Flux limitation in ultrafiltration: Osmotic pressure model and gel layer model

The characteristic permeate flux behaviour in ultrafiltration, i.e., the existence of a limiting flux which is independent of applied pressure and membrane resistance and a linear plot of the limiting flux versus the logarithm of the feed concentration, is explained by the osmotic pressure model. In the mathematical description presented here, a quantity ΔΠn/(Rmk) is introduced which is the ratio of the resistance caused by the osmotic pressure and the resistance of the membrane itself. For high values of this quantity (19) the flux is practically limited by the osmotic pressure. p]Factors leading to high values of the quantityΔΠnn/(Rmk) are discussed and it is concluded that in the ultrafiltration of medium molecular weight solutes (10,000 to 100,000 daltons) osmotic pressure limitation is more likely than gel layer limitatio

The osmotic pressure of 3He-4He mixtures along the phase separation curve

The osmotic pressure of 3He-4He mixtures was measured along the phase separation curve at temperatures up to 500 mK by balancing it with the fountain pressure of pure 4He. The usefullness of the secondary osmotic pressure thermometer was reinvestigated

Observations on the physiological development of trout eggs [Translation from: Roux. Arch. f. Entwicklungsmechanik der Organismen, 114. 771, 1929]

The osmotic pressure of the perivitelline fluid and the yolk of trout (Salmo trutta) eggs were measured separately by the Drucker-Schrein method. The permeability of the egg membrane and the variations in the osmotic pressure of the eggs when placed in salt solutions were also investigated

Unbinding Transition Induced by Osmotic Pressure in Relation to Unilamellar Vesicle Formation

Small-angle X-ray scattering and phase-contrast microscopy experiments were performed to investigate the effect of the osmotic pressure on vesicle formation in a dioleoylphosphatidylcholine (DOPC)/water/NaI system. Multi-lamellar vesicles were formed when a pure lipid film was hydrated with an aqueous solution of NaI. On the other hand, uni-lamellar vesicles (ULVs) were formed when a lipid film mixed with an enough amount of NaI was hydrated. To confirm the effect of the osmotic pressure due to NaI, a free-energy calculation was performed. This result showed that the osmotic pressure induced an unbinding transition on the hydration process, which resulted in ULV formation

Theoretical Framework for Microscopic Osmotic Phenomena

The basic ingredients of osmotic pressure are a solvent fluid with a soluble molecular species which is restricted to a chamber by a boundary which is permeable to the solvent fluid but impermeable to the solute molecules. For macroscopic systems at equilibrium, the osmotic pressure is given by the classical van't Hoff Law, which states that the pressure is proportional to the product of the temperature and the difference of the solute concentrations inside and outside the chamber. For microscopic systems the diameter of the chamber may be comparable to the length-scale associated with the solute-wall interactions or solute molecular interactions. In each of these cases, the assumptions underlying the classical van't Hoff Law may no longer hold. In this paper we develop a general theoretical framework which captures corrections to the classical theory for the osmotic pressure under more general relationships between the size of the chamber and the interaction length scales. We also show that notions of osmotic pressure based on the hydrostatic pressure of the fluid and the mechanical pressure on the bounding walls of the chamber must be distinguished for microscopic systems. To demonstrate how the theoretical framework can be applied, numerical results are presented for the osmotic pressure associated with a polymer of N monomers confined in a spherical chamber as the bond strength is varied

New Osmosis Law and Theory: the New Formula that Replaces van't Hoff Osmotic Pressure Equation

This article derived a new abstract concept from the osmotic process and concluded it via "osmotic force" with a new law -- "osmotic law". The "osmotic law" describes that, in an osmotic system, osmolyte moves osmotically from the side with higher "osmotic force" to the side with lower "osmotic force". In addition, it was proved mathematically that the osmotic process could be explained perfectly via "osmotic force" and "osmotic laws", which can prevent the difficulties in using current "osmotic pressure" concept to explain the osmotic process and phenomenon. A theory and equation to describe the curve of osmotic pressure vs. different ideal solution concentrations are also derived, which can overcome the limitedness and incompleteness of van't Hoff osmotic pressure formula (a linear equation) which is applicable to ideal dilute solution only

Ultrafiltration of protein solutions; the role of protein association in rejection and osmotic pressure

The monomer-dimer equilibrium of the protein β-lactoglobulin under neutral conditions appears to influence the rejection and the osmotic pressure build-up, both phenomena closely related to ultrafiltration. Rejection measurements indicate different rejections for the β-lactoglobulin monomers and dimers: the membrane rejects the dimer almost completely and the monomer only partially. The osmotic pressure turns out to be highly dependent on the protein concentration. A good agreement, up to high concentrations, is found between experimental data and theoretical osmotic pressures, calculated by taking into account the state of association, the excluded volume and the Donnan effects. The effect of changes in pH on the osmotic pressure has been measured: a minimum was found around pH = 4.5, where according to the literature, maximum protein-protein interaction occurs

Exact Solution of the Discrete (1+1)-dimensional RSOS Model in a Slit with Field and Wall Interactions

We present the solution of a linear Restricted Solid--on--Solid (RSOS) model confined to a slit. We include a field-like energy, which equivalently weights the area under the interface, and also include independent interaction terms with both walls. This model can also be mapped to a lattice polymer model of Motzkin paths in a slit interacting with both walls and including an osmotic pressure. This work generalises previous work on the RSOS model in the half-plane which has a solution that was shown recently to exhibit a novel mathematical structure involving basic hypergeometric functions ${}_3\phi_2$. Because of the mathematical relationship between half-plane and slit this work hence effectively explores the underlying $q$-orthogonal polynomial structure to that solution. It also generalises two other recent works: one on Dyck paths weighted with an osmotic pressure in a slit and another concerning Motzkin paths without an osmotic pressure term in a slit