Fernando Luiz

Sacomano Filho
email: fernando.sacomano@usp.br

Luís Eduardo De

Albuquerque Paixão E Freire De Carvalho

Artur Carvalho Santos

Aymeric Vié

Jeroen Adrianus Van Oijen

Impact of multi-component description of hydrophilic fuel droplets in propagating spray flames

Keywords: Multi-component droplets, Spray combustion, Phase change modeling, Differential diffusion, Ethanol

. Given these aspects, this work investigates the impact of accurately describing the heat and mass transfers on droplets interacting with flames. Numerical simulations of freely propagating flames in droplet mists are conducted with a detailed chemistry description. Different scenarios focus on the impact of water addition in the gaseous or in the liquid phase. Results demonstrated that accounting for the multi-component phase change significantly impacts the flame speed. This is shown to be a consequence of the hydrophilic property of the chosen fuel, which allows the conversion from single-component to multi-component droplets, thus modifying the flame structure.

Preprint submitted to Journal of L A T E X Templates September 22, 2023

Introduction

Typical commercial fuels are composed of a large number of species, and require multicomponent modeling for the numerical description of spray flames [START_REF] Filho | A new robust modeling strategy for multi-component droplet heat and mass transfer in general ambient conditions[END_REF][START_REF] Shastry | Numerical study of multicomponent spray flame propagation[END_REF][START_REF] Bonanni | Interaction of preferential evaporation and low-temperature chemistry in multicomponent counterflow spray flames[END_REF][START_REF] Santos | The general formulation of the energy equation and the impact of enthalpy diffusion on multi-component droplet heat and mass transfer[END_REF]. Investigations about the multi-component description of droplets in non-reacting atmospheres are found in the literature for single droplets (e.g. [START_REF] Filho | A new robust modeling strategy for multi-component droplet heat and mass transfer in general ambient conditions[END_REF][START_REF] Santos | The general formulation of the energy equation and the impact of enthalpy diffusion on multi-component droplet heat and mass transfer[END_REF][START_REF] Sazhin | Advanced models of fuel droplet heating and evaporation[END_REF][START_REF] Sirignano | Fluid Dynamics and transport of droplets and sprays[END_REF][START_REF] Ebrahimian | Towards a predictive evaporation model for multi-component hydrocarbon droplets at all pressure conditions[END_REF][START_REF] Zhang | Multicomponent vaporization modeling of bio-oil and its mixtures with other fuels[END_REF][START_REF] Tonini | An exact solution of the mass transport equations for spheroidal evaporating drops[END_REF][START_REF] Lupo | A numerical study of ethanol-water droplet evaporation[END_REF][START_REF] Pinheiro | Modelling of aviation kerosene droplet heating and evaporation using complete fuel composition and surrogates[END_REF]) and spray flows (e.g. [START_REF] Keller | The influence of intra-droplet heat and mass transfer limitations in evaporation of binary hydrocarbon mixtures[END_REF]). However, the interaction of multi-component droplets with reacting flows is not extensively explored. Spray combustion simulations are commonly conducted with single-component surrogate fuels (e.g. [START_REF] Franzelli | Large eddy simulation of swirled spray flame using detailed and tabulated chemical descriptions[END_REF][START_REF] Filho | On the interaction between turbulence and ethanol spray combustion using a dynamic wrinkling model coupled with tabulated chemistry[END_REF]) to avoid the complexity of modeling chemical reactions and droplet phase change.

