Forced Volume Research Articles

Three-Dimensional Numerical Study on the Metal Rotating Spray Transfer Process of High-Current GMAW

A three-dimensional numerical model based on the volume-of-fluid (VOF) method is typically preferred for studying high-current gas metal arc welding (GMAW) metal transfer mechanism and then controlling it. It is informed that the rotating spray transfer is extremely complicated, and some researchers have focused on simplified models without considering the energy conservation to make analysis manageable for the unstable metal transfer process. Using our created numerical model, the metal transfer of high-current GMAW with shielding gas of different conductivities has been studied by analyzing acting forces and fluid flows in the metal liquid column, especially for the contributions of the self-induced electromagnetic force, equivalent volume force of the capillary pressure of the surface tension (Named surface tension force in this work), static arc pressure. It is found that the unbalanced electromagnetic force greatly promotes the metal rotating motion in 500 A metal inert gas (MIG) welding with pure argon shielding gas and it pushes the metal liquid column to rotate. Considering the arc constricting effect in active shielding gas by simply changing the arc conductivity, it is found that the metal liquid column no longer rotates, it turns to swing since the unbalanced electromagnetic force is large enough to break the rotating motion. The calculated results of the metal liquid column deflected angle and rotating/swing frequency agree well with the experiment of high-speed camera observations.

Abdominal and Pelvic Floor Activity Related to Respiratory Diaphragmatic Activity in Subjects with and without Non-Specific Low Back Pain.

One of the advances in physiotherapy in recent years is the exploration and treatment by ultrasound imaging. This technique makes it possible to study the relationship between the musculature of the anterolateral wall of the abdomino-pelvic cavity, the pelvic floor muscles and the diaphragm muscle, among others, and thus understand their implication in non-specific low back pain (LBP) in pathological subjects regarding healthy subjects. Objective: To evaluate by RUSI (rehabilitative ultrasound imaging) the muscular thickness at rest of the abdominal wall, the excursion of the pelvic floor and the respiratory diaphragm, as well as to study their activity. Methodology: Two groups of 46 subjects each were established. The variables studied were: non-specific low back pain, thickness and excursion after tidal and forced breathing, pelvic floor (PF) excursion in a contraction and thickness of the external oblique (EO), internal oblique (IO) and transverse (TA) at rest. Design: Cross-sectional observational study. Results: Good-to-excellent reliability for measurements of diaphragm thickness at both tidal volume (TV) (inspiration: 0.763, expiration: 0.788) and expiration at forced volume (FV) (0.763), and good reliability for inspiration at FV (0.631). A correlation was found between the EO muscle and PF musculature with respect to diaphragmatic thickness at TV, inspiration and expiration, and inspiration at FV, in addition to finding significant differences in all these variables in subjects with LBP. Conclusion: Subjects with LBP have less thickness at rest in the OE muscle, less excursion of the pelvic diaphragm, less diaphragmatic thickness at TV, in inspiration and expiration, and in inspiration to FV.

Quantifying the impact load of rapid dry granular flows exerted on rigid slit structures using centrifuge experiments and DEM simulation

Granular flows are typical hazard in mountainous terrains. Slit structure has been shown to be a successful mitigating strategy. However, the interaction mechanism between granular flows and slit structure has not been completely elucidated, and the impact load and impact pressure distribution pattern of granular flow on slit structures also has not been fully discussed. Therefore, a novel centrifuge flume experiment and DEM simulation were designed. The centrifugal acceleration field and Coriolis field accounting for the Coriolis effect were also implemented in the DEM model. Results reveal that, the grain size almost has no effect on normal impact forces when the granular flows act as continuous characteristic, and the initial volume and impact force do not show a simple linear relationship. Furthermore, the impact pressure profiles indicate a trapezoidal distribution with a peak impact pressure at the bottom and a decline from the bottom to the top. In addition, the impact forces also showed a decreasing trend from the slit to the flume channel sidewall, making the inner part vulnerable. This study might contribute to the study of flow-slit structure interaction and provide scientific support for slit structure engineering design.

