Membrane elasticity

A number of refinements and applications are in the literature. Corrections may be made for discreteness of charge [36] or the excluded volume of the hydrated ions [19, 37]. The effects of surface roughness on the electrical double layer have been treated by several groups [38-41] by means of perturbative expansions and numerical analysis. Several geometries have been treated, including two eccentric spheres such as found in encapsulated proteins or drugs [42], and biconcave disks with elastic membranes to model red blood cells [43]. The double-layer repulsion between two spheres has been a topic of much attention due to its importance in colloidal stability. A new numeri-... 

If the surface of a liquid is regarded as an elastic membrane, then the surface tension is the breaking force of this membrane. Water has one of the highest surface tensions of all liquids. For example, the surface tension of ethanol at 20°C is 22 mN/m, while that of water is 72.75 mN/m. The surface tension of water decreases with temperature. 

This component consists of a housing with two fittings for the hose connections to the pressure sensor and to the lower suds container. The inner volume of the component is divided by an elastic membrane with a weight in the middle. A bore in the weight allows for the exchange of air between the chambers. Measuring of the water level is not affected because the bore always allows for pressure compensation. 

During the spinning cycle, the mass inertia of the weight with the elastic membrane generates a pressure signal when the suds container moves. As a result, extremely low-priced, robust acceleration detection is possible in these washing machines. 

Everybody is familiar with a number of phenomena which indicate that the surface of a liquid is in a condition of tension, or—to use a parallel which is graphic, while incorrect in one particular—behaves as if it were composed of an elastic membrane. If a camel-hair brush is submerged in water, the hairs remain separate as they do in air, but they collapse on being S.T. I... 

Acetylation rates have also been studied by Centola37 who treated natural and mercerized ramie fibers for varying times with acetic anhydride and sodium acetate and examined the reaction products chemically and by X-ray diffraction. The reagent was considered to penetrate into the interior of fibers. A heterogeneous micellar reaction was believed to occur that converted a semi-permeable elastic membrane around the micelles into the triacetate. The rate of acetylation of mercerized ramie was observed to be faster than that of unmercerized fiber. Centola concluded that about 40 % of the cellulose in native ramie is amorphous and acetylates rapidly. 

In the body of a liquid, intermolecular forces pull the molecules in all directions. At the surface of the liquid, the molecules pull down into the body of the liquid and from the sides. There are no molecules above the surface to pull in that direction. The effect of this unequal attraction is that the liquid tries to minimize its surface area. The minimum surface area for a given quantity of matter is a sphere. In a large pool of liquid, where sphere formation is not possible, the surface behaves as if it had a thin stretched elastic membrane or skin over it. The surface tension is the resistance of a liquid to an increase in its surface area. It requires force to break the attractive forces at the surface. The greater the intermolecular force, the greater the surface tension. Polar liquids, especially those that utilize hydrogen bonding, have a much higher surface tension than nonpolar liquids. 

A molecule of a liquid attracts the molecules that surround it, and, in its turn, it is attracted by them (Figure 1.2). For the molecules that are inside a liquid, the resultant of all these forces is neutral, and all of them are in equilibrium by reacting with each other. When these molecules are on the surface, they are attracted by the molecules below and by the lateral ones, but not toward the outside. The resultant is a force directed inside the liquid. In its turn, the cohesion among the molecules supplies a force tangential to the surface. So, a fluid surface behaves like an elastic membrane that wraps and compresses the liquid below. The surface tension expresses the force with which the surface molecules attract each other. It is common observation that, due to the surface tension, it takes some effort for some bugs to climb out of the water in lakes. On the contrary, other insects, such as the marsh treaders and water striders, exploit the surface tension to skate on the water without sinking (Figure 1.3). 

The surface molecules are under a different force field from the molecules in the bulk phase or the gas phase. These forces are called surface forces. A liquid surface behaves like a stretched elastic membrane in that it tends to contract. This action arises from the observation that, when one empties a beaker with a liquid, the liquid breaks up into spherical drops. This phenomenon indicates that drops are being created under some forces that must be present at the surface of the newly formed interface. These surface forces become even more important when a liquid is in contact with a solid (such as ground-water oil reservoir). The flow of liquid (e.g., water or oil) through small pores underground is mainly governed by capillary forces. Capillary forces are found to play a very dominant role in many systems, which will be described later. Thus, the interaction between liquid and any solid will form curved surface that, being different from a planar fluid surface, initiates the capillary forces. 

A new variation of interfacial polymerization was developed by Russell and Emrick in which functionalized nanoparticles or premade oligomers self-assemble at the interface of droplets, stabilizing them against coalescence. The functional groups are then crosslinked, forming permanent capsule shells around the droplets to make water-in-oil (Lin et al. 2003 Skaff et al. 2005) and oil-in-water (Breitenkamp and Emrick 2003 Glogowski et al. 2007) microcapsules with elastic membranes. 

Hydrostatic pressing and isostatic pressing are usually applied to expis that have been evacuated, frequently at elevated temps. Temps up to 130° and pressures up to 30000 psi have been used. The surfaces where pressure is applied thru elastic membranes are, of course, of relatively poorly defined form and dimensions. Hence, these pressing processes must almost invariably be followed by machining... 

The luminal surface of aorta is folded, and the folds reflect the goffers of the inner elastic membrane. The aorta s intima is covered with an entire layer of endothelio-cytes. The surface of these endotheUocytes is fine folded (Fig. 30.1a). The luminal surface of the femoral vein is covered by endotheUocytes, whose plasma membrane is also fine folded. The bounds which separate endotheUocytes appear as irregular lines (Figs. 30.1a-30.2a). 