From the published works accounting for multi-component droplets in reacting flows (e.g. [START_REF] Shastry | Numerical study of multicomponent spray flame propagation[END_REF][START_REF] Bonanni | Interaction of preferential evaporation and low-temperature chemistry in multicomponent counterflow spray flames[END_REF][START_REF] Miyagawa | Spray vaporization model for multi-component gasoline[END_REF][START_REF] Leite | Modeling of emulsion droplet vaporization and combustion including microexplosion analysis[END_REF][START_REF] Wang | The effects of multicomponent fuel droplet evaporation on the kinetics of strained opposed-flow diffusion flames[END_REF][START_REF] Kitano | Evaporation and combustion of multicomponent fuel droplets[END_REF][START_REF] Govindaraju | Group contribution method for multicomponent evaporation with application to transportation fuels[END_REF][START_REF] Stagni | The role of preferential evaporation on the ignition of multicomponent fuels in a homogeneous spray/air mixture[END_REF][START_REF] Govindaraju | Coupling of turbulence on the ignition of multicomponent sprays[END_REF]), both [START_REF] Shastry | Numerical study of multicomponent spray flame propagation[END_REF][START_REF] Bonanni | Interaction of preferential evaporation and low-temperature chemistry in multicomponent counterflow spray flames[END_REF] stand out. Shastry et al. [START_REF] Shastry | Numerical study of multicomponent spray flame propagation[END_REF] investigated one-dimensional flames propagating in multi-component sprays using a detailed description of the chemistry. Alkane mixtures representing Jet-A surrogates are evaluated following the ideal vapor-liquid equilibrium (VLE) approach and without considering differential diffusion of vapor into the gas flow. The importance of the multi-component description of droplets is noticed in terms of the stratified mass exchange caused by the different vapor pressures of different components. Differential diffusion effects in reacting flows are included in [START_REF] Bonanni | Interaction of preferential evaporation and low-temperature chemistry in multicomponent counterflow spray flames[END_REF], which also investigates alkane mixtures representing Jet-A surrogates. 1D Counterflow spray flames were simulated using a detailed description of the chemistry. Results outline that differential diffusion effects are necessary for modeling multi-component spray combustion.

All these previous studies considered mixtures of long hydrocarbons. When considering alcohols, the number of species is usually small in a commercial fuel (e.g. ethanol). However, these hydrophilic substances can absorb the air humidity and the water formed during combustion [START_REF] Filho | A new robust modeling strategy for multi-component droplet heat and mass transfer in general ambient conditions[END_REF][START_REF] Law | Alcohol droplet vaporization in humid air[END_REF][START_REF] Millán-Merino | Theoretical and numerical analysis of the evaporation of mono-and multicomponent single fuel droplets[END_REF]. This aspect reinforces the importance of the multi-component description of droplets for both reacting and non-reacting atmospheres. Another important aspect is the limitations of different models available in the literature to accurately describe droplets' heat and mass transfer process in reacting atmospheres. Recently, new models were proposed [START_REF] Filho | A new robust modeling strategy for multi-component droplet heat and mass transfer in general ambient conditions[END_REF][START_REF] Santos | The general formulation of the energy equation and the impact of enthalpy diffusion on multi-component droplet heat and mass transfer[END_REF], which can accurately describe the differential diffusion of vapor into the carrier phase for hydrophilic and non-hydrophilic droplets interacting with general reacting flows.

