Hydrostatic pressure difference

Fig. 6.4 Electroosmotic pressure. Hydrostatic pressure difference Ap compensates the osmotic pressure difference between the compartments 1 and 1 and prevents the solvent from flowing through the membrane 2...

As the liquid in the main part of the tank is virtually stationary, the pressure difference between point 1 and point 2 is just the hydrostatic pressure difference ... 

In a similar manner the actual hydrostatic pressure difference P produced by electric endosmose can he calculated, with the following result p 2 ( - V ) K... 

The equilibrium curvature of a liquid surface or meniscus depends not just on its surface tension but also on its density and the effect of gravity. The variation in curvature of a meniscus surface must be due to hydrostatic pressure differences at different vertical points on the meniscus. If the curvature at a given starting point on a surface is known, the adjacent curvature can be obtained from the Laplace equation and its change in hydrostatic pressure Ahpg. In practice the liquid... 

The pressure difference between points A and B must be equal to the hydrostatic pressure difference hpg (where p is the density of the liquid and the density of air is ignored). Thus, we obtain the result that... 

The Onsager reciprocity relation, when applied to the present context, predicts that the cross coefficients a2 and a, which determine the rate of flow ofliquid due to the applied electric field and the current passing due to a hydrostatic pressure difference, respectively, are equal, Le.,... 

SMART MATERIALS. From a technical and simple point of view, a smart material is a material that responds to its environment in a timely manner. To expand on this definition, a smart material is one that receives, transmits, or processes a stimulus and responds by producing a useful effect, which may include a signal that the material is acting upon it. Stimuli may include strain, stress, temperature, chemicals, an electric field, a magnetic field, hydrostatic pressures, different types of radiation, and other forms of stimuli. Transmission or processing of the stimulus may be in the form of an absorption of a photon, of a chemical reaction, of an... 

Toluene is to be chlorinated in a batch-operated bubble column such that, for any particular gas rate chosen, the height of the dispersion in the column is 2.2 m. The reactor will operate at a temperature of 20eC and a pressure of 1 bar (any effect of hydrostatic pressure differences in the column may be neglected). The catalyst will be stannic chloride at a concentration of 5 x 10 4 kmol/m3. 

Here An = RT cosm, Lp = permeability for solute (cm s 1), AP = hydrostatic pressure difference, An = osmotic pressure, a = reflection coefficient, Acs = solute concentration difference, and cs = average solute concentration in upstream solution. Membranes with a reflection coefficient cj —> 0 are permeable to all components whereas a membrane with <7—> 1 rejects all solutes. 

The osmotic flow of the liquid depends on the osmotic and hydrostatic pressure differences across the semipermeable membrane of the system. This phenomenon is the basic feature of nonequilibrium thermodynamics,... 

Pmax = maximum tolerated hydrostatic pressure difference across the membrane before the occurrence of deformation of the housing... 

Generally, the pure-water flux through a membrane layer, uw is directly proportional to the applied hydrostatic pressure difference (transmembrane pressure, AP) according to Darcy s law as follows ... 

Figure 12.1 illustrates the main structure of a nephron [1], The measurements to be reported in this chapter were performed on rats. A rat kidney contains approximately 30000 nephrons as compared to the one million nephrons in a human kidney. The process of urine formation starts with the filtration of plasma in the glomerulus, a system of 20-40 capillary loops. The presence of a relatively high hydrostatic pressure in this system allows water, salts and small molecules to pass out through the capillary wall and into the proximal tubule. Blood cells and proteins are retained, and the filtration process saturates when the protein osmotic pressure balances the hydrostatic pressure difference between the blood and the filtrate in the tubule. For superficial nephrons, the proximal tubule is visible in the surface of the kidney and easily accessible for pressure measurements by means of a thin glass pipette. 

If we consider a membrane having the same solute concentration on both sides, we have All 0 However, a hydrostatic pressure difference AP exists between the two sides, and we have a flow Jv that is a linear function of AP. The term Lp is called the mechanical filtration coefficient, which represents the velocity of the fluid per unit pressure difference between the two sides of the membrane. The cross-phenomenological coefficient Ldp is called the ultrafiltration coefficient, which is related to the coupled diffusion induced by a mechanical pressure of the solute with respect to the solvent. Osmotic pressure difference produces a diffusion flow characterized by the permeability coefficient, which indicates the movement of the solute with respect to the solvent due to the inequality of concentrations on both sides of the membrane. 

