Please do not adjust margins Journal Name ARTICLE Development of an in-­‐vitro model for antiperspirants ab
a
L. Simcox, R. Lazenby and P. R. Unwin
Received 00th January 20xx, Accepted 00th January 20xx DOI: 10.1039/x0xx00000x www.rsc.org/ a It is over a century since the first antiperspirants were developed, and they are still widely used today despite their speciation and mechanism of activity not being fully understood. Current methods of testing the efficacy of antiperspirants are not easy, expensive, and slow. A new laboratory based testing system was developed based on the use of a micropipette to mimic a sweat gland. The feasibility of using this system to identify differences in antiperspirant actives is discussed. A finite element method model was constructed to simulate the process, in order to understand flow through small channels and how this is influenced by blocking agents. The combination of both seeks to provide an insight into those unanswered questions about antiperspirants from a new perspective. Introduction Sweating and body odour are often connected by most people as two things that they would generally like to avoid, and consequently underarm products such as antiperspirants and deodorants are used every day. Indeed, efforts to mask body odour date back from around 5000 years ago, when the Egyptians recommended a scented bath followed by underarm 1
application of perfumed oils. In fact, sweating alone is not the cause of the offensive odour since sweat by itself is 1, 2
odourless; it only establishes a characteristic scent when exposed to moisture and bacteria on the surface of the skin, where the bacteria break down the sweat, resulting in an 1
unpleasant odour. Perspiration Sweating, or perspiration, comes from the sudiferous glands, 3
of which there are two types: apocrine and eccrine. Apocrine glands are associated exclusively with hair follicles, and are therefore generally found in densely haired areas of the body. These glands exist from birth but only become active from 2, 4, 5
puberty.
On the other hand, eccrine glands can be found over all parts of the body, except for the lips and penis, with the highest density being on the palms, arms, underarms, and 4
abdomen. There are approximately 3 to 4 million eccrine sweat glands across the body, that can produce up to 2 litres 6, 7
of fluid per hour. The structure of the two types of sweat glands is shown in Figure 1. Both can be divided into two distinct parts: the duct and the secretory coil. The apocrine sweat gland opens out into the hair canal, so the duct is very short and the gland’s secretory coil is in close proximity to the hair follicle and the skin surface. Conversely, the eccrine sweat gland is connected 8
to a pore on the skin via a longer duct (ca. 10 times longer). Of course, the structure of the sweat glands is related to their function. Probably the primary function of the whole perspiration mechanism is the regulation of core body 4
temperature, which is crucial for survival. This thermoregulation involves eccrine sweat glands, which is why they are distributed over the whole body. The reason for the long duct is the re-­‐absorption of ions from ‘primary sweat’. Sweat produced from the secretory coil is high in sodium chloride concentration, however these ions are re-­‐absorbed by the body from the sweat before it reaches the surface of the 9
skin. Apocrine sweat glands respond to emotional stimuli, such as anxiety, pain, and sexual arousal. Because of this, and the fact that the glands open into the hair follicle, the fluid produced is oilier, contains proteins, lipids, and steroids, and may be mixed with sebum. The activity of both types of sweat gland is directly controlled by the central nervous system, and so eccrine glands also respond to emotional stimuli to a lesser extent, as well as other conditions like ingestion of hot and 4
spicy food. 10
The composition of sweat varies with sweat flow rate and indeed varies widely between glands and individuals. Sodium chloride concentrations can vary from 5 mmol/L up to 148 mmol/L. The concentration of potassium ions is at an average of 4.5 mmol/L. Other components such as lactic acid and pyruvate are typically more concentrated in sweat than in the blood or urine, with values of 4 – 40 mmol/L and 0.1 – 0.8 mmol/L respectively. The pH of sweat also varies considerably. Generally, sweat becomes more alkaline (up to 6.8) at higher flow rates and for prolonged periods of sweating. Eccrine 11
sweat is more acidic than apocrine sweat. This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-­‐3 | 1 Please do not adjust margins Please do not adjust margins ARTICLE Journal Name 14, 15
(a) eccrine
Table 1. Typical composition of antiperspirants.
