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Physiologically-based pharmacokinetic models combine knowledge about physiology, drug product properties, such as physicochemical parameters, absorption, distribution, metabolism, excretion characteristics, formulation attributes, and trial design or dosing regimen to mechanistically simulate drug pharmacokinetics (PK). The current work describes the development of a multiphase, multilayer mechanistic dermal absorption (MPML MechDermA) model within the Simcyp Simulator capable of simulating uptake and permeation of drugs through human skin following application of drug products to the skin. The model was designed to account for formulation characteristics as well as body site- and sex- population variability to predict local and systemic bioavailability. The present report outlines the structure and assumptions of the MPML MechDermA model and includes results from simulations comparing absorption at multiple body sites for two compounds, caffeine and benzoic acid, formulated as solutions. Finally, a model of the Feldene (piroxicam) topical gel, 0.5% was developed and assessed for its ability to predict both plasma and local skin concentrations when compared to in vivo PK data.

Spray coating is a common method of distributing liquids over powders, especially in the pharmaceutical, detergent and food industries. During this process, liquid drops are deposited on the surface of particles. Liquid is then transferred between particles via particle collisions, in a process called liquid contact spreading. This contact spreading process facilitates inter-particle coating, in which wetting, de-wetting, mixing and drying are occurring simultaneously. This work presents the first experimental study of the mechanism of liquid contact spreading. In this work, a novel experimental method has been developed to investigate the mechanism of contact spreading, incorporating a newly developed image analysis technique, based on colourimetric measurements, to quantitatively determine coating behaviour via contact spreading.\ud \ud Here, experiments designed to isolate the contact spreading coating mechanism were performed in a tumbling drum using a model material system; alumina particles and dyed polyethylene glycol solutions of varying viscosities. The coating uniformity was quantified by the variation in inter-particle coating; the coefficient of variation (CoV). For all systems, the uniformity of the coating increased with time until the CoV decreased to an asymptotic value. The rate of the decrease in the CoV was successfully fitted using an exponential decay function.\ud \ud The viscosity of the coating solution had a significant effect on the rate of liquid transfer; the lower the viscosity the faster the contact spreading process. This effect is attributed to differences in the formation and stability of liquid bridges between the particles, influencing the extent of liquid transfer. The results also show that in most cases examined here, viscous forces play a main role in the contact spreading process, and the contribution of capillary forces are minimal. This understanding could assist the design and scale up for the wet coating processes.

We review the most recent studies of drainage/imbibition of foams placed on porous substrates: the latest theoretical models, simulation studies and experimental observations. Foam products are ideal for imbibition and penetration into porous media, and they have gained substantial interests in both industrial and scientific areas. Foams are suitable products in cosmetics and pharmaceutical industry and have recently been used in drug delivery processes due to the improved wetting behaviour. A description of the features and parameters affecting foam drainage placed on porous substrates is presented; complexity and simultaneous actions occurring in the process are discussed. The difference between free foam drainage and the drainage of foam placed on a porous substrate is clarified, and a new phenomenon, which is a formation of a free liquid layer at the foam/porous substrate interface, was theoretically predicted and experimentally verified. Considering the effect of parameters on the rate of imbibition into thick or thin porous substrate revealed the existence of three different regimes of the process. Recent theoretical predictions and simulation of wetted area, foam height and possibility of free liquid layer formation in the course of drainage and imbibition into thin porous layer showed a good agreement with experimental observations.

Initial wetting of crystals by binder droplets is a key rate process in spherical agglomeration, however there are no models to predict the kinetics and formation of agglomerate nuclei. Two new mathematical models are introduced for agglomerate nucleation by an immersion mechanism; immersion rate limited model and collision rate limited model. The agglomerate nucleation number developed in this work predicts different regimes; immersion rate limited, collision rate limited and intermediate. In an immersion rate limited regime, agglomerate size increases with square root of time. In a collision rate limited regime, size increases linearly with time if the bulk crystal volume fraction, φPb, is constant, or with an exponential decay rate for batch crystallisation with decreasing φPb. The timescale for nucleation is less than ten minutes for a broad range of conditions, significantly less than most crystallisation timescales. These models have great promise for population balance modelling and spherical agglomeration optimisation. Keywords: Spherical agglomeration, Immersion nucleation, Immersion rate, Collision rate, Binder droplet, Mathematical modelling

