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ENGINEERING ECOLOGY (Fig. 1 A and B): the flagellum or main branch, the rami so all fluid particles must pass through these structures. Only a (secondary branches perpendicular to the flagellum), and the few studies have tackled the case of permeable structures in an sensilla. The sensilla are mostly located on the rami. There is open flow field: Air partly flows through and is partly deflected a difference of four orders of magnitude in size between the around the whole structure (11, 18). We evaluated the propor- diameter of the sensilla (∼3 µm) and the total length of the tion of airflow passing between the sensilla and carrying the antenna (∼1 cm). This complex multiscale geometry made it dif- molecules potentially able to reach their surface, by performing ficult to investigate a complete antenna (11, 12). Indeed, the particle image velocimetry (PIV) on a large-scale 3D printed arti- geometry of an antenna, where boundary conditions have to ficial microstructure. As proposed by Cheer and Koehl (19), we be defined, is difficult to describe in an analytical formula or call this proportion the “leakiness” of the microstructure. This requires a huge number of elements in a numerical simulation. In leakiness provides a measurement of the airflow between sen- an experimental approach, building such complex objects is still a silla and, thus, also of the mean air velocity between sensilla. challenge, even with the help of three-dimensional (3D) printing This velocity is particularly important, as it defines the air veloc- (13). We therefore split the antenna into two levels of organi- ity used as an input in the model of mass transfer described zation: the flagellum plus the rami, and a single ramus plus its above (Fig. 2). sensilla. We focus here exclusively on the second of these levels In summary, our approach involved investigation of the geom- of organization, which we refer to hereafter as the microstruc- etry of the microstructure of the moth antenna (Fig. 1B), fol- ture, because the sensilla host the chemical detectors. One of lowed by the development of a model of mass transfer based the key parameters considered is the upstream orientation of the on a simplified geometry (Fig. 1C), and the production of a sensilla, longitudinal to the airflow. scaled-up 3D printed microstructure for the evaluation of leak- Two aspects of the architecture of the microstructure are iness by PIV (Fig. 1D). Finally, we combined the results of the particularly important and complicate attempts to determine previous two sections to calculate the capture efficiency of the capture efficiency: the geometry of the antenna and its leaki- microstructure (Fig. 2). ness, due to its finite dimensions (14). We dealt with these two aspects separately. The microstructure has an intricate shape, Results with sensilla located on each ramus (Fig. 1B). We modeled a sim- We first present the relative capture rates of pheromones pre- plified microstructure with a 2D array of longitudinal cylinders dicted by the model, followed by the experimental estimation of with diameters and lengths comparable to those of the sen- leakiness. By combining the two, we can calculate capture effi- silla. We adapted an analytical formula developed by Miyatake ciency, a relative measure. We then focus on the presence of and Iwashita (15) for heat transfer to measure mass transfer a spatially restricted region at the tip of the sensilla at which between a fluid and an infinite array of horizontal cylinders. capture is enhanced, confirming the presence of a previously The microstructure is also a finite permeable structure. In many observed “olfactory lens.” studies, permeable structures are located within tubes (16, 17), Pheromone Capture Efficiency Decreases with Increasing Flow Speed. By adapting the work of Miyatake and Iwashita (15), we deter- mined the local mass transfer Fcyl(z) on a slice of cylin- AB der of length dz depending on the local coefficient of mass transfer KM (z),

Fcyl(z) = KM (z)πd0 (cf (z) − ccyl) dz. [1]

Local mass transfer Fcyl(z) depends on the local pheromone concentration in the fluid cf (z), pheromone concentration at the surface of the sensillum ccyl, and the local coefficient of mass transfer KM (z). The local concentration cf (z) varies along the sensillum but is averaged within the fluid, in a direction perpen- dicular to the sensillum. The local coefficient of mass transfer can be obtained by using the local value of the Sherwood number Shloc(z), analogous to the Nusselt number (SI Appendix). As air flows along the sensilla, it is depleted of its molecules, CDaccounting for the dependence on concentration cf with z. Using a suitable mass balance on a slice of fluid around a sensillum, we can determine cf (z), as described in Fig. 4, Inset,