(b) apocrine
Ingredient sweat
pore
Aluminium chlorohydrate Isopropyl myristate Pyrogenic silica Perfume Ethoxylates / PPG stearyl ether Hydrogenated soybean oil Propellant Water re-absorptive
duct
Aerosol (% w/w) Roll-­‐on (%w/w) Function 4.50 14.30 Active 6.00 0.45 0.44 -­‐ -­‐ -­‐* Carrier Suspending agent Fragrance -­‐ 4.82 Surfactant -­‐ 2.86 Gelling agent 88.61 -­‐ -­‐ 78.02* Propellant Carrier *Includes perfume and other minor components such as emollients, preservatives, and chelators. secretory
coil
hair
follicle
Depth from skin surface:
Depth from skin surface:
2.7 - 3.0 mm
ca. 1.0 mm
Figure 14 . Illustration of the morphology of the (a) eccrine, and (b) apocrine sweat glands. Underarm products The rise of products to control underarm sweating and odour began a little over 100 years ago, but antiperspirants and deodorants have now grown to be one of the largest used health and beauty products in this category, second only to toothpaste. The first commercial product for underarm use was Mum deodorant in 1888, a waxy cream containing zinc oxide. This was subsequently followed by the first commercial antiperspirant in 1903, EverDry – an aqueous alcoholic solution of aluminium chloride. However, this compound is incredibly irritant and damages clothing, so it was succeeded in 1916 by the less irritant aluminium chlorohydrate (ACH) as the active ingredient of choice. Today, it remains the most common antiperspirant active, though there is now a whole series of formulations that are aluminium based, including activated aluminium chlorohydrate, activated aluminium sesquichlorohydrate (AASCH), and aluminium zirconium glycine complexes, utilising a range of delivery systems such as 1, 12, 13
aerosol, roll-­‐on, sticks, and gels.
Until now, the terms antiperspirants and deodorants have been written together, and are often used interchangeably by the public, but they are not entirely equivalent. Deodorants contain perfumes and antibacterial agents in order to eliminate body odour and stop us smelling bad; they do not reduce sweating and hence do not contain those aluminium actives. Antiperspirants do contain aluminium salts since their primary purpose is to reduce sweating, in addition to reducing body odour. Table 1 shows a typical antiperspirant composition for two popular formulations. As such, all antiperspirants are deodorants, but not all deodorants are antiperspirants, and so this work deals only with 1
antiperspirants. It is generally accepted that antiperspirants reduce sweating by forming a polymeric gel plug within the eccrine sweat gland, physically blocking the process of sweating. This mechanism of action was originally put forward by Reller and 16
17
Leudders in 1977, subsequently confirmed by Holzle and 18, 19
Quatrale,
and has gained wide acceptance since. Aluminium chlorohydrate is composed of a central aluminium atom in a tetrahedral configuration, surrounded by 12 aluminium atoms in an octahedral configuration, thus 20
giving the formula Al13O4(OH)24(H2O)12Cl7 (Figure 2a). Antiperspirant activity requires the formation of a polymeric gel plug, where the polymer is aluminium hydroxide. Conversion of aluminium chlorohydrate to aluminium hydroxide is a polymerisation involving a progressive reaction series. The ACH complex reacts to form an intermediate 3+
2+
Al(H2O)6 monomer, and its conjugate base Al(H2O)5OH at 21
pH 4 – 6 (note the pH of ACH in antiperspirant is 4 – 4.5). This monomer may then dimerise by a deprotonation-­‐dehydration reaction to join the two aluminium octahedra by a double hydroxide bridge, releasing two protons (Figure 2b). The basic unit of aluminium hydroxide is a six membered ring of aluminium octahedra. In this state, it is amorphous and will react rapidly, whereby these six membered rings combine, 22
thus developing crystallinity (Figure 2c). However, these studies were done in-­‐vitro, and not much is known about antiperspirant activity once it has been applied to the body. For example, the antiperspirant can react not only with sweat, but also the duct lining, lipids, and proteins like keratin. Neither is it known about the physical state and composition of the antiperspirant particles/solution once it has been applied to the skin, or how it is transported to the sweat pore, to say nothing about what occurs once the pore is blocked, whether the gland stops pumping, for how long, if 2 | J. Name., 2012, 00, 1-­‐3 This journal is © The Royal Society of Chemistry 20xx Please do not adjust margins Please do not adjust margins Journal Name (a)
ARTICLE Experimental (b)
Reagents aluminium chlorohydrate
Al13O4(OH)24(H2O)12Cl7
monomer
Solutions were prepared using Milli-­‐Q distilled water (Millipore Corp; >18 MΩ cm at 25 °C). Sweat mimic solution was made -­‐3
using 0.1 mol dm phosphate buffer at pH 6, comprised of -­‐1
potassium phosphate monobasic anhydrous (10.53 g L , Fisher Scientific) and sodium phosphate dibasic heptahydrate (3.30 g -­‐1
