Advancing Liquid Front Research Articles

Enhanced in-situ liquid transport investigation setup for pharmaceutical tablet disintegration analysis using terahertz radiation

The disintegration process of pharmaceutical solid dosage forms commences on contact with the dissolution medium and continues with subsequent spontaneous imbibition of the medium in the tablet matrix. Identifying the location of the liquid front in situ during imbibition, therefore, plays a significant role in understanding and modelling the disintegration process. Terahertz pulsed imaging (TPI) technology can be used to investigate this process by its ability to penetrate and identify the liquid front in pharmaceutical tablets. However, previous studies were limited to samples suitable for a flow cell environment, i.e. flat cylindrical disk shapes; thus, most commercial tablets could only be measured with prior destructive sample preparation. This study presents a new experimental setup named open immersion to measure a wide range of pharmaceutical tablets in their intact form. Besides, a series of data processing techniques to extract subtle features of the advancing liquid front are designed and utilised, effectively increasing the maximum thickness of tablets that can be analysed. We used the new method and successfully measured the liquid ingress profiles for a set of oval convex tablets prepared from a complex eroding immediate-release formulation.

The Fluidity of Aluminium Ductile Irons

The fluidity and the effective surface tension of Al-Ductile iron (Fe-3.2C-8.5Al-0.05Mg) were studied at different pouring temperatures. A fluidity test comprising strips 1, 2, 4-and 8-mm-thickness were molded in sodium silicate-bonded silica sand. Our results quantify the increase of melt fluidity with increasing casting modulus and pouring temperature and show that the effective surface tension of the alloy is about 1.8 N/m. Comparing this value with the surface tension of Si-ductile irons and Al-ductile irons of lower Al contents, we conclude that the high level of Al used in this study results in the formation of an alumina film on the advancing liquid front, which raises the effective surface tension, reduces fluidity by 100 mm and reduces the ability of the metal to enter narrow sections from 0.4 to 1.0 mm thickness.

Optical coherence tomography measurement of capillary filling in porous silicon

The use of nanoporous structures with known morphology allows studying the properties of fluids in conditions of strong spatial confinement. Alternatively, the capillary filling of nanoporous structures with simple fluids provides information on their morphology. When a liquid enters the porous structure there is an increase in the optical path of the porous layer, and measuring this optical path as a function of position and time allows evaluating the filling dynamics of the pores. In this work, we determined the capillary filling dynamics of nanostructured porous silicon (PS) by optical coherence tomography. The high spatial resolution of this technique allows one not only to follow the position of the liquid front as a function of time but also to resolve in detail the filling fraction profile of the liquid front inside the PS matrix. Moreover, these profiles contain information about the pore size distribution in the PS structure. Therefore, we show how the determination and analysis of the filling fraction profile along the advancing liquid front can be used as a method to study the pore size distribution inside PS structures.

Comparison between modelled and measured heat transfer rates during the departure of a steam bubble from a solid surface

This paper presents analysis of the heat transfer attendant upon the departure of a single steam bubble during pool boiling of water at atmospheric pressure. The flow of heat from a solid surface to liquid water during and immediately after bubble lift-off has been extracted from micro-scale measurements of the spatial and temporal variation of the temperature at the solid surface beneath the bubble. The numerical procedure used to extract the heat flux from the temperature variations at the solid surface has been assessed and verified, and applied to investigate the heat transfer during the bubble departure phase, and after the eventual bubble lift-off. Results confirm that fluid motion activated by a departing bubble is the cause of heat transfer enhancement. The phenomenon can be characterised as the process of rewetting, by an advancing liquid front, of a dry portion of wall area at the base of the bubble. The portion of wall area that is affected by the observed heat transfer augmentation mechanism has been found to be that of a circle of diameter roughly equal to half the bubble departure diameter. The current measurements enabled validation of interface-capturing numerical simulation of the hydrodynamics and heat transfer of single bubble formation and departure from a surface, including conjugate heat transfer in the solid substrate. From simulation results, the spatial and temporal variation of the heat flux at the solid surface beneath the bubble has been computed and monitored during bubble departure and after the eventual bubble lift-off. Heat transfer rates at bubble departure extracted from simulation have been found in good agreement with measurements. The simulation correctly captured experimental trends and was found to give an accurate estimate of the magnitude of the flows of heat to the liquid due to the bringing of cold fluid in the vicinity of the wall caused by the bubble departure process.

