Two-dimensional fluid

For an artificial lipid bilayer of any size scale, it is a general feature that the bilayer acts as a two-dimensional fluid due to the presence of the water cushionlayer between the bilayer and the substrate. Due to this fluidic nature, molecules incorporated in the lipid bilayer show two-dimensional free diffusion. By applying any bias for controlling the diffusion dynamics, we can manipulate only the desired molecule within the artificial lipid bilayer, which leads to the development of a molecular separation system. 

Direct observation of molecular diffusion is the most powerful approach to evaluate the bilayer fluidity and molecular diffusivity. Recent advances in optics and CCD devices enable us to detect and track the diffusive motion of a single molecule with an optical microscope. Usually, a fluorescent dye, gold nanoparticle, or fluorescent microsphere is used to label the target molecule in order to visualize it in the microscope [31-33]. By tracking the diffusive motion of the labeled-molecule in an artificial lipid bilayer, random Brownian motion was clearly observed (Figure 13.3) [31]. As already mentioned, the artificial lipid bilayer can be treated as a two-dimensional fluid. Thus, an analysis for a two-dimensional random walk can be applied. Each trajectory observed on the microscope is then numerically analyzed by a simple relationship between the displacement, r, and time interval, T,... 

Czolkos, I., Erkan, Y, Dommersnes, P., Jesorka, A. and Orwar, O. (2007) Controlled Formation and Mixing of Two-Dimensional Fluids. Nano Lett., 7, 1980-1984. 

With further cooling, the SmA LC, which is more ordered than the nematic, becomes the thermodynamic minimum. In the SmA, there is a spontaneous formation of layers, with long-range positional order normal to the layer planes. Thus, the SmA can be considered a stack of two-dimensional fluid layers with crystalline (long-range positional) order in the third dimension, but no... 

Figure 17. Normalized velocity autocorrelation function of a two-dimensional fluid plotted against reduced time. The plot shows the presence of the r 1 tail in Cv(t) at long time. The plot is at p = 0.6 and T = 0.7. The time is scaled by rsc = y/ma2/e. This figure has been taken from Ref. 188.

Previous computations (189) show that the critical value of Rat for non-Boussinesq conditions is approximately the same as that for a Boussinesq fluid in a box heated from below, at least when H2 is the carrier gas. Thus, results from the stability analysis of the classical Rayleigh-Benard problem of a two-dimensional fluid layer heated from below (see reference 190 for a review) may be used to indicate the type of behavior to be expected in a horizontal reactor with insulated side walls. As anticipated from this analysis, an increase in the reactor height from 2 to 4 cm raises the value of Rat to 4768, which is beyond the stability limit, Rat critical = 2056, for a box of aspect ratio 2 (188). The trajectories show the development of buoyancy-driven axial rolls that are symmetric about the midplane and rotating inward. For larger values of Rat (>6000), transitions to three-dimensional or time-de-... 

In the bilayer membrane model of the 1980s, cell membranes were based largely on a fluid lipid bilayer in which proteins were embedded [149,150]. The bilayer was highly dynamic lipids and proteins could flex, rotate, and diffuse laterally in a two-dimensional fluid. Based on this, the enhancing mechanisms of absorption enhancers on transcellular routes have been clarified. In summary, most of the mechanisms are strongly associated with membrane fluidity. The fluidity is likely to be changed by the following factors. 

In the 1970s, the fluid mosaic concept emerged as the most plausible model to account for the known structure and properties of biological membranes [41]. The fact that membranes exist as two-dimensional fluids (liquid disordered) rather than in a gel state (solid ordered) was clearly demonstrated by Frye and Ededin [42], who showed that the lipid and protein components of two separate membranes diffuse into each other when two different cells were fused. Since that time, numerous studies have measured the diffusion coefficient of lipids and proteins in membranes, and the diffusion rates were found to correspond to those expected of a fluid with the viscosity of olive oil rather than a gel phase resembling wax. 