Foams have recently been characterised as ideal products for pharmaceutical and topical use applications for the delivery of topical active agents. Foams are usually produced in a wet form but in a number of applications moderately dry foams are required. Drying of foam under terrestrial conditions proceeds under the action of gravity, which is impossible under microgravity condition. Below a new method of drying foams under microgravity condition is suggested. According to this method foam should be placed on a porous support, which will absorb the liquid from foam based on capillary forces only. The final liquid content inside the foam can be achieved by a proper selection of the porous support. The suggested method allows drying foams under microgravity conditions. Interaction of foams with porous support under terrestrial conditions was developed only recently and theoretically investigated (Arjmandi-Tash, O.; Kovalchuk, N.; Trybala, A.; Starov, V. Foam Drainage Placed on a Porous Substrate. Soft Matter2015, 11 (18), 3643–3652) followed by a theory of foam drainage on thin porous substrates (Koursari, N.; Arjmandi-Tash, O.; Johnson, P.; Trybala, A.; Starov, M. V. Foam Drainage Placed on Thin Porous Substrate. Soft Matter, 2019, (submitted)), where rate of drainage, radius of the wetted area inside the porous layer and other characteristics of the process were predicted. The latter model is modified below to investigate foam drying under microgravity conditions. Model predictions are compared with experimental observations for foam created using Triton X-100 at concentrations above CMC. Wetted radius inside the porous substrate was measured and results were compered to model predictions. Experimental observations for spreading area versus time show reasonable agreement with theoretical predictions for all investigated systems.

A mathematical model of free drainage of foam built up by a power-law non-Newtonian liquid is developed. The theory predictions are compared with the experimental data on the drainage of foams formed using commercially available Aculyn™22 and Aculyn™33 polymeric solutions. The rheological parameters of the polymeric solutions were independently measured and used in the calculations. The deduced dimensionless equations were solved using finite element method with appropriate boundary conditions. The numerical simulations show that the decrease in the foam height and liquid content is very fast in the very beginning of the drainage; however, it reaches a steady state at longer time. The predicted values of the time evolution of the foam height and liquid content are in good agreement with the measured experimental data.

Equilibrium of liquid droplets on soft deformable substrates is investigated. Disjoining pressure action in the vicinity of the apparent three phase contact line is taken into account. It is shown that the combined disjoining and capillary pressure action determine the substrate deformation. A simplified linear disjoining pressure isotherm and simple Winkler's model to account for the substrate deformation are used which allows deducing analytical solutions for both the liquid profile and the substrate deformation. The apparent equilibrium contact angle of the liquid droplet with the deformable substrate is calculated and its dependency on the system parameters is investigated.

There has been a substantial increase in the number of publications in the field of wetting and spreading since 2010. This increase in the rate of publications can be attributed to the broader application of wetting phenomena in new areas. It is impossible to review such a huge number of\ud publications; that is, some topics in the field of wetting and spreading are selected to be discussed below. These topics are as follows: (i) Contact angle hysteresis on smooth homogeneous solid surfaces via disjoining/conjoining pressure. It is shown that the hysteresis contact angles can be calculated via\ud disjoining/conjoining pressure. The theory indicates that the equilibrium contact angle is closer to a static receding contact angle than to a static advancing contact angle. (ii) The wetting of deformable substrates, which is caused by surface forces action in the vicinity of the apparent three-phase contact line, leading to a deformation on the substrate. (iii) The kinetics of wetting and spreading of non-Newtonian liquid (blood) over porous substrates. We showed that in spite of the enormous complexity of blood, the spreading over porous substrate can be described using a relatively simple model: a power low-shear-thinning non-Newtonian liquid. (iv) The kinetics of spreading of surfactant solutions. In this part, new results related to various surfactant solution mixtures (synergy and crystallization) are discussed, which shows some possible direction for the future revealing of superspreading phenomena. (v) The kinetics of spreading of surfactant solutions over hair. Fundamental problems to be solved are identified.