L , Sigma Aldrich). Antiperspirant solutions were prepared such that each contained 3 % w/w aluminium (equivalent to 12.2 – 15 % w/w active ingredient). The antiperspirant actives used were aluminium chlorohydrate (Guilini) and activated aluminium sesquichlorohydrate (URDPS). Experimental set-­‐up (c)
Al6(OH)126+.12H2O
aluminium
hydroxide
polymer
Al10(OH)228+.16H2O
Figure 2. Mechanism of the conversion of aluminium chlorohydrate to 22
aluminium hydroxide. (a) Structure of the aluminium chlorohydrate complex, showing the tetrahedral aluminium surrounded 3+by 12 aluminium atoms in an 4+
octahedral arrangement. (b) Monomeric Al(H2O)6 and dimeric Al2(OH)2(H2O)8 . (c) Development of crystalline aluminium hydroxide. sweat builds up or gets re-­‐absorbed. Moreover, the polymeric gel plug is not well characterised, especially when it is formed inside the sweat pore. Its size, structure, strength, depth and interaction with the duct wall are all unknown properties. Given the abundant use of antiperspirants, it is surprising that so many questions regarding its properties and mechanisms remain unanswered today. Even the current methods of testing the efficacy of antiperspirants remain quite primitive. Volunteers are kept in a hot room, under controlled conditions, with absorbent pads under their armpits to collect their sweat for a defined time after applying an antiperspirant. Since antiperspirants have an effect on the body, they are legally classified as a drug and therefore must reduce sweating 12
by a minimum of 20% in at least 50% of the volunteers. The aim of this work was twofold. The first goal was to begin to develop a new in-­‐vitro laboratory based testing system for antiperspirants. This system consists of a glass capillary that will mimic a sweat gland, through which artificial sweat is flowed to imitate the perspiration process. The second goal was to develop a finite element method model to simulate the processes occurring in the experiments. This combination of experiment and model would be useful in gaining more understanding of the mechanism and chemistry of the antiperspirants. Experiments were conducted in a cell, comprised of a Teflon base and a detachable glass cylindrical body. The base contained a centrally located hole through which a glass capillary was inserted. Tapered glass capillaries used in these blocking experiments were constructed from borosilicate glass capillaries (outer diameter 1.2 mm, internal diameter 0.69 mm; Harvard Apparatus) that had been pulled to a fine point using a micropipette laser puller (P-­‐2000, Sutter Instruments). The capillary was polished flat using a diamond impregnated polishing pad (0.5 μm; Buehler, UK) fixed to a fast spinning wheel, until an internal diameter of 80 μm was reached, since 4
the diameter of a sweat pore is 60 – 120 μm. In practice, since a new capillary was made for each experiment, the average internal diameter varied: 72 ± 18 μm. Finally, the capillary was flushed to remove sanded glass and extraneous matter: the capillary was repeatedly filled with distilled water and then ejected by a jet of nitrogen, subsequently repeated again with acetone and then water. Sweat mimic was flowed at defined flow rates from a syringe pump (model KD100, C-­‐P Instruments, UK) through Teflon tubing to a two-­‐way Teflon splitting device. One outlet was connected to a pressure sensor. The other outlet was connected through tubing to the end of the glass capillary that was inserted into the experimental cell. A simplified schematic of the set-­‐up is shown in Figure 3. The effectiveness of the antiperspirant block was determined by measuring pressure as a function of time, which built up when flow was occurring behind the blocked capillary. The change in pressure was monitored by the Figure 3. Schematic of the experimental set-­‐up. This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-­‐3 | 3 Please do not adjust margins Please do not adjust margins ARTICLE Journal Name pressure sensor (micro-­‐switch 26PC, Honeywell, USA), whereby the output was connected directly to a computer and recorded by a custom written LabVIEW (2013, National Instruments, USA) program, via a Lab-­‐PC-­‐1200 card (National 9
Instruments, USA). Blocking experiments The system (syringe, tubing and glass capillary) was filled with sweat mimic, before antiperspirant solution (10 mL) was added by pouring into the cell. A gel plug was formed almost immediately. The system was maintained under zero flow conditions for 15 minutes. Once this period had elapsed, a -­‐1
constant flow was applied at either 16 or 64 μL hour . The 9
pressure was monitored throughout. Unblocking experiments The system (syringe, tubing and glass capillary) was filled with -­‐1
sweat mimic, and then a constant flow of 8 μL hour was applied for 15 minutes. Antiperspirant solution (10 mL) was added by pouring into the cell. A gel plug began to be formed immediately. The system was maintained under these conditions for 15 minutes. Once this period had elapsed, the -­‐1