Cell membranes are two-dimensional fluids that exhibit a wide range of dynamic behaviors. Recent technical advances have enabled unprecedented views of membrane dynamics in living cells. In this technical review, we provide a brief overview of three well-studied examples of membrane dynamics lateral diffusion of proteins and lipids in the plane of the membrane, vesicular trafficking between intracellular compartments, and exchange of proteins on and off membranes. We then discuss experimental approaches to monitor membrane protein and lipid dynamics, and we place a special emphasis on the use of genetically encoded fluorescent probes and live cell-imaging techniques. 

In the popular fluid mosaic model for biomembranes, membrane proteins and other membrane-embedded molecules are in a two-dimensional fluid formed by the phospholipids. Such a fluid state allows free motion of constituents within the membrane bilayer and is extremely important for membrane function. The term "membrane fluidity" is a general concept, which refers to the ease of motion for molecules in the highly anisotropic membrane environment. We give a brief description of physical parameters associated with membrane fluidity, such as rotational and translational diffusion rates, order parameters etc., and review physical methods used for their determination. We also show limitations of the fluid mosaic model and discuss recent developments in membrane science that pertain to fluidity, such as evidence for compartmentalization of the biomembrane by the cell cytoskeleton. 

In this section we present the governing equations for the analysis of microchannel heat transfer in two-dimensional fluid flow. For steady two-dimensional and incompressible flow with constant thermophysical properties, the continuity, momentum and energy equations... 

Kavehpour et al. [20] solved the compressible two-dimensional fluid flow and heat transfer characteristics of a gas flowing between two parallel plates under both uniform temperature and uniform heat flux boundary conditions. They compared their results with the experimental results of Arkilic [3] for Helium in a 52.25x1.33x7500 mm channel. They observed an increase in the entrance length and a decrease in the Nusselt number... 

Neutron diffraction detects long-range order but it is sensitive also to less well-ordered systems such as two-dimensional fluids and multilayers. Recent studies, all on graphite substrates, have included He, Ar, Kr, 02, Nj, NO, NDj, CD, and the paraffins C2D6, CaDg, and C4Dio Diffraction... 

Figure 2 L/p/d aggregates. K) Micelle, spheroidal aggregate of single tailed fatty acid, the polar heads being in contact outside with water molecules. B Bi layer, two dimensional fluid, composed of glycerophospholipids or sphingolipids, each molecule possessing two hydrophobic tails. C) Liposome, spheroidal vesicle filled with water, bounded by a single bilayer. D) LDL, lipids/proteln/antioxidants aggregate, carrier of cholesterol in blood plasma.

Lipid bllayers are considered to be two-dimensional fluids what does this mean What drives the movement of lipid molecules and proteins within the bllayer How can such movement be measured What factors affect the degree of membrane fluidity ... 

A second approach attempts to relate the entropy of adsorption to the loss of mobility when a gas phase species, with three degrees of freedom, forms a two dimensional fluid on the surface. This line of reasoning leads to the conclusion that the entropy of adsorption must be negative and no larger than the total entropy of the adsorbate in the gas phase. The authors of this idea (M. Boudart et al. (1967)) go so far as to propose that... 

Falco, R.E., and Chu, C.-C., Measurement of two-dimensional fluid dynamic quantities using a photo chromic grid tracing technique, SPIE, 814. 706 (1987). 

Surface active molecules (surfactants) invariably contain two parts one (hydrophilic) part that prefers to be surrounded by water (the positive charged head of molecule A), and another (hydrophobic) part that prefers to be surrounded by air (or any nonpolar liquid immiscible with water) and shown as a wavy line, called tail. This constitution of the molecule makes it surface active because, clearly, it prefers to be situated at the interface. An example is hexadecyl trimethylammonium bromide (HDTAB) see Fig. 2.2. Not all the soap molecules are adsorbed at the film surfaces a few are present in the core of the film, this number being smaller, the larger the surface activity of the molecule is. The surface activity increases with the length of the tail. The adsorbed soap molecules form a monolayer behaving as a kind of two-dimensional fluid with a certain surface pressure. The (positive) surface pressure is equal to the surface tension of the solution without surfactant minus the surface tension of the solution with surfactant. Between the two surfaces one has the aqueous core containing ions from the added electrolyte (here, K, Br ) and from the soap. 