Turbulent Eddy Generation for the CFD Analysis of Hydrokinetic Turbines

This paper presents a novel theoretical and computational methodology for the generation of an onset turbulent field with prescribed properties in the numerical simulation of an arbitrary viscous flow. The methodology is based on the definition of a suitable distribution of volume force terms in the right-hand side of the Navier–Stokes equations. The distribution is represented by harmonic functions that are randomly variable in time and space. The intensity of the distribution is controlled by a simple PID strategy in order to obtain that the generated turbulent flow matches a prescribed turbulence intensity. A further condition is that a homogeneous isotropic flow is established downstream of the region where volume force terms are imposed. Although it is general, the proposed methodology is primarily intended for the computational modelling of hydrokinetic turbines in turbulent flows representative of tidal or riverine installations. A first numerical application is presented by considering the injection of homogeneous and isotropic turbulence with 16% intensity into a uniform unbounded flow. The analysis of statistical properties as auto-correlation, power spectral density, probability density functions, demonstrates that the generated flow tends to achieve satisfactory levels of stationarity and isotropy, whereas the simple control strategy used determines underestimated turbulent intensity levels.

Jammed solids with pins: Thresholds, force networks, and elasticity.

The role of fixed degrees of freedom in soft or granular matter systems has broad applicability and theoretical interest. Here we address questions of the geometrical role that a scaffolding of fixed particles plays in tuning the threshold volume fraction and force network in the vicinity of jamming. Our two-dimensional simulated system consists of soft particles and fixed "pins," both of which harmonically repel overlaps. On the one hand, we find that many of the critical scalings associated with jamming in the absence of pins continue to hold in the presence of even dense pin latices. On the other hand, the presence of pins lowers the jamming threshold in a universal way at low pin densities and a geometry-dependent manner at high pin densities, producing packings with lower densities and fewer contacts between particles. The onset of strong lattice dependence coincides with the development of bond-orientational order. Furthermore, the presence of pins dramatically modifies the network of forces, with both unusually weak and unusually strong forces becoming more abundant. The spatial organization of this force network depends on pin geometry and is described in detail. Using persistent homology, we demonstrate that pins modify the topology of the network. Finally, we observe clear signatures of this developing bond-orientational order and broad force distribution in the elastic moduli which characterize the linear response of these packings to strain.

Large‐strain analysis for cylindrical cavity contraction in strain‐softening geomaterials

AbstractThis study presents a large‐strain analysis for cylindrical cavity unloading–contraction problem in strain‐softening geomaterials. Based on the unified strength theory (UST) and non‐associated flow rule, the process of cavity contraction in cohesive‐frictional geomaterials is regarded as a large‐strain problem by introducing the UST parameters and the volumetric force of seepage into the conventional cylindrical cavity contraction analysis, the effects of strain‐softening characteristic, intermediate principal stress, large‐strain, and seepage are considered. Finally, according to the comparison of the results of the radius ratio with those in the published literature, the correctness and reliability of the theoretical method are proved. The results show that it is necessary to consider the effect of volume force of seepage in the stability of excavation problem in geomaterial, the larger the volume force of seepage, the smaller the plastic radius. The traditional two‐dimensional cavity contraction solution overestimates the plastic radius. The results provide a theoretical basis for the elasto‐plastic analysis of excavation in rich water geomaterial and have a certain reference value for engineering design.

Explanation of wind gusts induced by pressure changes. Turbulence in the air

The paper researches wind gusts that are caused by changes in pressure on a flat surface. To describe this phenomenon the equations of the state of a continuous medium are used. In the stationary case, these equations in the air are the equation of the decreasing exponent for the pressure gradient. Consequently, the volume force in the air cannot act permanently. It decreases at a distance of about a kilometer. This exponential damping solution is due to wind gusts. The paper concludes that the periodic dumping of volumetric forces leads to turbulence in the air. These disruptions or turbulence are also observed when the air rotates in cyclones and anticyclones. In the water, pressure fluctuation leads to periodic waves.

