Mass Transfer around Active Particles in Fluidized Beds 589 Dennis, J.S.; Hayhurst, A.N. & Scott, S.A. (2006). The combustion of large particles of char in bubbling fluidized beds: the dependence of Sherwood number and the rate of burning on particle diameter. Combustion & Flame, 147, 185-194. Donsì, G.; Ferrari, G. & De Vita, A. (1998). Analysis of transport phenomena in two component fluidized beds, In: Fluidization IX, Fan, L S. & Knowlton, T.M. (Eds.), pp. 421-428, Engineering Foundation, New York. Donsì, G.; Ferrari, G. & De Vita, A. (2000). Heat and mass transport phenomena between fluidized beds and immersed spherical objects. Recents Progress en Genie des Procedes , 14, 213-220. Frössling, N. (1938). The evaporation of falling drops (in German). Gerlands Beiträge zur Geophysik , 52, 170-216. Guedes de Carvalho, J.R.F. & Coelho, M.A.N. (1986). Comments on mass transfer to large particles in fluidized beds of smaller particles. Chemical Engineering Science, 41, 209- 210. 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Ziegler, E.N. & Brazelton, W.T. (1964). Mechanism of heat transfer to a fixed surface in a fluidized bed. Industrial and Engineering Chemistry Fundamentals, 3, 94-98. Ziegler, E.N. & Holmes, J.T. (1966). Mass transfer from fixed surfaces to gas fluidized beds. Chemical Engineering Science, 21, 117-122. 26 Mass Transfer Phenomena and Biological Membranes Parvin Zakeri-Milani and Hadi Valizadeh Faculty of Pharmacy, Drug Applied Research Center, Research Center for Pharmaceutical Nanotechnology, Tabriz University of Medical Sciences, Tabriz Iran 1. Introduction Mass transfer is the net movement of mass from one location to another in response to applied driving forces. Mass transfer is used by different scientific disciplines for different processes and mechanisms. It is an important phenomena in the pharmaceutical sciences; drug synthesis, preformulation investigations, dosage form design and manufacture and finally ADME (absorption, distribution, metabolism and excretion) studies. In nature, transport occurs in fluids through the combination of advection and diffusion. Diffusion occurs as a result of random thermal motion and is mass transfer due to a spatial gradient in chemical potential or simply, concentration. However the driving force in convective mass transport is the spatial gradient in pressure (Fleisher, 2000). On the other hand, there are other variables influencing mass transfer like electrical potential and temperature which are important in pharmaceutical sciences. In a complex system mass transfer may be driven by multiple driving forces. Mass transfer exists everywhere in nature and also in human body. In fact in the body, mass transport occurs across different types of cell membranes under different physiological conditions. This chapter is aimed at reviewing transport across biological membranes, with an emphasis on intestinal absorption, its model analysis and permeability prediction. 2. Transport across membranes Biomembrane or biological membrane is a separating amphipathic layer that acts as a barrier within or around a cell. The membrane that retains the cell contents and separates the cell from surrounding medium is called plasma membrane. This membrane acts as a lipid bilayer permeability barrier in which the hydrocarbon tails are in the centre of the bilayer and the electrically charged or polar headgroups are in contact with watery or aqueous solutions. There are also protein molecules that are attached to or associated with the membrane of a cell. Generally cell membrane proteins are divided into integral (intrinsic) and peripheral (extrinsic) classes. Integral membrane proteins containing a sequence of hydrophobic group are permanently attached to the membrane while peripheral proteins are temporarily attached to the surface of the cell, either to the lipid bilayer or to integral proteins. Integral proteins are responsible for identification of the cell Mass Transfer in Multiphase Systems and its Applications 594 for recognition by other cells and immunological behaviour, the initiation of intracellular responses to external molecules (like pituitary hormones, prostaglandins, gastric peptides,…), moving substances into and out of the cell (like ATPase,…). Concerning mass transport across a cell, there are a number of different mechanisms, a molecule may simply diffuses across, or be transported by a range of membrane proteins (Washington et al., 2000, Lee and Yang, 2001). 2.1 Passive transport Lipophilic drug molecules with low molecular weight are usually passively diffuses across the epithelial cells. Diffusion process is driven by random molecular motion and continues until a dynamic equilibrium is reached. Passive mass transport is described by Fick,s law which states that the rate of diffusion across a membrane (R) in moles s-1 is proportional to the concentration difference on each side of the membrane: R=(Dk/h).A.