Nakayama, K. Lerche, I. 1987. Basin analysis by model simulation—effects of geologic parameters on one-dimensional and two-dimensional fluid-flow systems, with application to an oil-field. American Association of Petroleum Geologists Bulletin, 71, 1120. 

When the fluid approaches the sphere from above, the fluid initially contacts the sphere at 0 = 0 (i.e., the stagnation point) because polar angle 6 is defined relative to the positive z axis. This is convenient because the mass transfer boundary layer thickness Sc is a function of 6, and 5c = 0 at 0 = 0. In the laminar and creeping flow regimes, the two-dimensional fluid dynamics problem is axisymmetric (i.e., about the z axis) with... 

In 1972 Singer and Nicolson first proposed he fluid mosaic model of membrane structure (Fig. 3-26). The membrane exists as a two-dimensional fluid of freely diffusing lipids, dotted or embedded with proteins that may function as chaimels, or transporters of solutes across the membrane, as linkages to the cytoskeleton, or as receptors. Some membrane proteins perform two of more of these functions. 

The stratified structure of a smectic liquid crystal imposes certain restrictions on the types of deformation that can take place in it. A compression of the layers requires considerable energy - very much more than for a curvature elastic distortion in a nematic - and therefore only those deformations are easily possible that tend to preserve the interlayer spacing. Consider the smectic A structure in which each layer is, in effect, a two-dimensional fluid with the director n normal to its surface. Assuming the layers to be incompressible, the integral... 

If the fluid surfactant aggregates consist of indefinitely long cylinders rather than bilayers, then two-dimensional fluid phases will be formed. The simplest and best established of these are the normal (Hi) and inverse (Hu) hexagonal phases. In the Hi phase, the surfactant... 

The current opinion, widely held, is that all biological membranes, including mammalian plasma membranes, have as a structural framework a phospholipid bilayer of which the characteristic feature is a parallel array of hydrocarbon chains, averaging 16 carbon atoms in length. This bilayer has some of the properties of a two-dimensional fluid in which individual lipid molecules can diffuse rapidly in the plane of their own monolayer, but cannot easily pass into the other monolayer. This lipid matrix provides the basic structure of the membrane. Whereas some protein molecules cover part of the membrane, particularly its outer surface, other protein strands penetrate the lipid layer, every here and there, and some of these strands are bunched together to form water-filled tubes or pores (Wallach and Zahler, 1966). These proteins are responsible for most of the membrane s functions, e.g. receiving and transduc-... 

Naqvi K. R., 1974, Difiusioft-cofitroUed reactions in two-dimensional fluids Discussion ttf measurements of lateral diffusion of lipids in bioiogicat raen ranes. Chem Phys. Lett. 28 280-284. 

Ferrario, M.,Fionino, A., Cicootti, G. Long-time tails in two-dimensional fluids by molecular dynamics. Physica A 240, 268-276 (1997). doi 10.1016/S0378-4371(97)00150-7... 

Above this temperature the small angle reflections remain unchanged whereas the width and the position of the wide angle halo change in a way characteristic of increased molecular distances and a broader distribution of the molecular distances. Thus the motions which set in at the glass transition occur only within the smectic layers in a direction parallel to the layer surface. The smectic layer acts as a two-dimensional fluid. 

The fluid velocity and temperature in this regime are equivalent to the corresponding wall conditions. The boundary layer approximations for a two-dimensional fluid flow in the Cartesian coordinates (x, y) are given below... 

A number of fundamental approaches have been taken to derive the necessary adsorption isotherm. If the adsorbed fluid is assumed to behave like a two dimensional nonideal fluid, then the Equation of State developed for three dimensional fluids can be applied to two dimensional fluids with a proper change of variables. The 2D-EOS adsorption isotherm equations are not popularly used in the description of data, but they have an advantage of easily extending to multicomponent mixtures by using a proper mixing rule for the adsorption parameters. 

---