace-Young law,Eq. (1) [127],... 

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... 

---