It constitutes the basement membrane of the comeal endothelium, separating it from the stroma. It is a strong, amorphous, and elastic membrane. It is about 10 pm in adulthood. It is synthesized by the endothelial cells from the fourth month of embryonic life. The Descemet s membrane has got two distinct sides ... 

SURFACE TENSION. Fluid surfaces exhibit certain features resembhng the properties of a stretched elastic membrane hence the term surface tension. Thus, one may lay a needle or a safety-razor blade upon the surface of water, and it will lie at rest in a shallow depression caused by its weight, much as if it were on a rubber air-cushion. A soap bubble, likewise, tends to contract, and actually creates a pressure inside, somewhat after the manner of a rubber balloon. The analogy is imperfect, however, since the tension in the rubber increases with the radius of the balloon, and the pressure inside, which would otherwise decrease, remains approximately constant while the liquid film tension remains constant and the pressure in the bubble falls off as the bubble is blown. 

Ottewill and co-workers106,200 have used a compression method to measure the double-layer repulsion between the plate-like particles of sodium montmorillonite. This is a particularly suitable system for such studies, since the particles are sufficiently thin (c. 1 nm) for van der Waals forces to be unimportant and surface roughness is not a problem. The dispersion was confined between a semipermeable filter and an impermeable elastic membrane and an external pressure was applied via a hydraulic fluid so that the volume concentration of particles and, hence, the distance of separation between the particles could be measured as a function of applied pressure. 

Following on from this work two types of mathematical model were developed that do not rely on measuring the contact area. These models are the "liquid-drop" model (Yoneda, 1973) and the elastic membrane model (Cheng, 1987a Feng and Yang, 1973 Lardner and Pujara, 1980). 

An analytical elastic membrane model was developed by Feng and Yang (1973) to model the compression of an inflated, non-linear elastic, spherical membrane between two parallel surfaces where the internal contents of the cell were taken to be a gas. This model was extended by Lardner and Pujara (1980) to represent the interior of the cell as an incompressible liquid. This latter assumption obviously makes the model more representative of biological cells. Importantly, this model also does not assume that the cell wall tensions are isotropic. The model is based on a choice of cell wall material constitutive relationships (e.g., linear-elastic, Mooney-Rivlin) and governing equations, which link the constitutive equations to the geometry of the cell during compression. 

The elastic membrane model assumes that the cell is a thin-walled sphere filled with incompressible fluid. Because the wall is thin, it may be treated as a mechanical membrane. It can be presumed that the wall cannot support out-of-plane shear stresses or bending moments. This situation is described as plane stress, as the only non-zero stresses are in the plane of the cell wall. Furthermore, the stresses can be expressed as... 

It is assumed that the cell is symmetrical across the equatorial plane and axi-symmetrical around the axis of compression, the tj axis. This symmetry allows the compression of the cell to be fully represented by a 2D curve in the positive r and p axis. To understand the elastic membrane model, the geometry of the spherical cell under compression can be represented by Figure 10. 

J. T. Oden and T. Sato, Finite Strains and Displacements of Elastic Membranes by the Finite Element Method, Int. J. Solids and Struct., 3, 471 -88 (1967). 

J. M. Charrier, S. Shrivastava, and R. Wu, Free and Constrained Inflation of Elastic Membranes in Relation to Thermoforming - non-axisymmetric Problems, J. Strain Anal., 24, 55-74 (1989). 

At a specified point in the tank, 100 cm of hydrochloric acid 1.2N(Cg0 = 0.83 moles. m- after complete mixing in the tank in the absence of reaction) were injected by means of a cylinder obturated at its lower end by an elastic membrane which becomes inflated and bursts out when submitted to the pressure of the liquid pushed by a piston. The acid was thus injected without any preferential direction. This locally released acid B triggers reactions f2j and 3]. If the local micromixing state is perfect, the acid is totally and instantaneously neutralized, as it is in stoichiometric defect with respect to A. The first reaction being very fast as compared to the second one, the precipitate S does not appear. Conversely, if mixing of the acid is not instantaneously... 

Figure 3.12. Structure of vessels. All vessels contain three layers the intima, media, and adventitia. In large elastic arteries, the intima is found beneath the internal elastic membrane and interfaces with the lumen. The media is found between the internal and external elastic membranes, and the adventitia is found outside the external elastic membrane. The media is less prominent in the other types of vessles.

To conclude, we presented a new method to account for the effect of the thermal fluctuations on the interactions between elastic membranes, based on a predicted intermembrane separation distribution. It was shown that for a typical potential, the distribution function is asymmetric, with an asymmetry dependent on the applied pressure and on the interaction potential between membranes. Equations for the pressure, root-mean-square fluctuation, and asymmetry as functions of the average distance (and the parameters of the interacting membranes) were derived. While no experimental data are available for two interacting lipid bilayers, a comparison with experimental data for multilayers of lipid bilayer/water was provided. The values of the parameters, determined from the fit of experimental data, were found within the ranges determined from other experiments. 

An alternate procedure to calculate the distribution of an elastic membrane in a harmonic potential has as starting point the direct integration of the partition function of the canonical ensemble in Fourier space21... 

This occurs in man as a thin homogenous sheet with a thickness of 8-14 pm. The rabbit eye does not possess this layer. It is not a true elastic membrane and does not regenerate when destroyed. This layer is not considered to be a barrier to drag absorption across the cornea. 

---