Non-sink conditions

Johnson and Swindell [77] developed a method for evaluating the complete particle distribution and its effect on dissolution. This method divided the distribution into discrete, noncontinuous partitions, from which Johnson and Swindell determined the dissolution of each partition under sink conditions. The dissolution results from each partition value were then summed to give the total dissolution. Oh et al. [82] and Crison and Amidon [83] performed similar calculations using an expression for non-sink conditions based on a macroscopic mass balance model for predicting oral absorption. The dissolution results from this approach could then be tied to the mass balance of the solution phase to predict oral absorption. 

B. Steady-State Kinetics Under Non-Sink Conditions... 

Unlike the previous kinetics imposed by the sink condition, steady-state transport kinetics under non-sink conditions will lead to equilibrium partitioning between the aqueous phase of the donor and receiver compartments and the cell mono-layer. In contrast to the sink condition wherein CR 0 at any time, under nonsink conditions CR increases throughout time until equilibrium is attained. As previously stated in Eqs. (1) and (3), the rate of mass disappearing from the donor solution is... 

A special case in dissolution-limited bioavailability occurs when the assumption of sink condition in vivo fails that is, the drug concentration in the intestine is dose to the saturation solubility. Class IV compounds, according to BCS, are most prone to this situation due to the combination of low solubility and low permeability, although the same could also happen for class II compounds, depending primarily on the ratio between dose and solubility. Non-sink conditions in vivo lead to less than proportional increases of bioavailability for increased doses. This is illustrated in Fig. 21.8, where the fraction of drug absorbed has been simulated by use of an compartmental absorption and intestinal transit model [35] for different doses and for different permeabilities of a low-solubility, aprotic compound. 

The constraints imposed by sink conditions may be overcome using various approaches. It may be accepted that non-sink conditions apply and that incomplete dissolution will occur. Alternatively, corrections may be made by increasing the volume of the dissolution fluids, removal of the dissolved drug by partition from the aqueous phase of the dissolution fluid to an organic phase either above or below the dissolution fluid, addition of selective adsorbents to remove the dissolved drug, addition of a water-miscible solvent... 

In vitro drug release kinetic was also performed in non-sink conditions using decane as solvent (to prevent drug loss from nanoparticles dissolution) and a laboratory designed release cell. About 10 mg of gliadins nanoparticles (containing 824 fig/g gliadins) were resuspended in 10 ml of decane. Aliquots were collected at successive time intervals and replaced by the same quantity of solvent in order to get a constant volume in the release cell. The samples were analysed by HPLC as described above for encapsulation experiments. 

The apparent permeability value is determined from the concentration of compound in the acceptor compartment after a given incubation time. Equation (15.8) has been derived from the differential equation (15.2), which describes diffusion kinetics under non-sink conditions. Experiments performed under non-sink conditions allow one to work with substantially higher concentrations in the acceptor compartment. This makes optical (UV) detection possible and greatly simplifies analytics when LC-MS is used. In (15.8) below r is the ratio of the absorbance in the acceptor chamber divided by the theoretical equilibrium absorbance (determined independently), Vr is the volume of the acceptor compartment, Vd is the donor volume, A is the accessible filter area (total filter area multiplied by porosity), and t is the incubation time. Equation 1 is obtained from the differential equation... 

The literature survey in this section suggests that the ideal in vitro permeability assay would have pH 6.0 and 7.4 in the donor wells, with pH 7.4 in the acceptor wells. (Such a two-pH combination could differentiate acids from bases and non-ionizables by the differences between the two Pe values.) Furthermore, the acceptor side would have 3% wt/vol BSA to maintain a sink condition (or some sinkforming equivalent). The donor side may benefit from having a bile acid (i.e., taurocholic or glycocholic, 5-15 mM), to solubilize the most lipophilic sample molecules. The ideal lipid barrier would have a composition similar to those in Table 3.1, with the membrane possessing a substantial negative charge (mainly from PI). Excessive DMSO/other co-solvents would be best avoided, due to their unpredictable effects. 