∆C (1) Where D is the diffusion coefficient of the drug in the membrane, k is the partition coefficient of the drug into the membrane, h is the membrane thickness, A is the area of membrane over which diffusion is occurring, and ∆C is the difference between concentrations on the outside and the inside of the membrane. However it should be noted that the concentration of drug in systemic blood circulation is negligible in comparison to the drug concentration at the absorption surface and the drug is swept away by the circulation. Therefore the driving force for absorption is enhanced by maintaining the large concentration gradient throughout the absorption process. The diffusion coefficient of a drug is mainly influenced by two important factors, solubility of the drug and its molecular weight. For a molecule to diffuse freely in a hydrophobic cell membrane it must be small in size, soluble in membrane and also in the aqueous extracellular systems. That means an intermediate value of partition coefficient is needed. On the other hand, it is necessary for a number of hydrophilic materials, to pass through the cell membranes by membrane proteins. These proteins allow their substrates to pass into the cell down a concentration gradient, and act like passive but selective pores. For example for glucose diffusion into the cell by hexose transporter system, no energy is expended and it occurs down a concentration gradient. This process is called non-active facilitated mass transport (Sinko, 2006, Washington et al., 2000). 2.2 Active transport In the cell membrane there are a group of proteins that actively compile materials in cells against a concentration gradient. This process is driven by energy derived from cellular metabolism and is defined as primary active trasport. The best-studied systems of this type are the ATPase proteins that are particularly important in maintaining concentration gradients of small ions in cells. However this process is saturable and in the presence of extremely high substrate concentration, the carrier is fully applied and mass transport rate is limited. On the other hand cells often have to accumulate other substances like amino acids and carbohydrates at high concentrations for which conversion of chemical energy into electrostatic potential energy is needed. In this kind of active process, the transport of an ion is coupled to that of another molecule, so that moving an ion out of the membrane down the concentration gradient, a different molecule moves from lower to higher concentration. Mass Transfer Phenomena and Biological Membranes 595 Depending on the transport direction this secondary active process is called symport (same directions) or antiport (opposite directions). Important examples of this process are absoption of glucose and amino acids which are coupled to transporter conformational changes driven by transmucosal sodium gradients (Lee and Yang, 2001). 2.3 Endocytic processes All the above-mentioned mass transport mechanisms are only feasible for small molecules, less than almost 500 Dalton. Larger objects such as particles and macromolecules are absorbed with low efficiency by a completely different mechanism. The process which is called cytosis or endocytosis is defied as extending the membrane and enveloping the object and can be divided into two types, pinocytosis and phagocytosis. Pinocytosis (cell drinking) occurs when dissolved solutes are internalized through binding to non-specific membrane receptors (adsorptive pinocytosis) or binding to specific membrane receptors (receptor- mediated pinocytosis). In some cases, following receptor-mediated pinocytosis the release of undegraded uptaken drug into the extracellular space bounded by the basolateral membrane is happened. This phenomenon called transytosis, represents an important pathway for absorption of proteins and peptides. On the other hand phagocytosis (cell eating) occurs when a particulate matter is taken inside a cell. Although phagocytic processes are finding applications in oral drug delivery and targeting, it is mainly carried out by the specialized cells of the mononuclear phagocyte systems or reticuloendothelial system and is not generally relevant to the transport of drugs across absorption barriers (Lee and Yang, 2001, Fleisher, 2000, Washington et al., 2000). 2.4 Pore transport The aqueous channels which exist in cell membranes allow very small hydrophilic molecules such as urea, water and low molecular weight sugars to be transported into the cells. However because of the limited pore size (0.4 nm), this transcellular pathway is of minor importance for drug absorption (Fleisher, 2000, Lee and Yang, 2001). 2.5 Persorption As epithelial cells are sloughed off at the tip of the villus, a gap in the membrane is temporarily created, allowing entry of materials that are not membrane permeable. This process has been termed persorption which is considered as a main way of entering starch grains, metallic ion particles and some of polymer particles into the blood. 