Within the context of one-dimensional simulations conducted with a detailed description of the chemistry, flames propagating in droplet mists have been demonstrated as an important setup to fulfill an old gap in the research of spray combustion. As well observed by Versaevel [START_REF] Versaevel | Combustion laminaire diphasique etude théorique et expérimentale[END_REF], spray combustion test cases are mainly found in two extreme setups: single-droplet or polydisperse disperse flows. The last case predominantly involves turbulent carrier phase flows and is not far from real application flames, which implies complex flow configurations. Since that study, new experimental and numerical setups have been proposed (e.g. [START_REF] Sirignano | Fluid Dynamics and transport of droplets and sprays[END_REF][START_REF] Castanet | Heat transfer within combusting droplets[END_REF][START_REF] Vié | Analysis of segregation and bifurcation in turbulent spray flames: A 3d counterflow configuration[END_REF][START_REF] Parant | Richecoeur, Adaptation of a ptv method for droplets evaporating in vicinity of a flame[END_REF][START_REF] Wang | Stability and structure of lean swirling spray flames with various degrees of prevaporization[END_REF]) to reduce the gap between these two extreme setups. Recently, contributions following the numerical setup of one dimensional flame propagating in droplet mists coupled with the detailed description of the chemistry have been increasing in the literature, e.g. [START_REF] Shastry | Numerical study of multicomponent spray flame propagation[END_REF][START_REF] Versaevel | Combustion laminaire diphasique etude théorique et expérimentale[END_REF][START_REF] Neophytou | Simulations of laminar flame propagation in droplet mists[END_REF][START_REF] Filho | Numerical analyses of laminar flames propagating in droplet mists using detailed and tabulated chemistry[END_REF][START_REF] Filho | A novel strategy to accurately represent the carrier gas properties of droplets evaporating in a combustion environment[END_REF][START_REF] Rochette | Effect of non-zero relative velocity on the flame speed of two-phase laminar flames[END_REF][START_REF] Filho | Effects of reaction mechanisms and differential diffusion in oxy-fuel combustion including liquid water dilution[END_REF]. Although the geometrical simplifications are clear in such a numerical setup, it allows a good adherence with experimental measurements as shown in [START_REF] Versaevel | Combustion laminaire diphasique etude théorique et expérimentale[END_REF]. Further, such a setup is quite effective for the evaluation of parametric variations in ambient conditions (e.g. temperature and pressure) and the characteristics of the two-phase flow (e.g. initial droplet diameter, gas and liquid composition).

This work presents numerical simulations of flames propagating in droplet mists to further investigate the impacts of the multi-component description of droplets in reacting flows. In contrast to previous studies, this work considers a rigorous modeling approach [START_REF] Filho | A new robust modeling strategy for multi-component droplet heat and mass transfer in general ambient conditions[END_REF] for the heat and mass transfer on droplets, which can accurately describe the energy and the mass transport of hydrophilic and non-hydrophilic fuels. Effects of liquid composition and the consideration of air humidity are systematically analyzed for different equivalence ratios.

The paper is structured as follows. After this introduction, modeling approaches are concisely described. Results are presented first focusing on the impact of air humidity, and then on the water addition in the fuel. The paper ends with conclusions.

Modeling approaches

The one-dimensional reacting flow solver CHEM1D [START_REF] Somers | The simulation of flat flames with detailed and reduced chemical models[END_REF] was used for the numerical simulations. It has been extended with a Lagrangian spray solver to study flames propagating in fuel and non-fuel droplet mists [START_REF] Filho | Numerical analyses of laminar flames propagating in droplet mists using detailed and tabulated chemistry[END_REF][START_REF] Filho | A novel strategy to accurately represent the carrier gas properties of droplets evaporating in a combustion environment[END_REF][START_REF] Filho | Effects of reaction mechanisms and differential diffusion in oxy-fuel combustion including liquid water dilution[END_REF]. Simulations of unstrained laminar flames propagating in mono-dispersed isotropic sprays are presented in this manuscript, similarly to [START_REF] Shastry | Numerical study of multicomponent spray flame propagation[END_REF][START_REF] Versaevel | Combustion laminaire diphasique etude théorique et expérimentale[END_REF][START_REF] Neophytou | Simulations of laminar flame propagation in droplet mists[END_REF][START_REF] Filho | Numerical analyses of laminar flames propagating in droplet mists using detailed and tabulated chemistry[END_REF][START_REF] Filho | A novel strategy to accurately represent the carrier gas properties of droplets evaporating in a combustion environment[END_REF][START_REF] Rochette | Effect of non-zero relative velocity on the flame speed of two-phase laminar flames[END_REF][START_REF] Filho | Effects of reaction mechanisms and differential diffusion in oxy-fuel combustion including liquid water dilution[END_REF]. In the following, the resolved equations are briefly presented.