flow was increased to either 80 or 150 μL hour . The pressure was monitored throughout. Simulation Figure 4. Effect of antiperspirant on the pressure build-­‐up in the capillary system. Antiperspirant was added initially, either ACH (black line) or AASCH (red line), and flow of sweat was commenced at 16 μL/hour after 15 minutes. One of these blocking experiments was left to run overnight. Here a larger pressure build up (up to 30 kPa) than in the shorter timescale experiments was observed, culminating in a sudden drop in pressure that corresponds to an unblocking event, where the plug was forced out of the capillary. Accordingly, it was proposed that if there is a A finite element method model was constructed using COMSOL Multiphysics (version 5.1, COMSOL AB, Sweden). Measurements for the pipette geometry were taken from an average size (80 μm) pipette, visualised by optical microscopy, using ImageJ (version 1.50a, NIH, USA). Results To examine the effect of the antiperspirant active in the blocking of sweat pores, two actives were tested: ACH, the most commonly used, and AASCH, a newer active thought to be more efficacious than ACH. Pressure transients were recorded from the capillary model system, and are shown in Figure 4. It can be seen that both antiperspirant actives give exactly the same build up in pressure, as both transients have the same gradient. Despite this, the optical microscopy recorded during the experiments does observe a slight difference in the appearance of the plugs formed from the antiperspirants, seen in Figure 5a and 5b. The plug formed from ACH appears to have a transparent, gel like consistency, whereas the plug formed from AASCH has a more opaque, compressed powder type consistency. However, since in both cases, the plug was formed and full blocking of the capillary occurred immediately on addition of the antiperspirant, it was reasoned that this methodology would not be able to distinguish between blocking caused by different antiperspirants, or indeed from any other method of blocking, since it is only measuring the pressure build-­‐up behind a capillary that is completely sealed. Figure 5. Photographs of the pipette and gel plug formed from (a) ACH, and (b) AASCH, under the same conditions. Photographs of the gel plug formed (c) internal, and (d) external, to the pipette. Magnification ×2. 4 | J. Name., 2012, 00, 1-­‐3 This journal is © The Royal Society of Chemistry 20xx Please do not adjust margins Please do not adjust margins Journal Name ARTICLE (a) Figure 6. Effect of antiperspirant on the pressure build-­‐up in the capillary system. Antiperspirant was added initially, either ACH (red line) or AASCH (blue lines, two repeats) and flow of sweat was commenced at 64 μL/hour after 15 minutes. difference between antiperspirant plugs, for example in structure or integrity, then the unblocking event might occur at different pressures. For instance, one of the plugs may bind more strongly to the walls of the capillary than the other. Consequently, the blocking experiment was repeated, and once the plug was formed and flow of sweat commenced, the system was left until an unblocking event occurred. The flow rate was increased to 64 μL/hour, purely to reduce the timescale of the experiment, since there is a linear relationship between the flow rate and the rate of pressure increase. The results of these experiments are shown in Figure 6 (images in Figure S1). For ACH, there was a linear increase in pressure once flow commenced, until around 60 minutes later, when the pressure reached 71 kPa before suddenly dropping back almost to zero. This corresponds with an unblocking event, and flow of sweat could clearly be seen by video microscopy emanating from the capillary. However, for AASCH, there was a similar linear increase, but instead there was a slight plateau in pressure before a sudden drop, and the pressure did not return to zero but rather to an ‘intermediate’ pressure. This occurred because of a leak that developed elsewhere in the system, so here the experiment did not work as planned and the data does not correspond to the antiperspirant plug whatsoever. Nevertheless, some information can still be gained about the formation of the gel plug. It was noticed in some repeats of the experiments that some gel plugs formed with a major proportion internal to the capillary, whilst others formed mainly external to the capillary (Figures 5c and 5d). Indeed, one experiment where flow was never commenced saw the plug form to a depth of around 1 cm from the pipette tip (Figure 5c). Consequently, it was reasoned that any internal plugs would not be able to be removed through the end of the pipette before either (1) the pressure sensor reached its detection limit, or (2) the experiment set-­‐up broke, e.g. tubes becoming disconnected. Therefore the experiments were re-­‐