Besides the resuspension of particles, the perfect sink model also neglects the effect of deposited particles on incoming particles. To overcome these limitations, recent models [72, 97-99] assume that particles accumulate within a thin adsorption layer adjacent to the collector surface, and replace the perfect sink conditions with the boundary condition that particles cannot penetrate the collector. General continuity equations are formulated both for the mobile phase and for the immobilized particles in which the immobilization reaction term is decomposed in an accumulation and a removal term, respectively. Through such equations, one can keep track of the particles which arrive at the primary minimum distance and account for their normal and tangential motion. These equations were solved both approximately, and by numerical integration of the governing non-stationary transport equations. 

Next the difficulties in obtaining a good description of the particle electrode interaction are noticed. For non-electrochemical systems several particle surface interaction models exist of which the perfect sink , that is all particles arriving within a critical distance of the electrode are captured, is the simplest one. However, the perfect sink condition can not be used, because it predicts a continuous increase in particle codeposition with increasing current density, which contradicts experimental observations. Therefore, an interaction model based on the assumption that the reduction of adsorbed ions is the determining factor for particle deposition is proposed. This electrode-ion-particle electron transfer (EIPET) model leads to a Butler-Volmer like expression for the particle deposition rate ... 

Also in the PAMPAmodel, alternatives to BSAhave been explored to improve the biorelevance of the model. To overcome the adsorption and/or absence of sink conditions, different additives that do not require an additional step of sample preparation as compared with the addition of albumin, have been proposed. Recently, the use of Double-Sink PAMPA (DS-PAMPA) was proposed as biorelevant alternative to the classic PAMPA methodology (Avdeef, 2003). In DS-PAMPA, a non-specific binding agent (lipophilic sink) was included in the receiver compartment to create sink conditions. 

The latter contribute to the fluxes in time-varying conditions and provide source or sink terms in the presence of chemical reaction, but they have no influence on steady state diffusion or flow measurements in a non-reactive sys cem. 

Non-Black-Surface Enclosures In the following discussion we are concerned with enclosures containing gray sources and sinks, radiatively adiabatic surfaces, and no absorbing gas. The calculation of interchange between a source and a sink under conditions involving successive multiple reflections from other source-sink surfaces in the... 

One particular characteristic of conduction heat transfer in micro-channel heat sinks is the strong three-dimensional character of the phenomenon. The smaller the hydraulic diameter, the more important the coupling between wall and bulk fluid temperatures, because the heat transfer coefficient becomes high. Even though the thermal wall boundary conditions at the inlet and outlet of the solid wall are adiabatic, for small Reynolds numbers the heat flux can become strongly non-uniform most of the flux is transferred to the fluid at the entrance of the micro-channel. Maranzana et al. (2004) analyzed this type of problem and proposed the model of channel flow heat transfer between parallel plates. The geometry shown in Fig. 4.15 corresponds to a flow between parallel plates, the uniform heat flux is imposed on the upper face of block 1 the lower face of block 0 and the side faces of both blocks... 

In both experimental and theoretical investigations on particle deposition steady-state conditions were assumed. The solution of the non-stationary transport equation is of more recent vintage [102, 103], The calculations of the transient deposition of particles onto a rotating disk under the perfect sink boundary conditions revealed that the relaxation time was of the order of seconds for colloidal sized particles. However, the transition time becomes large (102 104 s) when an energy barrier is present and an external force acts towards the collector. 

ASHRAE, Atlanta (1992)]. Process air stream 6, to be conditioned, passes through the adsorbent wheel, where it is dried. This is a non-isothermal process due to the release of heat of adsorption and transfer of heat from a wheel that may be above ambient temperature. The dry but heated air (7) is cooled in a heat exchanger that can be a thermal wheel. This stream (8) is further cooled, and the humidity adjusted back up to a comfort range by direct contact evaporative cooling to provide supply air. Regeneration air stream 1, which can be ambient air or exhausted air, is evaporatively cooled to provide a heat sink for the hot,... 

The gas ballast pump has the function of pumping the fraction of air, which is often only a small part of the water-vapor mixture concerned, without simultaneously pumping much water vapor. It is, therefore, understandable that, within the combination of condenser and gas ballast pump in the stationary condition, the ratios of flow, which occur in the region of rough vacuum, are not easily assessed without further consideration. The simple application of the continuity equation is not adequate because one is no longer concerned with a source or sink-free field of flow (the condenser is, on the basis of condensation processes, a sink). This is emphasized especially at this point. In a practical case of non-functioning of the condenser - gas ballast pump combination, it might be unjustifiable to blame the condenser for the failure. 

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