Определение неосесимметричных упругих полей в анизотропных телах вращения, вызванных действием объемных сил

The paper presents a technique for plotting elastic fields in transversely isotropic bodies bounded by coaxial surfaces of revolution, subjected to non-axisymmetric volume forces. Our theory uses the ideas of the boundary state method, which is based on state spaces describing a medium. Fundamental polynomials form the basis of the internal state space. A polynomial is placed in any displacement vector position in a planar auxiliary state, then transition formulas can be used to determine the spatial state. A set of such states forms a finite-dimensional basis that is used after orthogonalisation to expand the desired elastic field characteristics into Fourier series with identical coefficients. These series coefficients are dot products of given and base volume force vectors. The search for an elastic state is reduced to solving quadratures. We provide guidelines for constructing an internal state basis depending on the type of volume forces given by various cyclic functions (sine and cosine). We analysed a solution to a specific theory of elasticity problem concerning a transversely isotropic circular cylinder subjected to non-axisymmetric volume forces. We analysed the series convergence and graphically evaluated the solution accuracy

NURBS solid modeling for the three-dimensional limit analysis of curved rigid block structures

In this paper, we present a novel computational approach for the generalized three-dimensional upper bound limit analysis of curved rigid block structures. This approach allows to discretize structures with complex geometries into a finite number of curved blocks, while retaining an overall exact description of the structural geometry and improving the accuracy of the solution in terms of both collapse load multiplier and failure mechanism. To this aim, the discretization of a given spatial curved structure is obtained by using NURBS solids, where NURBS stands for Non-Uniform Rational B-Spline. A NURBS solid is a closed region of space delimited by NURBS boundary surfaces: no information is provided about the space within the volume, except for the mathematical expression of the boundary surfaces. NURBS solids allow to discretize a complex spatial structure into a finite number of solid elements while maintaining unaffected the initial geometry, independently on the number of elements used. Each NURBS solid element is considered as a rigid and infinitely resistant block and an upper bound limit analysis is applied to the obtained assembly. The external power is evaluated on the original geometry: the resultants of surface and volume forces, and the coordinates of the corresponding loaded points are evaluated through a new boundary integration formula, which allows avoiding any additional discretization based on standard regular elements (voxel or tetrahedral). On the other hand, the internal power is evaluated according to an associated flow rule on the common boundary NURBS surfaces between adjacent solid elements, thus representing zero-thickness interfaces. The upper-bound formulation stems into a linear programming problem, from which the kinematic load multiplier, the generalized velocities of each block, and contact forces at interfaces are obtained. Finally, the Gothic arches with curved cross-sections located within the Carmo Convent (Lisbon, Portugal) and a double curvature groin vault from the St John Hospital (Jerusalem) are studied to prove the effectiveness of the proposed NURBS solid-based approach for the three-dimensional limit analysis of generally shaped rigid block structures.

Onset of nonlinearity in oscillatory flow through a hexagonal sphere pack

We simulated laminar flow through a hexagonal sphere pack driven by a sinusoidal volume force using direct numerical simulation. We vary two independent parameters, the Hagen and Womersley numbers, representing the amplitude and frequency of the forcing. First, we determine for which regions in the parameter space nonlinear effects have to be considered. We judge the presence of nonlinear effects from the departure of the superficial velocity and kinetic energy from a linear behaviour as well as from the presence of higher harmonics in the discrete Fourier transform of the velocity field. We discuss the asymptotic behaviour of the onset of nonlinearity in the limits of low and high Womersley number, and we delineate approximately the parameter region that can be described using the linear theory. Second, we document the changes of instantaneous velocity fields with Hagen and Womersley numbers. We show that the onset of nonlinearity is accompanied by a loss of fore–aft symmetry of the flow, and subsequently, we employ the deviation from this symmetry to quantify the strength of nonlinear effects in the instantaneous velocity fields. Based on this analysis, we demonstrate that for higher Womersley numbers, the strongest nonlinear effects occur during the deceleration of the superficial velocity; consequently, the development of the nonlinearity is not in phase with the superficial velocity. Finally, we describe the leading-order nonlinear effects in the frequency domain and the interaction among the nonlinear Fourier modes that leads to a temporal variation in the strength of nonlinear effects.

Mechanism of matrix influencing the cryogenic mechanical property of carbon fibre reinforced epoxy resin composite

This study focuses on the cryogenic mechanical property of carbon fibre reinforced epoxy resin composite (CFRP) unidirectional laminate, and the cryogenic evolution mechanism is discussed from the microstructural perspective of resin free volume and intermolecular forces. The primary transition temperature (147 °C) and the secondary transition temperature (−25 °C) is identified through dynamic mechanical analysis. As the cryogenic condition (−196 °C) is significantly lower than the temperature of main-chain segmental and micro-structure unit motion, the resin molecular segments are frozen, free volume fraction and resin toughness are reduced, thus the brittleness increases. These effects reduce the cryogenic failure strain of CFRP at break by 43.7% compared to room temperature, resulting in a smoother fracture surface morphology. Resin molecules under cryogenic condition have higher packing density, stronger intermolecular forces, which increase the strength and modulus of both resin and CFRP.