Gas Phase

The description of the carrier phase follows a variable-density low Mach number formulation. Following the strategies presented in [START_REF] Filho | Numerical analyses of laminar flames propagating in droplet mists using detailed and tabulated chemistry[END_REF][START_REF] Filho | Effects of reaction mechanisms and differential diffusion in oxy-fuel combustion including liquid water dilution[END_REF][START_REF] Somers | The simulation of flat flames with detailed and reduced chemical models[END_REF][START_REF] Van Oijen | Modelling of premixed counterflow flames using the flamelet-generated manifold method[END_REF][START_REF] Van Oijen | State-of-theart in premixed combustion modeling using flamelet generated manifolds[END_REF], the set of equations employed here is

d ṁ dx = k S k , (1)
d( ṁY i ) dx - d dx (ρY i V i ) = ωi + δ ik S k , (2)
d( ṁh) dx = - d dx        -λ dT dx + ρ N i=1 Y i h i V i -RT N i=1 D T i X i M i dX i dx        + S h , (3)
where ṁ = ρu is the mixture mass flux, x is the spatial coordinate, and S k is the source term of vapor species k. Y i is the mass fraction of the species i ∈ [1, N s -1], N s is the total number of species, V i is the diffusion velocity, ωi is the reaction rate, and δ ik is the Kronecker delta. h is the absolute enthalpy, h i is the absolute enthalpy of each transported species i, while S h denotes the coupling term between phases. The first term on the RHS of Eq. 3 refers to the heat flux, in which λ is the thermal conductivity, T is the temperature, R is the gas constant, D T i is the thermal diffusion coefficient, X is the molar fraction, and M is the molar mass. The computation of the diffusion coefficients (D i,m and D T i ) is performed following Ern and Giovangigli [START_REF] Ern | Fast and accurate multicomponent transport property evaluation[END_REF]. To account for the chemical reactions, the mechanism proposed by [START_REF] Marinov | A detailed chemical kinetic model for high temperature ethanol oxidation[END_REF] has been employed. It describes the oxidation of ethanol in air by means of 57 species and 379 intermediate reactions.

Liquid Phase

Since multi-component droplets are accounted for, the main changes in the liquid phase modeling compared to the previous works [START_REF] Filho | Numerical analyses of laminar flames propagating in droplet mists using detailed and tabulated chemistry[END_REF][START_REF] Filho | A novel strategy to accurately represent the carrier gas properties of droplets evaporating in a combustion environment[END_REF][START_REF] Filho | Effects of reaction mechanisms and differential diffusion in oxy-fuel combustion including liquid water dilution[END_REF] refer to the heat and mass transfer. Herein, the model of [START_REF] Filho | A new robust modeling strategy for multi-component droplet heat and mass transfer in general ambient conditions[END_REF] is applied, which accounts for the differential diffusion of vapor into the gas phase 1Heat and mass transfer on a droplet are given by

qd = 4πRλ Nu 2 (T ∞ -T s ) + k ṁd,k L k , ṁd = -4πR d ρD k Sh k 2 B M,k . (4)
where qd is the heat transfer rate, R d the droplet radius, λ the heat conductivity of the gaseous mixture, Nu the Nusselt number, ṁd the mass transfer rate, ṁd,k the mass transfer rate of vapor species k, L k the vaporization enthalpy of species k, ρ the mixture density, D k the multi-component diffusion coefficient, and Sh k the Sherwood number of vapor species k. Subscript s refers to quantities evaluated at the droplet surface. By adopting uniform temperature and composition in the droplet interior qd = m d k Y L,k c L,k dT d /dt, where Y L,k the liquid mass fraction and c L,k is the liquid specific heat of vapor species k. Following [START_REF] Sazhin | Advanced models of fuel droplet heating and evaporation[END_REF], a general approach is to consider that

Nu = ln |B T + 1| B T Nu 0 , Sh k = ln B M,k + 1 B M,k Sh 0 k , (5)
Nu 0 = 2 + 0.57Re 1/2 Pr 1/3 , Sh 0 k = 2 + 0.57Re 1/2 Sc k 1/3 , (6)
where Nu 0 refers to empirical correlations derived from non-evaporating moving droplets, and Sh 0 k is its analogous for mass transfer (see Eq. 6). Re = ρ|u ∞u d |d/µ is the Reynolds number, u ∞ the bulk flow velocity, u d and d the droplet velocity and diameter, µ the dynamic viscosity, Pr the Prandtl number, and Sc k = µ/ρD k the species k Schmidt number. B T and B M,k are the Spalding numbers for energy and species k:

