Real time observation of the interaction between aluminium salts and sweat under microfluidic conditions

Aluminium salts such as aluminium chlorohydrate (ACH) are the active ingredients of antiperspirant products. Their mechanism of action involves a temporary and superficial plugging of eccrine sweat pores at the skin surface. We developed a microfluidic system that allows the real time observation of the interactions between sweat and ACH in conditions mimicking physiological sweat flow and pore dimensions. Using artificial sweat containing bovine serum albumin as a model protein, we performed experiments under flowing conditions to demonstrate that pore clogging results from the aggregation of proteins by aluminium polycations at specific location in the sweat pore. Combining microfluidic experiments, confocal microscopy and numerical models helps to better understand the physical chemistry and mechanisms involved in pore plugging. The results show that plugging starts from the walls of sweat pores before expanding into the centre of the channel. The simulations aid in explaining the influence of ACH concentration as well as the impact of flow conditions on the localization of the plug. Altogether, these results outline the potential of both microfluidic confocal observations and numerical simulations at the single sweat pore level to understand why aluminium polycations are so efficient for sweat channel plugging.

On the other hand, the 3,3-ionene polyelectrolyte tested did not show any aggregation inside 72 the sweat channel. Some aggregation can be seen outside of the sweat channel, but nothing 73 appears inside. Ionenes are cationic polymers composed of quaternary ammonium centres as 74 part of the main hydrocarbon chain, separated by a predefined number of methylene (CH2) 75 spacer units. 3,3-ionene used for these experiments 2 has a chain length around 100 nm and a 76 mean molecular weight of 20,000 Da. 77 78 SI4: Equations used in the numerical code ATSIM3D

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The numerical code ATSIM3D uses space discretization with space step al = 24 nm. Within the 81 discretized space, the microfluidic device is defined precisely, though of smaller dimensions to 82 save storage memory. At each time of a numerical simulation, the local number concentrations 83 ck of all the species k are known at any place of the system. The species are: sweat protein, 84 ACH molecule, and all the molecular clusters (combinations of ACH molecules and sweat 85 proteins consistent with the coordination number of every molecule) of hydrodynamic radius 86 not larger than al. The hydrodynamic radius of each molecular cluster is calculated with 87 formula 3 : 88 that is under the assumption that the cluster is fractal of fractal dimension df. According to 90 Jullien and Botet 4 , we can take: df = 2. All the molecular species move and react according to 91 the following laws: 92 i. species diffusion. The diffusion equation 5 for the species k in both channels is: in which ck(x,y,z,t) is the number concentration of the species k of hydrodynamic 96 radius ak at time t, in the discretized cube located in (x, y, z). The coefficient Φ /ak 97 is the Stokes-Einstein diffusion constant of species k, with Φ kBT )related 98 to dynamic viscosity of water, , at temperature T.
species advection by fluid motion 6 . If v denotes the fluid velocity vector at location 100 (x, y, z): iii. aggregation between molecular species 7 . The Smoluchowski coalescence equation 105 holds, namely: 106 107 in which Kij is the probability per unit of time of combining a cluster of species i 109 and a cluster of species j to form a cluster of species k. The kernel Kij is the product 110 of the Brownian kernel and of the probability that a pending bond of the cluster i 111 combines with a pending bond of the cluster j during a hit. 112 113 iv. species deposition on the gel: 114 115 in which Kgk is the probability per unit of time of combining a cluster of species k 117 with the gel (cg is the local gel concentration). The kernel Kgk is defined in the same 118 way as the quantities Kij above, with the gel as a motionless cluster of molecules. In 119 [si5], the exponential term, exp(-v/vk), is the probability for the deposition to be 120 effective onto the gel. Indeed, shear effects due to the sweat flow can prevent 121 deposition, and, in a crude approximation, the exponent of this exponential term is Various boundary and initial conditions can be used, and the final system state does not 140 seem to depend much of the definite initial conditions. In the present work, we focus on the 141 following conditions that correspond to the case where antiperspirant is applied while 142 sweating process is active (this is similar to the experimental microfluidic case): 143  initial conditions: cP(x,y,z,)  CP is realized inside the whole pore, and cACH(x,y,z,) 144  CACH in the whole ACH channel.

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 boundary conditions: protein concentration is constant = CP at the pore output zmax 146 (see Fig. 12), and ACH concentration is constant at the entrance of the ACH channel 147 (that is: cACH(xmin,y,z,t)  CACH for xmin = position of the ACH channel entrance, left 148 part of Fig. 12). 149 150 SI5: 1D numerical model ATSIM1D

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The numerical code ATSIM1D is a simplified variant of the 3D ATSIM3D code, in 153 which the concentrations of every chemical species are averaged over transversal planes. 154 As we have no information (due to the averaging process) on the spatial distribution of 155 gel within a given section, the local porosity of the gel is replaced by (a/a0) 2 , in which a0 is the 156 initial radius of the pore and a(z,t) the effective radius of the pore at the depth z at time t. In 157 other words, this effective radius is the radius of the pore as if all the matter composing the gel 158 formed a dense layer all around the pore surface. The section, S(z), of the pore at the depth z is 159 then simply: S(z) =  a 2 . 160 That way, the equations governing the evolution of these averaged concentrations are in which the characteristic length  S(z)(Q ak) if the process occurs at constant volume 166 flow rate Q, or  L w(ak S(z) P) if it occurs at constant pressure gradient P/L. The 167 notation a' represents the derivative of the effective radius a with respect to the depth z inside 168 the pore. The same boundary conditions are used as in the 3D case.

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This 1D numerical code can manage much bigger pore sizes than ATSIM3D, because 171 it deals with two variables (z and t) instead of four (x, y, z and t). However, one has to be aware 172 that the main approximation of ATSIM1D is serious: the sections of the pore with gel (gel 173 Inside the pore, sweat proteins and ACH molecules do not move through the same 181 mechanism: proteins are carried by the sweat flowing in the pore, while movement of ACH 182 molecules is essentially diffusive and hindered by sweat flow. Therefore, the concentration, cP, 183 in sweat proteins is approximately a constant, CP all inside the pore before the gel position 184 (because the flow feeds it at a constant rate), while the profile of the ACH concentration, cACH, 185 is decreasing fast with the depth, z, in the pore. We then consider the following simplified 186 problem in which ACH molecules diffuse along the pore walls while sweat protein 187 concentration remains constant. These approximations allow to obtain a crude estimation of the 188 position where both concentrations balance (that is the active region where plug can form). 189 The pore section is here circular of radius a0. The sweat flows downward the z-direction 190 of the pore at the average velocity: vP > 0.
where do a0 is the diameter of the pore. In most of the cases, the value of x is indeed close 199 to (that is the ACH molecules diffuse essentially along the pore wall), then: 200 In the ring domain between (x) a0 and a0, diffusion-advection of the ACH molecules is ruled Plug can form in the region where neither ACH molecules nor sweat proteins are totally 217 saturated. This region is characterized by the condition: cACH  cP (ACH molecule saturation 218 occurs when cP  ACH cACH, and sweat proteins saturation when cACH  P cP, with typical 219 coordination numbers ACH, P of order to). Therefore, the position zplug of the gel is 220 estimated to be: 221