Stress average rule derived through the principle of virtual power

AbstractStress and strain average rules are the key conceptual pillars of the wide field of continuum micromechanics of materials. The aforementioned rules express that the spatial average of (micro‐)stress and (micro‐)strain fields throughout a microscopically finite representative volume element (RVE) are equal to the (macro‐)stress and (macro‐)strain values associated with the corresponding macroscopically infinitesimal volume element (macroscopic material point). According to the famous contribution of Hashin, stress and strain average rules are derived from equilibrium and compatibility conditions, together with (micro‐)displacement and (micro‐)traction boundary conditions associated with homogeneous (macro‐)strains and (macro‐)stresses, respectively. However, as, strictly speaking, only displacements or tractions can be described at the boundary, the remaining average rule turns out as a mere definition. We here suggest a way to do without such a definition, by resorting to the principle of virtual power (PVP) as a means to guarantee mechanical equilibrium: at the boundary of the RVE, we prescribe virtual (micro‐)velocities, which are linked to arbitrary, but homogeneous virtual (macro‐)velocities and (macro‐)strain rates, while the latter are also linked, in a multilinear fashion, with the microscopic virtual strain rate fields inside the RVE. Considering, under these conditions, equivalence of the macroscopic and the microscopic expressions for the virtual power densities of the internal and the external forces yields the well‐known stress average rule and, in case of microscopically uniform force fields, a volume force average rule. The same strategy applied to an RVE hosting single forces between atomistic mass points, readily yields the macroscopic “internal virial stress tensor.”

Development of morphable polishing tools with labyrinth and dimple textures

Inspired by the physical nature and functionality of morphable surfaces, this paper develops the polishing tools with such surface characteristics. The surface textures of morphable polishing tools can be tuned and adapted according to the stage and requirements of the targeted surface finish and material removal rate. To investigate the performance of morphable surfaces in polishing, morphable polishing tools with labyrinth, dimple and hybrid textures were fabricated by curing silicone materials with different Young’s moduli. The morphable polishing tools can be produced with fast responsiveness and reversibility by controlling the air pressure in the tool cavity. Fixed-spot polishing experiments with the developed morphable tools were performed on a copper surface, and the surface morphology, surface roughness and removed volume of polished copper were measured with a laser confocal microscope. Furthermore, static and dynamic polishing forces, polishing pressure distribution and interfacial friction coefficient between the tool and workpiece were obtained and benchmarked in polishing experiments regarding the labyrinth, dimple and hybrid tools. The results show that under the investigated polishing parameters, the roughness of polished surface is the smallest with the dimple tool, higher with the hybrid tool and the labyrinth tool. The material removal volume, static and dynamic polishing forces under different tool offsets are larger in the polishing processes with a dimple tool. In addition, the theoretical and experimental study indicates that the tool surface texture significantly affects the polishing pressure distribution. Labyrinth tools show denser pressure distribution owing to the finer textures of a smaller characteristic length, while dimple tools show sparsely distributed pressure owing to the coarser surface texture.

Influence of Natural Convection and Volume Change on Numerical Simulation of Phase Change Materials for Latent Heat Storage

For the numerical simulation of a heat storage based on phase change materials (PCMs) an enhanced model is presented, considering the physical effects of convection flow in the liquid phase as well as the volume change during phase change. A modified heat capacity is used to realize the phase change. The phase change material is initially defined as a liquid with temperature-dependent material properties. A volume force is added to the Navier-Stokes equations to allow a circulating flow field in the liquid phase and prevent flow motion in the solid phase. The volume change is implemented with the Arbitrary Lagrangian-Eulerian method. A laboratory phase change experiment was performed using the PCM RT42 with a melting temperature of 42 °C. The laboratory experiment was calculated numerically using the enhanced model to evaluate the numerical model and to investigate the influence of the simulation parameters on the thermal behavior of the PCM. The thermal conductivity is determined as the main influencing parameter. A good agreement of the simulated melting front throughout a major part of the laboratory experiment has been shown. COMSOL Multiphysics provides a default model for phase change, which neglects convection flow and volume change. Compared to the default model, the enhanced model achieves more accurate results but requires more computational cost for complex latent heat storage systems. Using the default model without convection can be reasonable, considering that the heat storage design is either over-dimensioned or a suitable correction factor must be applied.