The hydrodynamics of a gas–liquid–solid fluidized bed was investigated by applying the S statistics method to pressure fluctuations measured under various operating conditions in a laboratory-scale bed. S statistics tests reveal the existence of three transition velocities, especially at low gas velocities. Four distinct fluidization regimes, namely, the compacted bed, agitated bed and coalesced and discrete bubble regimes were detected. A comparison of reconstructed attractors of pressure fluctuations measured at different axial positions along the riser and with various solid loadings showed significant differences in the signals compared before fluidization, especially at minimum liquid agitation velocity. Close to the minimum liquid fluidization velocity and high liquid velocities, the variation in particle size has an insignificant effect on the bed hydrodynamics. Therefore, S statistics is a reliable method to demarcate different fluidization regimes and to characterize the influence of various operating conditions on the hydrodynamics of gas–liquid–solid fluidized beds. The method is applicable in large-scale industrial installations to detect dynamic changes within a bed, such as regime transitions or agglomeration.

Drainage of foams placed on porous substrates has only recently been theoretically investigated (O. Arjmandi-Tash, N. Kovalchuk, A. Trybala, V. Starov, Foam Drainage Placed on a Porous Substrate, Soft Matter, 2015, 11(18), 3643–3652), where an equation describing foam drainage (with non-slip boundary conditions on the liquid–air interfaces) was combined with that of imbibition of liquid into the thick porous substrate. Foam-based applications have been used as a method of drug delivery, which is a recent and promising area of research related to application of medicinal products onto the skin or hair, which are both thin porous layers. A theory of foam drainage (taking into account surface viscosity) placed on a completely wettable thin porous layer is developed: the rate of foam drainage and imbibition inside the porous layer and other characteristics of the process are predicted. The “effective slip” caused by the surface viscosity increased a movement of the top boundary of the foam. The theoretical predictions are compared with experimental observations of foam drainage placed on thin porous layers. The comparison showed a reasonable agreement between the theoretical predictions and experimental observations. One of the phenomena during foam application is the possibility of a build-up of a free liquid layer on the foam/porous layer interface, which can be very useful for applications. Three different regimes of spreading/imbibition process have been predicted. Conditions and durations of free liquid layer formation have been theoretically predicted and compared with experimental observations.

The sampling process of dried blood spot (DBS) is spreading of blood, which is non-Newtonian fluid, over porous substrates. Spreading/imbibition behaviour of blood samples over Whatman 903 filter paper in complete wetting case has been investigated earlier (Tzu Chieh Chao et al., 2015). The spreading behaviour of DBS sampling has been investigated below in the case of partial wetting. Nitrocellulose membranes (NCM) with different pore size and silanized Whatman 903 blood saving card have been used as porous substrates. The spreading experiments have been applied to obtain the time evolution of spreading parameters, such as, radius of droplet base, dynamic contact angle and radius of the wetted region. The result of spreading on NCM showed that the spreading process was a partial wetting spreading. A separation of red blood cells (RBCs) and blood plasma has been found in the case of the blood drop spreading over 0.2 and 3.0 μm NCMs. Important that while the RBCs were not damaged in this process. This opens a completely new opportunity to (1) investigate RBCs and plasma separately; (2) to use this method for non-destructive separation of living cells from aqueous solutions.

Surfactants are broadly used to improve wetting properties of aqueous formulations. The improvement is achieved by essential reduction of liquid/air and solid/liquid interfacial tensions resulting in the decrease of contact angle. For moderately hydrophobic substrates, there is a range of surfactants providing complete wetting of substrate. With the decrease of substrate surface energy, this range of surfactants reduces very quickly and only trisiloxane surfactant solutions are capable to wet completely such highly hydrophobic substrates as polypropylene and parafilm. That is why these surfactants are referred to as superspreaders. The most intriguing feature of wetting surfactant solutions is their ability to spread much faster than pure liquids with spread area, S, being proportional to time, t, S~t, as compared to S~t(0.2) for pure liquids, which wet completely the solid substrate. Trisiloxane surfactant solutions spread faster than other aqueous surfactant solutions, which also provide complete wetting, being superspreaders in the sense of spreading rate as well. The mechanism of fast spreading of surfactant solutions on hydrophobic substrates and much higher spreading rates for trisiloxane solutions are to be explained. Below the available experimental data on superspreading and surfactant-enhanced spreading are analysed/summarised, and possible mechanisms governing the fast spreading are discussed.