run, except this time the antiperspirant was added (and so the plug was formed) under low flow conditions, rather than no (b) Figure 7. (a) Effect of sweat flow rate on a plug formed from ACH. Flow of sweat was initially at 8 μL/hour for 15 minutes before antiperspirant was added, and then after a further 15 minutes flow of sweat was increased to either 150 μL/hour (red line) or 80 μL/hour (green line). (b) Effect of antiperspirant on the pressure build-­‐up in the capillary system. Flow of sweat was initially at 8 μL/hour for 15 minutes before antiperspirant was added, either ACH (green and blue lines) or AASCH (black and red lines) and then after a further 15 minutes flow of sweat was increased to 80 μL/hour. Letters correspond to images in Figure S4. flow conditions. Additionally, the variation in plug position, despite being run under seemingly identical conditions, was attributed to slight variation in residual flow from initially filling the capillary with sweat before starting the experiment. Hence, future experiments were timed so that each action (filling capillary, starting flow, etc.) were completed after the same duration of time for every experiment. The results from these experiments are shown in Figure 7. Figure 7a shows three repeats of ACH, where antiperspirant was added 15 minutes after continuous sweat flow at a low rate (8 μL/hour), left under these conditions for a further 15 minutes, before the flow rate was increased to either 80 or 150 μL/hour. Each experiment gives a completely different pressure transient, and further repeats gives similar somewhat unpredictable results (imagery in Figure S2). One transient (red line) is seen to increase until a pressure of 30 kPa before dropping back to baseline. Another transient (green line) is seen to increase to a certain pressure, drop suddenly and then continue increasing, which occurs twice before reaching a higher pressure (50 kPa) and dropping to baseline. This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-­‐3 | 5 Please do not adjust margins Please do not adjust margins ARTICLE Journal Name Other transients (red line) climb steadily to a low pressure (5 kPa) and stabilise, while others may not change in pressure whatsoever. Some of these observations can be attributed to explanations but some cannot. For example, those that showed minor unblocking events was often where sweat was leaching or flowing through the gel plug, thus re-­‐initiating polymerisation until the gel plug was resistive enough to flow again (refer to Figure S3). However, in other cases, once faster flow began, the sweat easily forced its way through the plug, and the flow appeared too strong to allow the plug chance to reform. This suggests either the plug was poorly formed to start with, or it could not maintain its integrity well enough. In terms of identifying a difference between the two actives, Figure 7b shows two repeats of each, and it can be seen that both can give strong and weak pressure increases, therefore it cannot confidently be believed that there is any difference. Simulation Figure 8. Schematic diagram of the simulation domain. Geometry A finite element method model was constructed using COMSOL Multiphysics software in order to gather information regarding the velocity and pressure of sweat flowing through the pipette, and the diffusion of antiperspirant into the pipette. A schematic of the simulated domain is shown in Figure 8. The model consists of a square box of width 10 mm and height 10 mm, along coordinates r and z respectively, producing a 2D axisymmetric cross section, symmetric along boundary axis 1, which represents the cylindrical experimental cell. The pipette is created by inserting a wall at r = 150 μm that is 80 μm thick, hence dividing the r axis into two parts: the inside of the pipette (boundary 4) and the base of the cell (boundary 3). Boundary 2 represents the bulk antiperspirant solution. Within the geometry there are two domains defined, A and B, with different material properties, though initially they will be the same. Domain B is located at the opening of the pipette in order to represent the gel plug formed during blocking, whilst domain A has the properties of water, representing an aqueous solution: either sweat for the area inside the pipette, or antiperspirant solution for the area external to the pipette. Boundary conditions The model consisted of two physics components: laminar flow, from the flow of sweat, and transport of diluted species, from the addition of antiperspirant solution. Laminar flow. Laminar fluid flow is based on the Navier-­‐Stokes equation (Eq. 1) together with the continuity equation (Eq. 2): 𝜌 𝐮 ⋅ ∇ 𝐮 = ∇ ⋅ [−𝑝𝐈 + 𝜇(∇𝐮 + (∇𝐮)! )] + 𝐅
∇ ⋅ 𝜌𝐮 = 0
(1)
(2)
where ρ is the density (1 g/L), u is the velocity vector, p is the pressure, μ is the dynamic viscosity at 293 K, T is the matrix transpose operator, I is the identity matrix, and F is the volume 23, 24
force vector.