3. Intestinal drug absorption Interest has grown in using in vitro and in situ methods to predict in vivo absorption potential of a drug as early as possible, to determine the mechanism and rate of transport across the intestinal mucosa and to alert the formulator about the possible windows of absorption and other potential restrictions to the formulation approach. Single-pass intestinal perfusion (SPIP) model is one of the mostly used techniques employed in the study of intestinal absorption of compounds which provides a prediction of absorbed oral dose and intestinal permeability in human. In determination of the permeability of the intestinal wall by external perfusion techniques, several models have been proposed (Ho Mass Transfer in Multiphase Systems and its Applications 596 and Higuchi, 1974, Winne, 1978, Winne, 1979, Amidon et al., 1980). In each model, assumptions must be made regarding the convection and diffusion conditions in the experimental system which affects the interpretation of the resulting permeabilities. In ad- dition, the appropriateness of the assumptions in the models to the actual experimental situation must be determined. Mixing tank (MT) model or well mixed model has been previously used to describe the hydrodynamics within the human perfused jejunal segment based on a residence time distribution (Lennernas, 1997). This model has also been used in vitro to simulate gastrointestinal absorption to assess the effects of drug and system parameters on drug absorption (Dressman et al., 1984). However complete radial mixing (CRM) model was used to calculate the fraction dose absorbed and intestinal permeability of gabapentine in rats (Madan et al., 2005). Moreover these two models (MT and CRM) were utilized to develop a theoretical approach for estimation of fraction dose absorbed in human based on a macroscopic mass balance approach (MMBA) (Sinko et al., 1991). Although these models have been theoretically explained, their comparative suitability to be used for experimental data had not been reported. The comparison of proposed models will help to select the best model to establish a strong correlation between rat and human intestinal drug absorption potential. In this section three common models for mass transfer in single pass perfusion experiments (SPIP) will be compared using the rat data, we obtained in our lab. The resulting permeability values differ in each model, and their interpretation rests on the validity of the assumptions (valizadeh et al., 2008). 4. Mass transfer models Three models are described that differ in their convection and diffusion assumptions (Fig 1). Fig. 1. Velocity and concentration profiles for the models. The concentration profiles are also a function of z except for mixing tank model (Amidon et al., 1980) These models are the laminar flow, complete radial mixing (diffusion layer) for convective mass transport in a tube and the perfect mixing tank model. It is convenient to begin with the solute transport equation in cylindrical coordinates (Sinko et al., 1991, Elliott et al., 1980, Bird et al., 1960): Mass Transfer Phenomena and Biological Membranes 597 z CC Gz r zrrr ** **** 1 () ν ∂ ∂∂ = ∂ ∂∂ (2) Where, Z* = Z / L, r* = r / R, z * υ = z ν / Vm, Gz = πDL/2Q , R = radius of the tube, L = length of the tube, Vm = maximum velocity, Q = perfusion flow rate This relationship is subject to the first-order boundary condition at the wall: ww r C PC r * * * 1= ∂ =− ∂ (3) where w P * = Pw R/D = the dimensionless wall permeability. The main assumptions achieving Eq. 1 are: (a) the diffusivity and density are constant; (b) the solution is dilute so that the solvent convection is unperturbed by the solute; (c) the system is at steady state (∂C/∂t = 0); (d) the solvent flows only in the axial (z) direction; (e) the tube radius, R, is independent of Gz; and (f) axial diffusion is small compared to axial convection (Bird et al., 1960). The boundary condition (Eq. 2) is true for many models having a tube wall but does not describe a carrier transport of Michaelis-Menten process at the wall, except at low solute concentrations. 4.1 Complete radial mixing model For this model the velocity profile as with the plug flow model is assumed to be constant. In addition, the concentration is assumed to be constant radially but not axially. That is, there is complete radial but not axial, mixing to give, uniform radial velocity and concentration profiles. With these assumptions, the solution is written as: C m /C 0 = exp (-4 e ff P * Gz) (4) where e ff P * replaces w P * (Ho and Higuchi, 1974, Winne, 1978, Winne, 1979). Since no aqueous resistance is inc1uded in the model directly, the wall resistance is usually augmented with a film or diffusion layer resistance. That is, complete radial mixing occurs up to a thin region or film adjacent to the membrane. In this model the aqueous (luminal) resistance is confined to this region. Hence, the wall permeability includes an aqueous or luminal resistance term and can be written as: wa eff wa PP P PP ** * ** = + (5) where w P * is the true wall permeability and a P * , is the effective aqueous permeability. The aqueous permeability often is written as: a PD δ = (6) Or a PR * δ = (7) Mass Transfer in Multiphase Systems and its Applications 598 where δ is the film thickness and represents an additional parameter that needs to be determined from the data to obtain w P * . For typical experiments, a P * or R/δ is an empirical parameter, since the assumed hydrodynamic conditions may not be realistic at the low Reynolds numbers. The complete radial mixing model also can be derived from a differ- ential mass balance approach (Ho and Higuchi, 1974) and often is referred to as the diffusion layer model. The Calculated eff P * values for tested drugs and the corresponding plot are shown in Table 2 and Fig. 2 respectively. Fig. 2. Plot of dimensionless permeability values vs human P eff values in complete radial mixing model 4.2 Laminar flow model For flow of a newtonian fluid in a cylindrical tube, the exit concentration of a solute with a wall permeability Pw is given by (Amidon et al., 1980): C m /C o = n 1 ∞ = ∑ M n exp (-β n 2 G z ) (8) Where, Cm = "cup-mixing" outlet solute concentration from the perfused length of intestine, Co = inlet solute concentration; Gz = πDL/2Q; (9) Gz is Graetz number, the ratio of the mean tube residence time to the time required for radial diffusional equilibration. D = solute diffusivity in the perfusing fluid L = length of the perfused section of intestine Q = volumetric flow rate of perfusate = πR2(υ) R = radius of perfused intestine (υ) = mean flow velocity [...]