The tonoplast does not have an appreciable difference in hydrostatic pressure across it. A higher internal hydrostatic pressure would cause an otherwise slack (folded) tonoplast to be mechanically pushed outward. The observed lack of such motion indicates that AP is close to zero across a typical tonoplast. If the tonoplast were taut, AP would cause a stress in the membrane, analogous to the cell wall stresses discussed in Chapter 1 (Section 1.5C) namely, the stress would be rAPI2t for a spherical vacuole (see Eq. 1.15). However, the tensile strength of biological membranes is low—membranes can rupture when a stress of 0.2 to 1.0 MPa develops in them. For a tonoplast 7 nm thick with a maximum stress before rupturing of 0.5 MPa surrounding a spherical vacuole 14 pm in radius, the maximum hydrostatic pressure difference across the tonoplast is... 

A. What is the hydrostatic pressure difference across the barrier ... 

To illustrate the rather small contribution that the pressure term, VjP, makes to differences in the chemical potential of a charged substance across a membrane, we will compare VjAP with the contribution of the electrical term, ZjFAE. We will use a typical electrical potential difference (AE) across a biological membrane of 100 mVand a hydrostatic pressure difference (AP) of 0.5 MPa (= 0.5 x 106 Pa = 0.5 x 106 N m 2 = 0.5 x 106 J m 3), and we... 

LP is the hydraulic conductivity coefficient and can have units of m s-1 Pa-1. It describes the mechanical filtration capacity of a membrane or other barrier namely, when An is zero, LP relates the total volume flux density, Jv, to the hydrostatic pressure difference, AP. When AP is zero, Equation 3.37 indicates that a difference in osmotic pressure leads to a diffusional flow characterized by the coefficient Lo Membranes also generally exhibit a property called ultrafiltration, whereby they offer different resistances to the passage of the solute and water.14 For instance, in the absence of an osmotic pressure difference (An = 0), Equation 3.37 indicates a diffusional flux density equal to LopkP. Based on Equation 3.35, vs is then... 

T is the reflection coefficient while Att and AP are the osmotic and hydrostatic pressure difference across the membrane... 

Direct contact membrane distillation is a form of membrane distillation in which both the heated feed (liquid) and cold permeate (liquid) are kept in contact with porous hydrophobic membrane (Figure 19.1). In the absence of hydrostatic pressure difference, liquid-vapor interfaces are formed at the entrance of each membrane pore, and a vapor pressure difference is maintained on both sides of the membrane by applying a temperature difference. Water molecules evaporate from the hot liquid-vapor interface, diffuses through the membrane in the form of vapor, and get condensed on the permeate hquid-vapor interface kept at... 

In this model also the decrease of the pore radius due to the formation of an adsorbed layer is incorporated. Flow 1 in Fig. 9.9 is the case of combined Knudsen molecular diffusion in the gas phase and multilayer (surface) flow in the adsorbed phase. In case 2, capillary condensation takes place at the upstream end of the pore (high pressure Pi) but not at the downstream end (P2), and in case 3 the entire capillary is filled with condensate. The crucial point in cases 3 and 4 is that the liquid meniscus with a curved surface not only reduces the vapour pressure (Kelvin equation) but also causes a hydrostatic pressure difference across the meniscus and so causes a capillary suction pressure Pc equal to... 

Permeability is a parameter defined to measure the physical influence of a porous structure on fluid flow, and for a CVI process it is an important physical parameter for fibre preforms. Another important parameter for porous structure is the porosity, which is the most important geometrical property. According to Darcy s law, the volumetric flow rate Q of a fluid through a porous medium is proportional to the hydrostatic pressure difference (AP) across the structure (see Figure 2.16), the permeability and the cross-section area, and is also inversely proportional to the length of the structure and the viscosity of the fluid, as given by [26]... 

The mass transfer through the membranes is achieved by application of an external driving force. The mass transport through porous membranes is enabled by a hydrostatic pressure difference (driving force) between the feed-side and the... 

Consider Figure 1, which depicts the conventional hemodialysis system in counter-current mode. This dlalyzer set-up maximizes the concentration difference across the membrane and thus ensures maximum solute transfer. However this configuration also maximizes the transmembrane hydrostatic pressure difference and thus, maximizes the water flux. During hemodialysis the hydrostatic pressure of the blood must always be higher than the pressure of the dialysate to ensure sterility in the event of a membrane rupture. One has the following constraints during... 

Hydrostatic pressure differences created by internal vaporization rates exceeding the rate of vapor transport through the solid to the surroundings Combinations of the above mechanisms... 

It also follows that the osmotic pressure will be higher in the compartment containing the polyelectrolyte, and water will be drawn in until the osmotic pressure is equal on either side, provided that this would not provoke a hydrostatic pressure difference. Accurate prediction of the osmotic pressure is intricate, because of large nonideality, and we will only consider the osmolality. As long as the volumes remain unchanged, a difference in osmolality of... 

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