Workspace and Accuracy Analysis on a Novel 6-UCU Bone-attached Parallel Manipulator

With the increasingly more extensive application of the medical surgical robot in the clinic, higher requirements have been put forward for medical robots. The bone-attached robot, a popular orthopedic robot in recent years, has a tendency of miniaturization and refinement. Thus, a bone-attached parallel manipulator (PM) based on 6-UCU (universal-cylindrical-universal) configuration is proposed, which is characterized by small volume, compact structure, high precision and six-dimensional force feedback. To optimize the structure and make it more compact, the workspace of the 6-UCU PM is analyzed based on the analysis of three kinds of constraint, and workspace model is established through spherical coordinate search method. This study also analyzes the influence of structural parameters on workspace, which may contribute to improving the efficiency of design and ensuring small-sized robots possess relatively large workspace. Moreover, to improve the motion accuracy, an error modeling method is developed based on the structure of 6-UCU PMs. According to this established error model, the output pose error curves are drawn using MATLAB software when the structure parameters change, and the influence of the structure and pose parameters change on the output pose error of PMs is analyzed. The proposed research provides the instruction to design and analysis of small PMs such as bone-attached robots.

Simulated transit vibration effects on the postharvest quality of persimmon during storage

The mechanical damage of fresh fruit due to postharvest transport vibration is a major problem in the agricultural industry that dramatically impacts product quality. The quality loss is mainly affected by vibration frequency. In this study, the effects of different simulated vibration frequencies (5, 10, and 15 Hz) on the postharvest quality of persimmons were assessed. Changes in physical properties (weight, geometric mean diameter, surface area and volume), mechanical properties (firmness and rupture force) and chemical properties (pH and total soluble solids) were measured during 4 days of shelf life at 20 °C. Transport vibration contributed to the deterioration of the quality of persimmons during storage, resulting in increased weight loss, pH and total soluble solids, and decreased geometric mean diameter, surface area, volume, firmness and rupture force. After 4 days of shelf life, persimmons subjected to vibration frequencies of 5, 10 and 15 Hz exhibited weight losses of 2.12 %, 2.63 % and 3.26 %, respectively, in comparison to 0.83% on the samples without vibration stress (control). The average values of firmness for the control samples decreased 18%, while these changes for samples subjected to vibration frequencies of 5, 10 and 15 Hz, were 34 %, 56 % and 52 %, respectively. The corresponding mean values for the rupture force were 11 %, 19 %, 38 % and 31 %, respectively. The average pH value of the control samples was 5.72 on the first day, which was increased to 6.16 on the fourth day of storage, at a rate of about 7 %, while the increasing rates for the vibration stressed samples with frequencies of 5, 10 and 15 Hz were about 21 %, 33% and 30 %, respectively. Vibration with a frequency of 10 Hz caused the most severe mechanical damage in persimmons.

A Direct-Forcing Immersed Boundary Method for Incompressible Flows Based on Physics-Informed Neural Network

The application of physics-informed neural networks (PINNs) to computational fluid dynamics simulations has recently attracted tremendous attention. In the simulations of PINNs, the collocation points are required to conform to the fluid–solid interface on which no-slip boundary condition is enforced. Here, a novel PINN that incorporates the direct-forcing immersed boundary (IB) method is developed. In the proposed IB-PINN, the boundary conforming requirement in arranging the collocation points is eliminated. Instead, velocity penalties at some marker points are added to the loss function to enforce no-slip condition at the fluid–solid interface. In addition, force penalties at some collocation points are also added to the loss function to ensure compact distribution of the volume force. The effectiveness of IB-PINN in solving incompressible Navier–Stokes equations is demonstrated through the simulation of laminar flow past a circular cylinder that is placed in a channel. The solution obtained using the IB-PINN is compared with two reference solutions obtained using a conventional mesh-based IB method and an ordinary body-fitted grid method. The comparison indicates that the three solutions are in excellent agreement with each other. The influences of some parameters, such as weights for different loss components, numbers of collocation and marker points, hyperparameters in the neural network, etc., on the performance of IB-PINN are also studied. In addition, a transfer learning experiment is conducted on solving Navier–Stokes equations with different Reynolds numbers.