A note on the aerodynamic splashing of droplets

When a drop of a low-viscosity liquid of radius $R$ impacts against an inclined smooth solid substrate at a velocity $V$, a liquid sheet of thickness $H_{t}\ll R$ is expelled at a velocity $V_{t}\gg V$. If the impact velocity is such that $V>V^{\ast }$, with $V^{\ast }$ the critical velocity for splashing, the edge of the expanding liquid sheet lifts off from the wall as a consequence of the gas lubrication force at the wedge region created between the advancing liquid front and the substrate. Here we show that the magnitude of the gas lubrication force is limited by the values of the slip length $\ell _{\unicode[STIX]{x1D707}}$ at the gas–liquid interface and of the slip length $\ell _{g}\propto \unicode[STIX]{x1D706}$ at the solid, with $\unicode[STIX]{x1D706}$ the mean free path of gas molecules. We demonstrate that the splashing regime changes depending on the value of the ratio $\ell _{\unicode[STIX]{x1D707}}/\ell _{g}$ – a fact explaining the spreading–splashing–spreading–splashing transition for a fixed (low) value of the gas pressure as the drop impact velocity increases (Xu et al., Phys. Rev. Lett., vol. 94, 2005, 184505; Hao et al., Phys. Rev. Lett., vol. 122, 2019, 054501). We also provide an expression for $V^{\ast }$ as a function of the inclination angle of the substrate, the drop radius $R$, the material properties of the liquid and the gas, and the mean free path $\unicode[STIX]{x1D706}$, in very good agreement with experiments.

Advancing liquid front shape control in capillary filling of microchannel via arrangement of microposts for microfluidic biomedical Sensors

This paper presents the effect of micropost arrangements on the meniscus shape of the advancing liquid front for capillary filling in a microchannel of biomedical diagnostic sensors. Four different arrangements of cylindrical microposts inside microchannels including hexagonal array with smooth sidewall, hexagonal array with rugged sidewall, rectangular array with smooth sidewall, and rectangular array with rugged sidewall were considered. The meniscus shape of the fluid front were estimated by the volume-of-fluid based computational simulation and compared with experimental results. For hexagonal array, overall meniscus shapes of the advancing liquid front were concave form regardless of sidewall shape. On the other hand, capillary filling through rectangular arrangement of microposts occurred as a step-wise movement with maintaining the flat shape of the advancing liquid fronts. Sidewall microposts affected the capillary filling times rather than the meniscus shape of advancing liquid front. The shape of advancing liquid front and capillary filling time could be passively controlled by arrangement of microposts inside microchannel.

Temperature effects on dynamic water absorption into paper

Mechanisms controlling short time water absorption and the effect of temperature on water absorption into paper were investigated by analyzing previously published data. A dynamic contact angle effect caused by contact line friction explained the liquid uptake dynamics at short times. The water absorption rate increase with temperature is suggested to be controlled by the molecular processes occurring in front of the advancing liquid front. The increase in the non-equilibrium vapor pressure at air–liquid interface leads to higher water molecule adsorption onto fibers and associated lowering of the solid–gas interfacial tension, thereby increasing the wetting velocity and water absorption. The classical Lucas–Washburn equation was found to be inadequate for predicting water absorption into paper both at short times and as a function of temperature.