B T = (T ∞ -T s ) k c p,k ṁd,k qd -k ṁd,k L k , B M,k = ṁd Y k,s -ṁd Y k,∞ ṁd,k -ṁd Y k,s . (7)
The multi-component diffusion coefficient D k is computed with the Wilke approach [START_REF] Fairbanks | Diffusion coefficients in multicomponent gas mixtures[END_REF], as in [START_REF] Filho | A new robust modeling strategy for multi-component droplet heat and mass transfer in general ambient conditions[END_REF][START_REF] Santos | The general formulation of the energy equation and the impact of enthalpy diffusion on multi-component droplet heat and mass transfer[END_REF]. Binary diffusion coefficients are computed with the Fuller-Giddings method [START_REF] Fuller | Diffusion of halogenated hydrocarbons in helium. the effect of structure on collision cross sections[END_REF]. For all simulations conducted with the MC approach, non-ideal VLE is accounted using the van Laar model [START_REF] Poling | The Properties of Gases and Liquids[END_REF]. The surrounding gas properties used for droplet phase change (i.e., µ, λ, c p , and D i j ) are computed following [START_REF] Filho | A novel strategy to accurately represent the carrier gas properties of droplets evaporating in a combustion environment[END_REF], where the gas composition in the far field follows the species diluted approach (SD) including all participating species. The procedure adopted to couple both phases is detailed in [START_REF] Filho | Numerical analyses of laminar flames propagating in droplet mists using detailed and tabulated chemistry[END_REF], which has been straightforwardly extended to multi-component mists.

Results

Results are presented in two sections. The focus is on the laminar flame speed, a major quantity for turbulent flame modeling, and on the influence of the multi-component modeling on this quantity. The first one is concentrated on the impacts of the multi-component modeling on flames propagating in droplets mists of pure hydrophilic fuel in humid or dry air. The second one investigates the consequences of considering droplets composed of a mixture of this fuel and water for flames propagating in sprays.

Droplets are injected 30 mm upstream of the flame front with an initial diameter (d 0 ) of 50 µm. Variations of initial droplet diameter have been investigated previously in [START_REF] Filho | Numerical analyses of laminar flames propagating in droplet mists using detailed and tabulated chemistry[END_REF][START_REF] Filho | A novel strategy to accurately represent the carrier gas properties of droplets evaporating in a combustion environment[END_REF][START_REF] Filho | Effects of reaction mechanisms and differential diffusion in oxy-fuel combustion including liquid water dilution[END_REF] for single-component fuel and non-fuel droplets. Herein, the initial droplet size has been selected as an intermediate value between small droplets < 25 µm, which predominantly interact with the flame pre-heating zone, and large ones > 75 µm, which respectively tend to penetrate far into the flame oxidation zone. The one-dimensional computational domain extends from -100 mm to 400 mm, in which the flame front is held at the coordinate 0.0 mm2 . By setting an overall equivalence ratio φ over , the mass flow of liquid is adjusted accordingly [START_REF] Filho | Numerical analyses of laminar flames propagating in droplet mists using detailed and tabulated chemistry[END_REF]. In all simulated cases, the inlet and initial droplet temperatures are 298 K 3 . Here, humid air refers to 100% relative humidity, i.e. X H 2 O = 0.032 at 298 K. Finally, results are presented for different φ over , which refer to the overall equivalence ratio, i.e. the equivalent φ to when the spray is completely pre-vaporized.