The objective of the present work is to investigate wetting of hair tresses with the solutions of two polyacrylate polymers broadly used in cosmetic products. Wetting properties of the neutralized Aculyn-22™ (A22) and Aculyn-33™ (A33) polymer solutions on dry hair tresses are studied. Wetting behaviour on the dry undamaged hair tresses is drastically different between the two polymers and, in a first approximation, not directly linked with their bulk rheology. In the case of A22 the droplet spreads and remains on the tress after spreading for at least half an hour, during which it slowly evaporates and possibly penetrates inside the hair. For A33 fast penetration of the droplet inside the hair tress is observed when the advancing contact angle reaches a critical value of about 60°. It can be attributed to the so-called Cassie–Wenzel wetting transition, in which the liquid starts to penetrate inside the hair array.

Initial wetting of crystals by binder droplets is a key rate process in spherical agglomeration, however there are no models to predict the kinetics and formation of agglomerate nuclei. Two new mathematical models are introduced for agglomerate nucleation by an immersion mechanism; immersion rate limited model and collision rate limited model. The agglomerate nucleation number developed in this work predicts different regimes; immersion rate limited, collision rate limited and intermediate. In an immersion rate limited regime, agglomerate size increases with square root of time. In a collision rate limited regime, size increases linearly with time if the bulk crystal volume fraction, φPb, is constant, or with an exponential decay rate for batch crystallisation with decreasing φPb. The timescale for nucleation is less than ten minutes for a broad range of conditions, significantly less than most crystallisation timescales. These models have great promise for population balance modelling and spherical agglomeration optimisation.

A new theory of foam drainage in the presence of a porous support was introduced and accordingly, a mathematical model which combines the foam drainage equation with the equation describing imbibition into the porous substrate was developed. Proposed dimensionless equations were solved using finite element method. Boundary conditions were zero liquid flux on the top of the foam and continuity of flux on foam/substrate interface. It was found that the kinetics of foam drainage depends on three dimensionless numbers. The result indicated that there are two possible scenarios for the interaction of foam with a porous substrate: (i) a rapid imbibition, the liquid volume fraction at the bottom of the foam is a decreasing function of time. In this regime the imbibition into the porous substrate dominates and it is faster as compared with the foam drainage; (ii) a slow imbibition, the liquid volume fraction at the interface experiences a peak point and imbibition into the porous substrate is slower for some time as compared with the foam drainage.

Effective time series analysis techniques in time and frequency domains were applied to characterize three-phase fluidization under a wide range of gas and liquid velocities. The experiments were carried out in a laboratory scale fluidized bed, operated under ambient conditions. Standard deviation of pressure fluctuations successfully detected four distinct regimes, namely compacted bed, agitated bed, coalesced and discrete bubble regimes (or discrete and dispersed bubble regimes at extremely low gas velocities). A minimum in skewness and average cycle frequency and a maximum in flatness indicated a minimum deviation from larger structures of the bed. A transition between macro and finer structures occurred during agitated bed regime and accordingly, minimum liquid fluidization velocity was perceived by skewness, flatness, and average cycle frequency analyses. The results showed that at very low liquid velocities in the compacted bed regime, the power spectrum at lower frequencies slightly increased with increasing liquid velocity. This results in the consecutive appearance of single bubbles of low frequencies. With further increase in the liquid velocity at agitated bed regime the power spectrum at lower frequencies gradually decreased. At higher liquid velocities near ULmf, the peak dominant frequency is transmitted from low frequency ranges of 2 Hz to the higher frequency of about 10 Hz.

Predicting formation mode of double emulsion drops in microfluidic emulsification is crucial for controlling the drop size and morphology.A three-phase Volume of Fluid-Continuum Surface Force (VOF-CSF) model was developed, validated with analytical solutions, and used to investigate drop formation in different regimes. Experimental investigations were done using a glue-free demountable glass capillary device with a true axisymmetric geometry, capable of readjusting the distance between the two inner capillaries during operation.A non-dimensional parameter (ζ) for prediction of double emulsion formation mode as a function of the capillary numbers of all fluids and device geometry was developed and its critical values were determined using simulation and experimental data. At logζ5.7, drops were formed in dripping mode; the widening jetting occurred at 5logζ5.7; while the narrowing jetting was observed at logζ5. The ζ criterion was correlated with the ratio of the break-up length to drop diameter. The transition from widening to narrowing jetting was achieved by increasing the outer fluid flow rate at the high capillary number of the inner fluid. The drop size was reduced by reducing the distance between the two inner capillaries and the minimum drop size was achieved when the distance between the capillaries was zero.