The Reynolds number measures how turbulent the fluid flow is. Low Reynolds numbers indicate laminar flow, and when it is very small (<< 1) then the Navier-­‐Stokes equations can be reduced to Eq. 3: 0 = −∇𝑝 + ∇ ⋅ (𝜇(∇𝐮 + ∇𝐮 ! )
(3)
This is an accurate assumption, since the Reynolds number, Re, for this system is calculated as follows: Re =
!"#
!
= 8.21×10!!
(4)
where ρ is the density (0.001 kg/L), U is a fluid velocity scale -­‐5
-­‐6
(1.19 × 10 m/s), L is the pipe diameter (6.9 × 10 m), and μ is the dynamic viscosity (0.001 Pa s), and so the calculation in Eq. 24
4 confirms that the Reynolds number is indeed very small. A no-­‐slip boundary condition was applied at boundary 3, which represent the walls of the pipette and experimental cell. This condition assumes that there are no viscous effects at the wall, hence no boundary layer develops. An inlet boundary condition was applied at boundary 4, to represent the fluid inflow from the pipette. This is a Dirichlet boundary condition, which specifies the values that a solution needs to take along a surface, i.e. the boundary of the 25
domain. The prescribed inlet condition is m, the mass flow rate, as defined in Table 2. Therefore the integral of the density and velocity with respect to the whole surface is applied at a constant flux across the boundary, which was defined to be 16 μL/hour. An outlet boundary condition was applied at boundary 2, to represent fluid outflow into the bulk solution. Here, fluid moves down a pressure gradient defined by the equation in Table 2, where p0 is the relative pressure at the boundary (= 1 atm) and n is the boundary normal pointing out of the domain. 6 | J. Name., 2012, 00, 1-­‐3 This journal is © The Royal Society of Chemistry 20xx Please do not adjust margins Please do not adjust margins Journal Name ARTICLE Transport of diluted species. The mass transport of antiperspirant was also considered, since a concentration gradient is established when the antiperspirant solution is added. This diffusion was modelled in conjunction with convection, which occurs from the bulk fluid motion and should contribute to the flux of antiperspirant species (this is discussed later). The movement is governed by Fick’s laws (Eq. 26
5 and 6): 𝐍𝐢 = −𝐷! ∇𝑐! + 𝑐! 𝐮
𝝏𝒄𝒊
𝝏𝒕
(5)
+ ∇ ⋅ 𝐍𝐢 = 0
(6)
Boundaries 2 and 4 were both applied with the inflow boundary condition: the flow of antiperspirant from the bulk 3
solution (boundary 2) was defined to be c0,a = 0.68 mol/m whilst the flow of sweat from the pipette (boundary 4) was 3
defined to be c0,s = 0 mol/m , because there will be no antiperspirant flowing into the system via this manner. Solving the model In order to simulate the blocking event, i.e. the formation of the gel plug, a parametric sweep was implemented. A region (domain B) was defined to be a separate material to represent the gel plug, whilst domain A represents aqueous solution, applicable to both the antiperspirant solution and sweat. Initially, both domains carry identical material properties. The parametric sweep varies the dynamic viscosity of domain B: increasing from 1 to 2500 mPa s, in steps of 50 mPa s. Optical microscopy recorded during the experiments suggests that this increasing viscosity method is a realistic approach of simulating the plug formation. A mesh was generated consisting of 2702 elements, and the model was run under stationary conditions to calculate the steady state solutions to the equations mentioned. Results Once the velocity, pressure, and concentration profiles were determined, plots were produced of these variables along the z axis for each viscosity time step. These are shown in Figure 9. Table 2. Summary of boundary conditions used in the simulation. Boundary 1 2 Boundary type Axis of symmetry Bulk solution Equations None [−𝑝𝐈 + 𝜇(∇𝐮 + (∇𝐮)! )]𝐧
= −𝑝!