Fin(z) − Fout(z) = Fcyl(z), [2]

with Fin(z) = wmodcf (z) [3]

Fig. 1. Geometries of the natural and artificial antennae. (A) Scanning Fout(z) = wmodcf (z + dz), [4] electron micrograph of the macrostructure, consisting of the flagellum and 2 rami. (B) Magnification of the tip of a ramus, revealing the sensilla. (C) Array and wmod = 4s is the volume flux per cylinder in a square array of semiinfinite cylinders. The cylinders are arranged in a square array of side of side 2s (Fig. 1C). Thus 2s. The direction of airflow is indicated by the arrow: The cylinders face the flow. The number of cylinders is infinite in the direction orthogonal to wmodcf (z) − wmodcf (z + dz) = KM (z)πd0dz (cf (z) − ccyl). the direction of the flow. The local mass transfer coefficient is determined assuming semiinfinite cylinders, but the total mass transfer is integrated [5] only on the red portion (from the tip to the length of the sensillum). (D) The 3D printed microstructure used for leakiness assessments in the PIV Hence, the variation of the fluid pheromone concentration along experiments. a cylinder is given by

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Flow sider Increasing with Increases Leakiness and line yellow 4, (Fig. velocity model increasing the with of efficiency capture The microstructure, the of ciency 2. Fig. afrBnjee al. et Jaffar-Bandjee and leakiness, the is Le model, the model. the in of input efficiency an as used sw oee nifiiearyo yidr,w eeable were we cylinders, of array infinite an modeled we As obnto fmdladeprmnst bantecpueeffi- capture the obtain to experiments and model of Combination F ref mod 1 η − s and w safnto of function a as 6 h eeec asflxi h oueflwrate flow volume the is flux mass reference The . mod 18 n yitgaigtelclms u ln a along flux mass local the integrating by and 6 F Mta 21b860274)adobtained and 8.6.0.267246) R2015b (Matlab dc n ekns;Fg ) ece a max- flat a reaches 2), Fig. leakiness; and dz s F v rmtefli otesnilmi obtained is sensillum the to fluid the from f n F s s η = −1 = and ref mod m η . K Z s v 0 Fg ,sldrdln) h mass The line). red solid 4, (Fig. ∞ M = v L = v ∞ s (z ∞ v stefrfil velocity, far-field the is F w F ∞ −1 I xeiet rvddus provided experiments PIV . )π ref F (Eq. mod mod cyl η s IAppendix). (SI d s (z curdfrteartificial the for occurred 0 η c . ftesnilmb divid- by sensillum the of s (c ∞ )dz osbttt variables substitute to 14) F erae monotonically decreases η f . s (z m . Le ihEq. with h rdc fthe of product the , ) F − s nrae monoto- increased ewl o con- now will We c ytereference the by IAppendix). SI cyl η L ). v s s n stecapture the is . ethen We 7. stevelocity the is [9] [7] [8] [6] eto h au ftefrfil ocnrto,a h mass the as concentration, far-field indepen- the is flow concentration of result low (Eq. This value equation at transport effect. the pronounced depletion of particularly prox- the dent half the is to distal than due effect molecules The velocities, This more 5B). half. captures (Fig. always imal capture sensillum sen- a pheromone the of in rates, of capture sensillum length local a the these along integrating capture (Eq. spatially leading in of a tip, By decrease the As depleted sillum. at strong sensillum. is efficient the a air more along to is The flows transfer sensillum. it mass the as consequence, molecules of pheromone length its increas- the sensillum, the The of down the tip constant. very ing sensillum, remains the at and the smallest interactions is neighbors, layer of dynamic its boundary with fluid length sensillum the the each by of of constrained is most layer Over boundary sen- 5A). the along (Fig. decrease a Lens.” silla shows “Olfactory capture the molecule of of distribution by Existence the pass for at Explanation which occurs regimes molecules, two efficient the the sufficiently m·s of between 0.2 not transition about portion is The large which rapidly. too sensilla, a limited of capture is array capture to sur- mass the the velocities, to higher to struc- At due diffuse sensilla. the to allowing the around time sensilla, of face sufficient flows between molecules slowly air pheromone flows is the the air leakiness of remaining velocities, most The low as ture. At factor, model. limiting the the of efficiency capture h aeo lrt,w niaeteln nyin velocities. For only other leakiness. line the the of for indicate position determination same we the clarity, for of measured sake was the used flux the which (C microstructure. of the to tive 3. Fig. EF CD A ,2 5}m·s 2, 0.5, {0.05, ,w a sesterltv motneo ahhl of half each of importance relative the assess can we 1), eoiyfil rela- field Velocity (B) setup. Experimental (A) experiments. PIV −1 c . . −1 h ht otdln in line dotted white The . slna ihrsett pheromone to respect with linear is 10) –F eoiyfil o a-edvelocities far-field for field Velocity ) B NSLts Articles Latest PNAS u twslctda the at located was it but C, C niae h on at point the indicates h spatial The | f8 of 3 F v cyl ∞