Time series analysis techniques in time domain and average cycle frequency were applied to characterize bubbling fluidization. The experiments were carried out in a laboratory scale fluidized bed, operated under ambient conditions and various sizes of particles, measurement heights, and different superficial gas velocities. It was found that a minimum in average cycle frequency and flatness and a shift of skewness from negative to positive against velocity correspond to shift from macrostructures and finer structures of the flow rather than transition velocity from the bubbling to turbulent regime. The power spectrum estimation of the measured pressure fluctuations shows that the peak dominant frequency of the pressure fluctuations is about 1.5–2.5 Hz which is corresponding to the macrostructures of the bed. Accordingly, the onset of turbulent fluidization regime was detected through standard deviation analysis. It was shown that the simple analysis techniques still have interesting information about hydr...

A model for drainage/imbibition of a foam placed on the top of a porous substrate is presented. The equation of liquid imbibition into the porous substrate is coupled with a foam drainage equation at the foam/porous substrate interface. The deduced dimensionless equations are solved using a finite element method. It was found that the kinetics of foam drainage/imbibition depends on three dimensionless numbers and the initial liquid volume fraction. The result shows that there are three different regimes of the process. Each regime starts after initial rapid decrease of a liquid volume fraction at the foam/porous substrate interface: (i) rapid imbibition: the liquid volume fraction inside the foam at the foam/porous substrate interface remains constant close to a final liquid volume fraction; (ii) intermediate imbibition: the liquid volume fraction at the interface with the porous substrate experiences a peak point and imbibition into the porous substrate is slower as compared with the drainage; (iii) slow imbibition: the liquid volume fraction at the foam/porous substrate interface increases to a maximum limiting value and a free liquid layer is formed between the foam and the porous substrate. However, the free liquid layer disappears after some time. The transition points between these three different drainage/imbibition regimes were delineated by introducing two dimensionless numbers.

The process of dried blood spot sampling involves simultaneous spreading and penetration of blood into a porous filter paper with subsequent evaporation and drying. Spreading of small drops of blood, which is a non-Newtonian liquid, over a dry porous layer is investigated from both theoretical and experimental points of view.A system of two differential equations is derived, which describes the time evolution of radii of both the drop base and the wetted region inside the porous medium. The system of equations does not include any fitting parameters. The predicted time evolutions of both radii are compared with experimental data published earlier.For a given power law dependency of viscosity of blood with different hematocrit level, radii of both drop base and wetted region, and contact angle fell on three universal curves if appropriate scales are used with a plot of the dimensionless radii of the drop base and the wetted region inside the porous layer and dynamic contact angle on dimensionless time. The predicted theoretical relationships are three universal curves accounting satisfactorily for the experimental data.

Introduction: Atherosclerosis is a focal disease that susceptibly forms near bifurcations, anastomotic joints, side branches, and curved vessels along the arterial tree. In this study, pulsatile blood flow in a bifurcation model with a non-planar branch is investigated. Methods: Wall shear stress (WSS) distributions along generating lines on vessels for different bifurcation angles are calculated during the pulse cycle. Results: The WSS at the outer side of the bifurcation plane vanishes especially for higher bifurcation angles but by increasing the bifurcation angle low WSS region squeezes. At the systolic phase there is a high possibility of formation of a separation region at the outer side of bifurcation plane for all the cases. WSS peaks exist on the inner side of bifurcation plane near the entry section of daughter vessels and these peaks drop as bifurcation angle is increased. Conclusion: It was found that non-planarity of the daughter vessel lowers the minimum WSS at the outer side of the bifurcation and increases the maximum WSS at the inner side. So it seems that the formation of atherosclerotic plaques at bifurcation region in direction of non-planar daughter vessel is more risky., BioImpacts; ISSN 2228-5660

Introduction: In this research the behavior of coronary arteries has been studied with symmetric and asymmetric consecutive stenosis, and grafted vessels. Methods: The incompressible Navier-Stokes and energy equations were discretized with second-order upwind method. Assumptions such as Newtonian fluid, wall rigidity and steady-flow were used. Results: All the calculations showed the same results with Newtonians and non-Newtonian fluids. It was found that the possibility of stenosis be reduced by increasing the graft angle. However, there exists further stenosis possibility. Among the three graft angles 20, 30 ̊ and 40, the 30 ̊ was found to be the reliable ones. Conclusion: Based on these findings, it can be deduced that there would be a high risk of further atherosclerosis when the first stenose has the maximum percentage., BioImpacts; ISSN 2228-5660