The uniform capillary model for packed beds and particle wettability

The distribution and movement of fluids in porous media are important in a variety of situations arising naturally and industrially (e.g., water migration in soils, oil recovery, chromatography, filtration and separation processes). Our specific interest is in deriving advancing and receding contact angles from capillary pressure measurements in packed beds of particles partially saturated with liquids. The simplest model of a porous medium treats the porous body as an equivalent uniform capillary giving rise to the same capillary pressure. Pressure measurements were performed successfully with advancing as well as receding liquids. For an advancing liquid front a measurement with a second liquid is needed to calibrate the equivalent capillary radius and obtain the advancing contact angle. For a receding liquid front – an additional determination of the amount of liquid trapped behind in smaller pores is required. The equivalent capillary radius is mainly determined by the porosity of the packed bed and is easily corrected to account for capillary retention. Only then can the receding contact angle be obtained reliably. This new methodology for contact angle measurement was validated with model systems and applied successfully to various real particulate systems.

On the transient coating of a straight tube with a viscoelastic material

We examine the pressure-driven coating of a straight, long tube with a finite amount of viscoelastic liquid. This combines the formation and elongation of an open bubble pushing the liquid downstream with the motion of the advancing liquid front and the deposition of a film along the tube wall. The mixed finite element method is combined with the discontinuous Galerkin method for computing the polymeric contribution to the stress tensor, while a quasi-elliptic grid generation scheme is used for tessellating the highly deforming domain. Global remeshing is adopted to overcome local distortion and coarsening of the mesh which arises from the attachment of advancing front nodes on the wall. The accuracy of the solution is achieved by selectively refining the mesh along areas where sharp boundary layers in stress arise and in particular at the bubble front. An extensive parametric analysis is performed using the affine, single-mode Phan-Tien and Tanner constitutive model. The thickness of the remaining film increases as the solvent contribution to viscosity decreases, because of the sharply increased normal viscoelastic stresses along the bubble front. The effect of decreasing the extensional parameter ɛ PTT is similar because this decreases the shear and extensional thinning in the liquid. The transient nature of the process delays the development of the viscoelastic stresses as the Deborah number increases. The streamlines relative to the liquid tip follow the usual ‘fountain flow’ pattern as long as the bubble and the liquid front do not interact. The non-affine, multi-mode PTT model with constants obtained from the literature for a PIB solution in C14 predicts a slightly thinner deposited film and a flatter bubble front because of its stronger shear thinning. Moreover, it predicts a higher dimensionless bubble velocity because of the very small viscosity ratio of the solvent and a V-shape in the radial distribution of the first normal stress difference and the birefringence just behind the contact line in qualitative agreement with experiments and theory for planar fountain flow.

Multi-curvature liquid meniscus in a nanochannel: Evidence of interplay between intermolecular and surface forces

We examined the formation of a multiply curved meniscus inside rectangular nanochannels, whose width ranges from 50 to 800 nm at a constant height of 200 nm. When the channel width is smaller than approximately 400 nm under partial wetting conditions, a distinct multi-curvature meniscus was observed at the advancing front with an edge disjoined from the wall. In contrast, a typical pre-wetting film was observed at the front regardless of the channel size for complete wetting conditions. Our theoretical analysis demonstrated that the multi-curvature meniscus is generated from the increased contribution of an extra pressure due to intermolecular interactions near the wall. In particular, a plug-like meniscus profile was observed at the advancing liquid front for the 50 nm wide channel owing to an overlap between convex curvatures at the channel walls. Finally, we showed that the filling velocity of liquid can be decreased by decreasing the channel size due to the reduced wettability.

Capillary filling in patterned channels

We show how the capillary filling of microchannels is affected by posts or ridges on the sides of the channels. Ridges perpendicular to the flow direction introduce contact line pinning, which slows, or sometimes prevents, filling, whereas ridges parallel to the flow provide extra surface that may enhance filling. Patterning the microchannel surface with square posts has little effect on the ability of a channel to fill for equilibrium contact angle theta_{e} less than approximately 30 degrees . For theta_{e} greater than approximately 60 degrees , however, even a small number of posts can pin the advancing liquid front.