Robust electrical contacts integrating a liquid metal bridge for mechanical switches

Intrinsic roughness of solid surfaces causes a series of inevitable shortcomings in the use of mechanical electrical contacts, among which one of the most fatal is the repulsive electrodynamic force arising from high currents. A large contact force coming from a heavy holding mechanism helps to suppress the repulsive effect whereas the mechanism consumes energy and remains to be challenging for a compact switching device. Here, a liquid metal (LM) bridge is introduced to wet solid electrodes to eliminate contact issues. Four instability patterns induced by the electromagnetic pinch effect are identified to characterize LM bridge’s response to high currents. Simulation results reveal that an inner vortex caused by uneven distributions of current density and electrodynamic volume force leads to the rupture of a necked LM bridge. With a uniform structure, a cylindrical LM bridge is proved to be robust with respect to an impulse current higher than 10 kA, exceeding a commercial compact relay by a factor of more than 10 in terms of current withstand performance. Our research facilitates compact and energy-saving switch equipment and has a potential to realize arbitrary desired levels of high current withstand without the use of a holding mechanism. This paper also offers deep insights into the high current applications of LM from the perspective of fluid related physical mechanisms.

A new preconditioning algorithm for computable compressible flow

Low velocity flows often exhibit incompressible properties, and one of the most prohibitive aspects of these problems is a large number of computer resources required, including both CPU time and memory. Various numerical schemes used to calculate incompressible flow are constantly updated to accelerate convergence and reduce resource occupation, but incompressible flow is an ideal model for studying theoretical problems after all. In addition, it is a common phenomenon that high-speed and low-speed flow regions exist in the same system, and the influence of heat and volume force cannot be ignored in some cases. The artificial compressibility method is based on the idea that the numerical algorithms for compressible flows are used to solve incompressible flow. The system of compressible flow governing equations at very low Mach numbers is stiff due to the large disparity in acoustic wave speed, <i>u</i> + <i>c</i>, and the waves convecting at fluid speed, <i>u</i>. The preconditioning algorithm is effective to change the eigenvalues of the compressible flow equations system so as to remove the large disparity in wave speed, and the essence is to multiply the time derivatives with a suitable matrix. A function in low growth rate with Mach number as a variable is used to construct another new preconditioning matrix. Compared with other matrices of Dailey, Weiss, Choi and Pletcher, the new matrix can well improve the stiffness of the governing equations and the smoothness of eigenvalues in all-speed domain. A one-dimensional numerical example shows that the preconditioning matrix has ability to improve the efficiency of solving low-speed flow problems. These preconditioning matrices are extended to two-dimensional problems to simulate inviscid flow passing through a pipe with bulge and viscous flows passing through a flat and cavity. The results indicate that the new matrix has not only better accuracy but also higher efficiency than Weiss’s and Pletcher’s.

Liquid volume and squeeze force effects on nasal irrigation using Volume of Fluid modelling

For various sinonasal conditions, including chronic rhinosinusitis, saline irrigation is an accepted standard-of-care treatment. This study was aimed at determining the effect of increased irrigation volumes and greater squeeze force on mucosal irrigation. A sinonasal cavity computational model was reconstructed from high-resolution CT scans of a healthy, unoperated 25-year old female. Seven combinations of irrigation volumes (70, 150, 200, and 400 mL) and squeeze forces (ramp time 0.1, 0.5, and 1.0 s) at a fixed head tilt of 0 degrees to the horizontal (Frankfort position) were performed. Velocity, pressure, and wall shear stress, together with mapping of surface coverage and residual volumes at specific locations and time were demonstrated. Higher volume irrigation (400 mL) and greater squeeze force (ramp time 0.1 s) improved irrigation coverage on the ipsilateral and contralateral sinonasal surfaces and increased shear force (approximately 140 Pa). An increase in irrigation volume from 70 to 150 mL approximately doubled sinus surface coverage and from 70 to 200 mL tripled sinus surface coverage. A faster squeeze also contributed to increased sinus surface coverage but its effect was less influential. We infer that the greater irrigation volume and squeeze force improve therapeutic benefit in terms of lavage and distribution of topical medications.