ENGINEERING ECOLOGY of absolute capture flux observed for steady-state flux might be deceptive: A toy model of a finite pheromone puff shows that, in this case, the microstructure total capture is propor- tional to efficiency (SI Appendix). Thinking in terms of capture efficiency therefore enables us to identify both the physical phe- nomena limiting capture and the velocity range at which the microstructure is the most effective. The capture performance of a microstructure depends on var- ious features, the two most important being its finite dimensions and particular geometry (24). We argue that low levels of leaki- ness decrease the air velocity in the vicinity of sensilla, allowing more time for the pheromone molecules to be trapped by the surface of the sensilla via diffusion alone. The finite dimen- sions of the microstructure therefore have a crucial impact on capture performance through leakiness. Capture efficiency is fur- thermore modified by the specific geometric arrangement of the sensilla, the second key feature. The model of mass transfer in an infinite array of semiinfinite longitudinal cylinders facing the airflow captures the essence of this geometric problem (15). According to our model, the capture efficiency of a microstruc- ture is the product of its leakiness and the efficiency of the infinite model. This result is in accordance with Kanaujia and Fig. 4. Capture rate of the microstructure (red triangles), calculated as a Kaissling (14) where leakiness is called ‘transmissivity” and effi- combination of leakiness (blue triangles) and model capture rate (yellow ciency of the model is called “adsorptivity.” As leakiness and triangle). The blue curve is an exponential fit to leakiness, with the equa- efficiency of the infinite model are both defined as ratios rang- tion Le = 32.4 exp(0.352 ln v∞). The yellow and red curves are fits to the ing between 0 and 1, their product also lies between 0 and 1 and, model capture efficiency and the capture efficiency of the microstructure more importantly, is always inferior to each term. Thus, for a obtained from fitted leakiness, respectively. Inset shows the control volume used to determine the mass flux on a sensillum. Air flows in the direction of given air velocity, the efficiency of the microstructure is majored by their smallest values. We found that leakiness was very low increasing z. Fin is the mass flux entering the control volume, Fout is the mass flux leaving the control volume, Floc is the mass flux reaching the surface of at low velocity, at which it was the limiting factor, whereas a the sensillum, and ds is the diameter of a sensillum. larger proportion of the air passed between the sensilla at high velocities (Fig. 4). However, at these high velocities, only a small proportion of the pheromone molecules had sufficient time to diffuse to the sensilla. We conclude that an efficient microstruc- Discussion ture should have both a high leakiness and a small distance Assumptions of the Model. In this study, we made a number between sensilla. The first of these conditions implies a decrease of assumptions regarding the printed microstructure, the fluid in the number of sensilla. The second requires an increase in the dynamic experiments, and the model. In SI Appendix, we discuss number of sensilla. We thus observed a trade-off between these these assumptions. two limiting conditions, implying an efficiency optimum at inter- mediate values of air velocity. This trade-off between leakiness The Capture Efficiency Is the Result of a Trade-off. The captured and capture efficiency can be understood in terms of advection pheromone flux monotonically increases with respect to the air and diffusion. At low velocity, advection through the antenna is velocity (SI Appendix). Thus, the faster a moth flies, the more it the limiting factor, whereas, at high velocities, the time required captures. However, drag increases with the square of the veloc- for diffusion is too long for most of the molecules to reach the ity at high Reynolds numbers, leading to an energy vs. capture sensilla (SI Appendix). trade-off. This might be part of the explanation why one does not see insects flying with monstrous antennae. Similar arguments Implications for Moth Behavior and Antenna Geometry. As are used to explain the limits imposed on other exaggerated observed in previous studies (25–27), the position of the sensilla sexual traits (22, 23). Furthermore, the monotonically increase relative to the supporting structure varies considerably between