... Dev Ind Pharm, 35, 1496-502 27 Heat and Mass Transfer in Packed Bed Drying of Shrinking Particles Manoel Marcelo do Prado1 and Dermeval José Mazzini Sartori2 1Federal 2Federal University of Sergipe, Department of Chemical Engineering University of São Carlos, Department of Chemical Engineering Brazil 1 Introduction Drying is the most widespread heat and mass transport process with applications in several... (mg/min/cm2) Examples of the compounds of this category include propranolol, metoprolol, verapamil and antipyrin which exhibit a high dissolution and absorption However according to intestinal permeability estimates in rat, metoprolol is assigned in class III  616 Mass Transfer in Multiphase Systems and its Applications Fig 10 Classification of tested drugs based on their rat intestinal permeability and. .. framework in Table 5 As it was mentioned before, the mean small intestinal transit time was found to be 199 minutes with a standard deviation of 78 minutes (Yu, 1999, Zakeri-Milani et al., 2009b) This means that as a worst case, the small intestinal transit in some individuals may be only 43 minutes (mean 612 Mass Transfer in Multiphase Systems and its Applications small intestinal transit time – 2 × standard... solid particles throughout the bed, and minimizing the mechanical damages to the material Moreover, investigations into packed bed dryers become increasingly important to obtain information on fluid-particle interactions, because this type of dryer provides the base for better understanding the simultaneous phenomena of heat and mass transfer which occur inside each particle in the bed, and the transfer. .. 604 Mass Transfer in Multiphase Systems and its Applications drugs with a broad range of physicochemical properties for both high and low permeability classes of drugs In fact more poorly absorbed drugs (cimetidine and ranitidine) have been included in the present work and therefore it is likely that the obtained equations will give a more reliable prediction of the human intestinal permeability and. .. rinsed with saline (37oC) and attached to the perfusion assembly which consisted of a syringe pump and a 60 ml syringe was connected to it Care was taken to handle the small intestine gently and to minimize the surgery in order to maintain an intact blood supply Blank perfusion buffer was infused for 10 min by a syringe pump followed by perfusion of compounds at a flow rate of 0.2 ml/min for 90 min... particulate bed, thus affecting the fluid-particle interaction The complexity increases as the extent of shrinkage is also process dependent That is the result of the moisture gradient in the product, which, in turn, induces stresses and, thus, mechanical deformation (Eichler et al., 1997) A scientific understanding of heat and mass transfer in drying of deformable porous media and the role of shrinkage... and optimization of drying operating conditions In this sense, mathematical modelling is very important A large variety of models has been developed to describe the heat and mass transfer inside deep bed dryers Comprehensive reviews of these models and simulation methods are available in the literature (Brooker et al., 1992; Cenkowski et al., 1993) 622 Mass Transfer in Multiphase Systems and its Applications. .. 2008) As a consequence, any attempt to simulate and optimise the operation of drying of shrinking particles requires an experimental investigation that aims to obtain the mass transfer coefficient involved in this operation Knowledge of the shrinkage mechanism, and of the influence of the process variables on shrinkage, improves the understanding of drying kinetics (Hashemi et al., 2009; Bialobrzewski... to provide comprehensive information on theoreticalexperimental analysis of coupled heat and mass transfer in packed bed drying of shrinking particles The modelling of the physical problem is first presented and, then the factors that influence its simulation are discussed The focus is on the shrinkage phenomenon and its effects on the heat and mass transport coefficients Finally, the validity of the . starch grains, metallic ion particles and some of polymer particles into the blood. 3. Intestinal drug absorption Interest has grown in using in vitro and in situ methods to predict in vivo absorption. 1401-1426. Vanderschuren, J. & Delvosalle, C. (1980). Particle-to-particle heat transfer in fluidized bed drying. Chemical Engineering Science, 35, 1741-1748. Mass Transfer in Multiphase Systems. Combustion Institute, 19, 1087-1092. Mass Transfer in Multiphase Systems and its Applications 590 La Nauze, R.D. & Jung, K. (1983a). Combustion kinetics in fluidized beds, In: Proceedings