Hydrocarbons imbibition for geometrical characterization of porous media through the effective radius approach

Surface energetic characterization of porous solids usually requires the determination of the contact angle. This quantity is deduced by imbibition experiments carried out in such media with high surface tension liquids. Now then, this methodology needs the geometrical characterization of the porous medium by means of the deduction of its effective radius. Normally, this is made by imbibition experiments with n-alkanes, liquids whose surface tension is low enough as to suppose their contact angles with the solid surface are null. However, this last procedure is not free from some criticisms. Among them, the possible influence of the imbibition velocity on the contact angle, the effect of the precursor liquid film ahead the advancing liquid front on the driving force that gives rise to the movement, or the dependence of the effective radius on the length of the hydrocarbon chain of the n-alkanes. In an attempt of going deeply in these questions, imbibition experiments with n-alkanes have been carried out in porous columns of powdered calcium fluoride. These experiments have consisted of the measurement of the increase in the weight of the columns caused by the migration of the liquids through their interstices. The analysis of their results has been carried out by means of a new procedure based on the study of the velocity profile associated to the weight increase. This analysis has permitted us to conclude that, at least in the calcium fluoride columns, the contact angle of the n-alkane is not influenced by the capillary rise velocity, it taking in fact a null value during the process. On the other hand, it has been also proved that the driving force of the movement is caused by the replacement of the solid–vapour interface by the solid–liquid interface that happens during the imbibition, which means that only the Laplace's pressure, and not the precursor liquid film, contributes to the development of the phenomenon. Finally, it has been compared the values of the effective radius associated to each n-alkane, similar values being found independently from the particular liquid employed in the experiments, fact that indicates that the porous solid can be considered as a bunch of cylindrical and parallel capillaries of the same radius.

Capillary penetration in fibrous matrices studied by dynamic spiral magnetic resonance imaging

The dynamic spiral nuclear magnetic resonance (NMR) imaging technique was used to investigate the water imbibition into cellulose fiber matrices. The advancing water boundary, water concentration distribution, and swelling degree within the fiber matrix samples were monitored as a function of time over the entire absorption process. A combined image that shows the time evolution of the absorbed water concentration distribution within the fiber matrix was synthesized from the dynamically acquired NMR image data set. The NMR imaging data clearly demonstrated that water imbibition into a fiber matrix consists of two different processes: water penetration into capillaries between fibers and water diffusion into the cellulose fibers. The advancing liquid front is primarily determined by the water capillary flow and can be quantitatively described by Washburn equation. The slower water diffusion process in fibers is mainly responsible for the fiber swelling. The time evolution of the absorbed water concentration distribution can be qualitatively interpreted in terms of steady capillary flow and concentration-gradient-driven diffusion into fibers with a constant permeability. The effects of pore morphology, tortuosity, and surface heterogeneity to the water absorption process are also discussed.

Finite element simulation of fountain flow in injection molding

AbstractFountain flow is the phenomenon of deceleration and outward motion of fluid particles as they approach a slower moving interface. The use of a general purpose finite element program for the appropriate boundary conditions made possible the detailed flow description behind an advancing liquid front moving at constant speed inside two‐dimensional channels and tubes. The results were qualitatively the same for both Newtonian and shear‐thinning fluids.

Some effects of substrate roughness on wettability

The influence of substrate roughness on wettability has been investigated at room and high temperatures using sixteen material combinations, mostly liquid metals and solid ceramics but also water, glycerol and solid nickel. The contact angles assumed by both wetting and non-wetting drops of all but two material combinations increased linearly with the relative steepness of the surface features, the effect being less for experiments conducted at high temperatures. In contrast, the contact angles of good wetting drops of glycerol and exceptionally good wetting drops of Easy-flo decreased when their silica and nickel substrates were roughened. Similarly, contact angles of both wetting and non-wetting drops were decreased by ultrasonic vibration. The experimental data can best be interpreted in terms of the metastable equilibrium configuration models in which an advancing liquid front has to overcome energy barriers associated with surface features. This occurs more readily if these barriers are small relative to the energy of the liquid which our data suggest can be equated with the enthalpy of the liquid. This interpretation enables the effects of substrate roughness at one temperature or with one liquid to be used to predict behaviour at other temperatures and with other liquids.