ci = c0,a
3 u=0
Wall −
4 Pipette !!
𝜌 𝐮 ⋅ 𝐧 𝑑!" dS = 𝑚
ci = c0,s
Figure 9. Plots of (a) velocity, (b) pressure, and (c) concentration of antiperspirant, along the z-­‐axis of the domain of the model, plotted for each viscosity. The opening of the pipette occurs at z = 650 μm, whilst the gel plug domain occurs at z = 510 – 700 μm. The velocity of sweat flow increases exponentially on approach to the tip, reaching its maximum at the opening of This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-­‐3 | 7 Please do not adjust margins Please do not adjust margins ARTICLE Journal Name Figure 10. Plot of concentration of antiperspirant along the z-­‐axis of the domain, when the model is run without any flow from the pipette (black line) and with flow (red line). the pipette, before quickly dropping again. It is unclear why there is a discontinuity between time steps. As the viscosity of the plug increases, the pressure inside the pipette increases. This matches with the experimental results. From the model, the pressure is uniform throughout the aqueous solution in the pipette, and then begins to drop when travelling through the gel plug, before becoming slightly relatively negative at the pipette opening and then stabilising at a constant pressure in the bulk solution. The concentration of antiperspirant has the same profile along the z-­‐axis regardless of the viscosity of the gel plug. This is interesting, since it could be suggested that as the viscosity of the gel plug increases, diffusion into the pipette decreases. In the experiments, most of the gel plugs formed external to the capillary and grew outwards, because of the fluid flow out of the capillary. In order to confirm that the model can account for this, the simulation was run without fluid flow, i.e. in Equation 5, u = 0. The concentration of antiperspirant along the z-­‐axis was then plotted, and the results of both are seen in Figure 10. With the effect of flow, the concentration profile shifts further out of the capillary; in other words, the antiperspirant does not diffuse as far into the capillary than it does when there is no flow. Conclusions Although the use of antiperspirants (and deodorants) is ubiquitous, not much is understood of the properties of these materials or their mechanistic action. The first aim of this project was to develop an experimental method to test antiperspirant efficacy. Unfortunately, no firm conclusions can be drawn regarding a difference between the two actives, given the variability of results of both. Further experiments would need to be completed, including optimisation of conditions for plug formation, in order to give consistent, reproducible results so that any potential trend can be seen. Nevertheless, some information concerning the gel formation can be gleaned. Flow rate definitely has an effect on the position of plug formation: low/no flow rates when antiperspirant is added give plugs further inside the capillary. Furthermore, once the plug is formed, it does not get removed as a whole entity, despite the very large pressures (170 kPa) built up behind it. Rather, the gel appears to be somewhat porous and can allow sweat to leach through. The second aim of the project was to build a model to simulate the process. The ‘gelation’ method of simulation acts as a good representation, and data can be gathered about the velocity and pressure of sweat in the capillary as the plug forms. Moreover, the model has confirmed what was seen in the experiments, in that flow of sweat has an effect on the diffusion of antiperspirant into the capillary. The basis of the model is fluid flow through a channel, and diffusion of an external species into that channel. Consequently, the model could be extended or taken advantage of by other applications, such as simulating the dentine tubules in teeth and the diffusion of toothpaste or other substances into them. Whilst it is doubtful that the mysteries of antiperspirants and their activity will be solved completely in the near future, it is hoped that this work has contributed marginally to the understanding of how these everyday products work. Acknowledgements The author would like to thank Dr. Max Joseph for his help and support throughout the project, and is particularly appreciative of his expertise regarding the modelling. The author would also like to thank Dr. Alex Ashcroft and Dr. Michael White at Unilever PLC. Notes and references 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. E. S. Abrutyn, in Cosmetic Dermatology: Products and Procedures, ed. Z. D. Draelos, Wiley-­‐Blackwell, Oxford, UK, Editon 1st, 2010, pp. 150-­‐155. S. 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