AB

−3 Fig. 5. The olfactory lens mechanism. (A) Change in mass flux Floc captured along a sensillum for a far-field concentration c∞ of 1 g·m at various air velocities. (B) Relative importance of the first half of the sensillum.

4 of 8 | www.pnas.org/cgi/doi/10.1073/pnas.2007871117 Jaffar-Bandjee et al. Downloaded by guest on September 24, 2021 Downloaded by guest on September 24, 2021 est ula h aeo eslu,adicesn toward increasing and sensillum, a of pore base a the Kaissling showing at evidence and null morphological Kanaujia density by by supported described and explain first (14) to lens,” mechanisms, sufficient “olfactory are reinforcing distance geometry, the two with antenna These on increases solely layer tip. dependent this the time cross fluid from the to the Thus, downstream molecule sensillum. Secondly, a the for of sensilla. length grad- taken the and the tip, down of outward-oriented increases concentra- the tip ually at pheromone thinnest the that is at layer such boundary maximal sensilla, molecules pheromone is the its along tion of flows depleted it is as air lens” “olfactory Firstly, the of 38–40). phenomenon (14, the into insight with us vided female locate to moths male atmospheric for by (37). useful emitters generated concen- are are and and which (36) flow of turbulence 35) forced incoming patterns (12, temporal of also puffs of pheromone model aspects characterization shapes the steady-state geometric antenna precluding a on tration, of use focus diversity to the The the us which nature. to to particular in generalized extent the found the be to Focusing decreases can costs. attention geometry results its particular This had one cylinder. however, on architecture geometry, a antenna antennal as of the features if simple even matter as rate, they that was capture shown the the have to defining mod- 34) orientation (33, for previous and considered than scales been where here nature have of cases flow in other studied geometry few found geometry The detailed that (32). the the els to to closer antenna, much attention an being our of in microstructure lies the topic 31), this on 12, studies published (11, to relative contribution, main Our the be Conclusion to and designed parameter be velocities. flight critical might at a microstructure efficient thus most the is that sensilla velocities appears symmetry, of lower it density By at The maxima too. 6). their values (Fig. have higher should to the structures expect shift sparser reasonably to can we curves efficiency that efficiency so maximal values, capture higher and to leakiness shifted increase are small both can a density, for velocities sensilla Indeed, max- realistic, antenna. of the complete still a of but for shift higher, expected a be even and to to leakiness velocities efficiency in higher imum decrease at a capture However, leakiness pheromone this apply. both and In of velocities effects 30). limiting low stud- (20, same at previous the antennae expect whole by A would of we shown sensilla. case, interactions leakiness as its the dynamic expected, measuring fluid and be ies and ramus would rami single them 50 a between about through has antenna, flow studied antenna of we real that portion fact a the refer- by only (more tempered is 29) reality (28, and moths Saturniid of in ences velocities m·s flight 0.5 the of to velocities far-field the at maximal by flagellum. was the produced and the other wake rami the of the as as such ahead in structures, information, sustaining entrapped located larger more recently quickly sensors extract are as (24), locations can al. Second, structure et area. supporting the Waldrop contact by decreasing with the shown may one sensilla greatly increase longitudinal than microstructure, considerably without whole leaky the Thus, less of leakiness surprising probably microstructure sensilla. a the is First, longitudinal sensilla for species. findings this transverse explanations our in with two antenna by the have confirmed of geometry We as Appendix). than tube, positioned efficiently (SI horizontal cylinder more molecules a longitudinal captures length, a flow similar the a to for transverse as, surprising is in this This In and nature. in species found moth combination possible every with species, afrBnjee al. et Jaffar-Bandjee u oeigo nen emtyadms rnfrpro- transfer mass and geometry antenna of modeling Our investigated microstructure the of efficiency the that found We .Ti odmthbtenorexpectations our between match good This Appendix). SI h eslafc h flow. the face sensilla the mori, Bombyx −1 o3m· 3 to s −1 close , rcse r epnil o h niheto dr ttetip the at odors of enrichment the physicochemical for surface responsible undisclosed are has yet processes It as velocities. that flight is the observed suggested which at of sensilla, been results 70% the our of and with half 60% accordance distal between in the that on found located They are (10). pheromone it of tip the architecture. antennal (Bottom) dense to (Top) sparse from density, sensilla 6. Fig. oaino h aia drcpueefiinya ucinof function as efficiency capture odor maximal the of Location NSLts Articles Latest PNAS | f8 of 5

