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. 

Bivas, Isak, Free Energy of a Fluctuating Vesicle. Influence of the Fluctuations on the Laplace Law, 6, 93 see also Mechanical Properties of Lipid Bilayers Containing Grafted Lipids, 6, 207. 

Lavosier and Laplace Law It states, "the amount of heat evolved or absorbed in chemical change is equal to heat evolved or absorbed when the reaction is reversed". 

The theoretical basis of the Hg-injection method is defined by Laplace law. By using a capillary model where the porous medium is assimilated to a bundle of cylindric capillary tubes the capillary pressure is Pc = y(l/Rci+l/Rc2) = 2y cos0 /Rc (3) where Pc is the capillary pressure Rd and Rc2 are mutually perpendiculcir radii of a surface segment R is the average pore-throat size (pm) 0is the angle between mercury menisc and pore wall (for mercury 0=140°) y is the interfacial tension (for mercury y = 0.480 N/m). 

For spherical particles bS = Snrbr and bV= 4nr2br. Substitution of these expressions into eq. (1.11) readily yields the Laplace law. 

According to the Laplace law, the pressure in a liquid drop increases with increasing interfacial curvature. The increase in pressure causes an increase in the chemical potential of the liquid equal to Ap, which, assuming that the liquid is incompressible, can be written as... 

Therefore, it is proved a posteriori that it is legitimate to use electroneutrality to calculate the concentration profiles. However, the Laplace law is too approximate in numerical terms to give a correct value for the potential. Therefore, to determine this profile one needs to use the concentration profiles, as already described above. 

The pressure measurement, achieved by use of the Textilpress device, is an indirect measuring method, which is based on die Laplace Law. Ltq>lace Law has been widely used to calculate the pressure delivered to a cylindo of known radius by a bric under known tension. However, this Law was originally developed by Laplace in 1806 to explain the surface tension phenomenon in liquids and their ability to form droplets or soap bubbles [6]. The Laplace Law is illustrated in Figure 3 and by equaticm (1). 

Harada explored the relarionship betweoi the d ree of skin stretch artd die d ree of dibric stretch in coryuncdon with the proximiQ of the garmmit to the borty. They utilised Laplace Law to relate to clodiing pressure, di is brought about through the radius of the human curved surfoce. This r roach was to determine how closely the fabric should conform to the body for optimum comfort levels. 

Laplace Law relates pressure, tension and radius of curvature in the following way ... 

When an aneurysm ruptures, the patient s blood escapes the vessel under arterial pressure, which results in rapid blood loss. The prognosis for a patient with a ruptured AAA is low. The initial mortahty rate for patients whose ruptures occur outside a hospital setting is approximately 50%, and the survival rate decreases by about 1% per minute when there are additional delays (O Connor, 2011). Ruptures are beheved to occur when the wall tissue strength is exceeded by the mechanical stress acting on the aneurysm wall. This tension can be calculated using the Laplace Law for wall tension ... 

Among these, the first two case studies describe invariable coupling whereas the third one is devoted to variable coupling. The piston example demonstrates the usefulness of a thermodynamical approach in this mechanical domain and outlines the difference between a global pressure and a local pressure. In the ion distribution, the exponential function ruling the capacitive relationship in physical chemistry and corpuscular domain is exported to the electrodynamical domain. The last case study Bubble introduces the surface energy variety and demonstrates the Laplace law in capillarity. 

Laplace law. The big law in these domains, which span from capillarity to wetting, through diphasic systems, is Laplace s law. This law is demonstrated here in the most general case, with a curvature of the interface separating the two phases that can be of any shape. Physically speaking, this law assumes a simple coupling relationship between efforts. 

The principle of left ventricular reduction according to Batista is to improve myocardial waU tension by reducing ventricular size based on Laplaces law. This is done by direct resection of a variable myocardial portion (partial left ventriculectomy) from the anterior, lateral, or posterior wall. In most patients having undergone this procedure, a circumscribed scar is visualized at the site of the ventriculotomy. In patients with left ventricular aneurysms, linear aneurysmal resection in which the aneurysmal sac is incised and the vital myocardium approximated by simple linear suture has become rare. The most widely used alternative technique is the Dor procedure where the aneurysm is incised and phcated by a purse-string suture around its neck. The remaining defect is covered with a synthetic patch over which the... 

The first model proposed for approximated analysis of the left ventricle of the heart was a spherical shell (Pao, 1980a and Mirsky, 1974) which was adopted by Woods in 1892 so that the Laplace law could be applied for calculation of the wall stresses. When the biplane silhouettes can be obtained by the X-ray technique, the left ventricle has since been analyzed as axisymmetric thick-walled shells. The advances in computer-aided tomography in recent years make it possible to image and reconstruct the cross-sectional shapes of the heart (Ritman, 1983). As a result of this development, the true three-dimensional structural shape of the heart can be accurately formed by stacking of the reconstructed cross sections together. Various finite element models have been proposed (Figure 1) for the analyses of the ventricles as well as for the cardiac valves both natural and prothetic (Pao,... 

FIGU RE 1.3 Derivation of the Laplace law for a rigid shell and for a buhhle. 

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