ENGINEERING ECOLOGY of the sensors (40). We provide an alternative rational explana- able to assume a null concentration at the surface of the sensillum given tion for this “olfactory lens” mechanism based on the processes the very low concentration of pheromone molecules in air: The sensillum described above. surface is unlikely to be close to its saturation capacity. Third, the fluid was The intricacies of flow dynamics with complex geometries pre- assumed to be fully laminar. Fluid flowing into the volume was considered clude broad conclusions about pheromone capture efficiency. to have a constant and uniform velocity vn and a concentration c∞. Fourth, the far-field concentration c∞ was assumed spatially uniform, implying that The tremendous variety of antenna forms and orientation of sen- the microstructure is reached by a filament of odor with a cross-section per- sors observed in insects (41) may be understood by a combination pendicular to the direction of flow and larger than the frontal area of the of experiments with 3D printed mock-ups and modeling of trans- microstructure. We set the far-field concentration at 1 mg·m−3 (47). Fifth, port phenomena, as reported here, when applied to particular we considered the steady state, in which fluid flow and mass transfer are types of antenna geometries. This applies equally to the micro- dependent on space (i.e., position along the sensilla), but remain constant cantilever based gas sensors (see ref. 42 for a review and ref. over time. By definition, the cylinders modeled experience a flow that is 43 for a specific case). In all cases, the hydrodynamical interac- bound to pass through the tubular array, the near flow. tions between the cantilevers within large arrays—being sensilla, nanowires, or arrays of micropillars (44, 45)—will depend on Experiments. Some of the air flows around the whole microstructure, rather their relative positions, the flow speed, and flow direction. than through it, so the molecules it carries are out of reach of the sensilla. The reference flux Fref must therefore be defined according to v∞ and not Materials and Methods vn as used for the reference flux of the model (Eq. 8). We determined the leakiness of the microstructure by PIV visualizations. Natural Antennae. Cocoons of the moth S. cynthia were obtained from Fabrication of an artificial microstructure by additive manufacturing. An Office Pour les Insectes et leur Environnement. After emergence, moths artificial microstructure was produced in black photoreactive resin (Form- were frozen (by placing in a freezer) and allowed to dry at room temper- labs) with a Form2 3D printer (Formlabs). It was produced scaled up by a ature for a month. Their antennae were then removed and observed in factor of α = 300 relative to the natural structure, for two reasons. Firstly, a scanning electron microscope (SEM) (Quanta 450, Field Electron and Ion it needed to be large enough for flow to be measured accurately. Secondly, Company) without metal coating. the sensilla needed to be thick enough to survive mechanical loading dur- Sensillum density and shape were observed on the SEM images obtained. ing the building process. The artificial microstructure was 13 cm long, with Measurements were made on 12 rami from five antennae from five male a ramus of 1.5-cm diameter and sensilla of 0.9-mm diameter. moths. The rami had a diameter of 54 ± 7.0 µm (mean ± SE). We measured PIV. We ran PIV experiments with the artificial microstructure in oil to five sensilla at each location. The sensilla were found to be 123 ± 34 µm obtain the velocity field (Fig. 3). We measured the velocity field on a long for a diameter of 2.3 ± 0.79 µm. In our model, we considered ramus cross-section in the middle of the artificial microstructure, to limit the diameter to be equal to 50 µm, and the sensilla were considered to be influence of edge effects (for more details on the experimental setup, 150 µm long and to have a diameter of 3 µm. see SI Appendix). We used a wide range of velocities to cover the ampli- tude of flows through an antenna induced by wind on a resting moth, or Mass Transfer Modeling. The goal of our model was to provide a solution flows occurring during a simulated moth flight. We therefore considered for the concentration ccyl of pheromone along a sensillum in steady flow an air velocity span of three orders of magnitude and chose the veloci- − conditions and to derive an expression for local mass transfer Fcyl along the ties {0.002, 0.005, 0.1, 0.2, 0.5, 1, 2, 5} m·s 1 for study. In terms of Reynolds sensillum (Fig. 4). numbers, using the sensillum diameter as the characteristic length, we The classical mass transport equation is obtained the following values:

∂c 2 + (~vair.∇)c = D∇ c, [10] ds*vair ∂t Reair = , [11] νair with c as the concentration of pheromone in air, ~vair as the velocity of air, and with ds as the sensillum diameter (3 µm), D as the diffusion coefficient of the pheromone in air (all variables are vair as the velocity of air, and −6 2 −1 ◦ shown in Table 1). νair as the kinematic viscosity of air (15.6 × 10 m ·s at 20 C). The equation is not easy to solve, given the complex geometry of the We changed both the velocity and the viscosity of the fluid to keep microstructure, and we resorted to an approximate semianalytical formu- the same Reynolds number while working with an artificial microstructure lation. We modeled the microstructure as a 2D infinite square array of two orders of magnitude larger than the natural microstructure. Instead sensilla, with each sensillum modeled as a semiinfinite cylinder with a diam- of working in air, we ran our experiments in rapeseed oil, which has a eter equal to that of the sensilla (Fig. 1C). As the array was infinite, each measured kinematic viscosity of 50 × 10−6 m2·s−1 at 29 ◦C (Rolling ball vis- cylinder can be considered to behave in an identical manner, and a single cometer: Lovis 2000, Anton Paar). The correspondence between oil and air cylinder with appropriate boundary conditions mimicking the infinity of the velocities is indicated in Table 2. array can therefore be considered. A semiinfinite cylinder can be used to Estimating leakiness. Leakiness corresponds to the proportion of molecules model the effect of a sensillum facing the flow, and we restricted the results available to the sensilla. It is defined as the flow (velocity times area) pass- to a length equal to that of a natural sensillum, starting from the tip of ing through the microstructure divided by the flow passing through an the cylinder. We also assumed that the presence of the rest of the cylinders identical frontal area in the absence of the microstructure (19). The frontal downstream had no marked effect on upstream flow. area is equal to the area of the microstructure projected onto a plane per- Heat transfer in arrays of semiinfinite longitudinal cylinders has been pendicular to the direction of the flow. Leakiness is thus the ratio of the investigated by Miyatake and Iwashima (15). We made use of the well- measured flux to the reference flux. A leakiness of zero indicates that the known similarity between heat and mass transfers to apply their model structure is impermeable. As the permeability of the structure increases, to our problem. Heat and mass transfers are both convective phenomena its leakiness increases to a maximum of 1, corresponding to a completely characterized by a diffusion coefficient and similar transport equations. permeable structure, equivalent to no structure at all. However, at such Replacing the thermal diffusivity α and the temperature T with mass dif- low Reynolds numbers, wall effects are not negligible anymore and tend fusivity D and pheromone concentration c, respectively, converts the heat to artificially increase leakiness (48). We thus ran simulations on a simpli- transfer equation into the mass transfer equation. As a consequence, heat fied model of the microstructure and determined a coefficient of correction transfer results can be adapted to mass transfer problems and vice versa. for each velocity that we applied to the leakiness obtained experimen- The definitions of the variables are listed in Table 1, and the analogies tally (SI Appendix). Leakiness is a relative measurement, and we worked are summarized in SI Appendix, Table S1. The diffusion coefficient of the in steady state. Leakiness can therefore be considered to be identical in pheromone was determined as described by ref. 46 (SI Appendix). dynamically scaled configurations or, in other words, in configurations with We also ensured that our boundary conditions were equivalent. First, equal Reynolds numbers. We were therefore able to measure leakiness on the cylinders were considered to be distributed in a square array of side a scaled-up microstructure in oil and apply the resulting measurements to a 2s (Fig. 1C). Second, the concentration at the surface of the sensilla cs natural microstructure in air. was assumed to be uniform and null. This is equivalent to considering a We were interested in the flow bringing molecules into the neigh- pheromone molecule reaching the surface of a sensillum to be absorbed borhood of the sensilla. We therefore compared the flow between the by the surface and not released into the air again. Biologically, it is reason- most outward-facing sensilla of the microstructure (flow through the

6 of 8 | www.pnas.org/cgi/doi/10.1073/pnas.2007871117 Jaffar-Bandjee et al. Downloaded by guest on September 24, 2021 Downloaded by guest on September 24, 2021 hsclparameters Physical afrBnjee al. et Jaffar-Bandjee and microstructure with leakiness: of expression following the reference in (the resulted area This equal 3). an (Fig. through flux) flow far-field the and microstructure) Variables parameters Geometric model the in used constants and variables of List 1. Table iesols numbers Dimensionless parameters Experimental D ν ν uNsetnme See number Sherwood number Nusselt Gz Sh Nu v w d L η η c c F F F w w w L d α Re Le c c v v v v d φ σ s L S Re IAppendix (SI calculations Further w f ∞ cyl n ant cyl out in s n ∞ oil air antart front oil air m s s sart 0 mod ref through PIV ref air oil = w sterfrneflow. reference the as d through s steflwbtentetootrotsnil fthe of sensilla outermost two the between flow the as al .Eprmna enlsnmesadrltv eoiisi i n oil and air in velocities relative and numbers Reynolds Experimental 2. Table aharvlct htw atdt investigate. to wanted we that velocity air each mm·s velocity oil Experimental m·s velocity Air enlsnmesi ae n i eestt qa ausfrdtriaino h i eoiycrepnigto corresponding velocity oil the of determination for values equal to set were oil and water in numbers Reynolds 4.5 50 15.6 m·s length Antenna cm 1 m 3 g·m g·m g·m g·s g·s 150 m m m 300 900 g·m g·m m·s m·s m·s m·s 9.7 10.7 16 cm 13 m µm 3 3 3 3 2 × −1 −1 ·s ·s ·s ·s µm −1 −1 −1 −1 −1 × −3 −3 −1 −3 −3 µm µm −1 −1 −1 −1 × 10 10 ·s 10 Le −6 ntDsrpinDetails Description Unit −1 −6 −6 = m m −1 hwdthat showed ) w m 2 2 ·s through w ·s 2 −1 ·s −1 ref −1 , −1 eslu length Sensillum imtro natfiilsensillum artificial an of Diameter afdsac ewe sensilla between distance Half cln factor Scaling iesols pcn ewe sensilla between spacing Dimensionless cylinders between distance Dimensionless microstructure artificial the of Length ieai icst frpse i t29 at oil rapeseed of viscosity Kinematic ifso ofceto pheromone of coefficient Diffusion 20 at air of viscosity Kinematic eslu diameter Sensillum enfli eoiya h nrnet h microstructure the to entrance the at velocity fluid Mean model the in cylinder per rate flow Volume atr fcec ftemicrostructure the of z efficiency on Capture depending model sensilla the the of between efficiency fluid Capture the in concentration pheromone Mean fluid the in concentration Pheromone oa asflxt eslu ufc nFg 4 Fig. in surface 4 sensillum Fig. a in to described flux volume mass control Local 4 the Fig. of in out described flux volume Mass control the into as flux taken Mass area, equivalent an for sensilla Flux outermost two the between Flux experiment the in cylinder per rate flow Volume nfr ocnrto ttesraeo sensillum concentration a pheromone of Far-field surface the at concentration Uniform enlsnme nair in number Reynolds microstructure the to close velocity experiment air PIV Mean the in velocity air Far-field velocity Oil velocity Air area Frontal imtro h yidri h ettase model transfer heat the in cylinder the of Diameter enlsnme nair in number Reynolds reznumber Graetz Leakiness .0 .100 .40102041 0.4 0.2 0.1 0.04 0.02 0.01 0.004 .105 .721 .41. 1453.4 21.4 10.7 5.34 2.14 1.07 0.53 0.21 .200 . . . 5 2 1 0.5 0.2 0.1 0.05 0.02 [12] in o ohtecpueefiinyo sensillum, a of sensillum, efficiency a capture on the flux both mass Experiment. for PIV the sions and Model the Combining equivalently, or, enlsnumber Reynolds ◦ C F through ◦ C o uda velocity at fluid a for F s (v n v ,dpnigon depending ), n Le = = Le v v * ∞ v n ∞ , . w w d φ σ d Measurements Measurements Measurements See Measurements Eq. See Re Measurement See See Eq. sart 0 = mod PIV = h oe rvdsexpres- provides model The oil = NSLts Articles Latest PNAS v 12 11 ∞ σ 2s/d IAppendix SI IAppendix SI IAppendix SI IAppendix SI IAppendix SI = = = d = − v s αd (4 n αd (4 1 h I experiment PIV The . s * ν s s s * oil * 2 s v 2 oil − − η π π s * (v ( * ( d n 2 d 0 ,adthe and ), 2 0 ) 2 ) 2 ) * | ) v * v ∞ f8 of 7 ∞ mod [14] [13]

ENGINEERING ECOLOGY 2 Fs(v∞) vn4s provided information about leakiness, that is, the relationship between the ηm(v∞) = . [17] mod v 4s2 far-field velocity v∞ and the velocity at the entrance to the microstructure, Fref (v∞) ∞ vn(v∞). By combining modeling and experimental results, it is possible to express the capture efficiency of a sensillum according to far-field velocity According to Eqs. 9, 13, and 14, we obtained v∞, ηs(v∞). We did the same for the mass flux on a sensillum Fs(v∞). Thus, given Eq. 14, we hereafter express all values of the model according to v∞. ηm(v∞) = ηs(v∞)Le(v∞). [18] For determination of the capture efficiency of a microstructure ηm, we had to take into account its leakiness, which decreases the velocity from v∞ Data Availability. Template for artificial microstructure, Comsol code, Mat- to v . The easiest way to determine efficiency is to return to the mass flux n lab code, and raw PIV data are available on Figshare under the name on a sensilla F (v ) and define a new reference mass flux F depending s ∞ ref Microstructure data (https://doi.org/10.6084/m9.figshare.12631340.v1) (49). on v∞. 2 Fref = wc∞ = 4s v∞c∞. [15] ACKNOWLEDGMENTS. We thank the two anonymous reviewers for their The capture efficiency of the microstructure ηm is defined as comments which greatly improved the quality of this article. We thank Magaly Caravanier and Ben´ edicte´ Montigny for their help determining Fs(v∞) ηm(v∞) = . [16] the rapeseed oil viscosity, Josh Loessberg-Zahl for 3D printing our arti- Fref(v∞) ficial microstructure, and Jean-Franc¸ois Dufrecheˆ for the formula about the diffusion coefficient. We acknowledge the Centre Val de Loire region mod By multiplying the numerator and denominator by Fref (v∞) and using the for providing PhD funding for M.J.-B. and the PHEROAERO (Pheromone expressions of the reference flows (Eqs. 8 and 15), we obtained Capture by Aerosols) grant.

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