Pure hydrophilic fuel droplet in humid air

The laminar flame speeds of spray flames in humid and dry air are presented in Fig. 1. Singlephase laminar flame speeds are also included for reference in both conditions, i.e. humid and dry air. The general trends are consistent with the literature (e.g. [START_REF] Versaevel | Combustion laminaire diphasique etude théorique et expérimentale[END_REF][START_REF] Neophytou | Simulations of laminar flame propagation in droplet mists[END_REF][START_REF] Filho | A novel strategy to accurately represent the carrier gas properties of droplets evaporating in a combustion environment[END_REF][START_REF] Filho | Effects of reaction mechanisms and differential diffusion in oxy-fuel combustion including liquid water dilution[END_REF]). Here, the focus is on the behaviors observed among the different modeling assumptions under various conditions. A specific discussion about the faster flames observed for two-phase flows when compared with single-phase (SP) ones is conducted in the Appendix A, where a novel justification for this phenomenon is presented.

Focusing first on the SC results, as it occurs for single-phase flames, the inclusion of water vapor into the air stream leads to lower flame speed values compared to the results achieved with dry air. The consideration of this reaction product already in the reactants stream may also justify the anticipation of the quenching point to lower values of φ over , when compared with the dry air cases. However, the deviations between both SC cases are to be noticed. They increase as φ over increases, which is counter-intuitive, as less vapor is proportionally found in rich mixtures than in lean ones. Nevertheless, this characteristic resembles what is observed for the fastest SP flames. According to Liang et al. [START_REF] Liang | Experimental and numerical studies on laminar premixed flames of ethanol-water-air mixtures[END_REF], the chemical kinetic effects of water addition over the single-phase laminar flame speed are very small compared to thermophysical effects, so the explanation must be found in the latter option.

The importance of the consideration of a multi-component (MC) approach to describe hydrophilic fuel droplets is clearly evident in Fig. 1. By comparing SC and MC cases in dry air, flame speeds with the MC approach are always faster than with the SC simplification. Deviations increase as φ over increases to approximately 10%. By considering the MC approach, the water formed during the combustion reaction is allowed to interact with the hydrophilic droplets 4 . Although a non-ideal VLE model is applied, droplet temperatures are bounded by the boiling point temperatures of individual components, i.e. T b,C 2 H 5 OH = 351.5 K and T b,H 2 O = 373.2 K. Hence, when droplets do not evaporate before reaching the reaction zone, a cold liquid structure interacts with the flame. When the MC approach is turned on, water formed in the combustion process is able to condensate on the droplet surface, releasing heat to heat up both gaseous and liquid phases.

Water condensation on droplets surfaces was predicted before starting this study, but such an impact on flame speeds was unexpected. These results are clearly novel, but not as intriguing as those seen in Fig. 1 for the MC approach in humid atmospheres. As observed for SP cases and those of two-phase flows using the SC approach, by adding humidity, the laminar flame speed decreases for the entire φ over span. In contrast, the inclusion of humidity when modeling droplets with an MC approach, the flame propagation becomes clearly faster as φ over increases. Flames are about 20% faster than those computed in dry air. In humid air, the differences are even larger between MC and SC, but what is more intriguing is the totally different behaviors when adding humidity: while humid air leads to slightly decreased flame speeds in the SC approach, there is a very strong increase in flame speed in the MC approach, with almost 20% faster flames.

To investigate these behaviors, Ethanol and water mass fractions profiles of the gaseous mixture are presented with the gas temperature of flames for φ over = 3.0 in Fig. 2. When focusing on the dry air scenario, the presented profiles are close to each other. Some deviations are easier to be noticed in the Y H 2 O profiles, in which the MC case depicts lower values of this quantity in the region where droplets penetrate into the oxidation zone (see Fig. 3). Such lower values indicate that water vapor formed by combustion reactions condensates on droplet surfaces if the MC description is enabled. The condensation is confirmed through the profiles of liquid mass fractions and the coupling source terms presented in Figs. 3 and4. Due to the exothermic characteristic of the condensation mechanism, the temperature of both gaseous and liquid phases increases. Although minimal, this can already be noticed in the gas temperature for the dry air scenario by comparing MC and SC cases, but it is clearly more pronounced in the humid air scenario. On the other hand, the increase of the droplet temperature is evident in Fig. 3 for both scenarios. Such a heat transfer caused by the condensation mechanism, which is consequently induced by the hydrophilic nature of the fuel, partially justifies the higher flame speed values indicated in Fig. 1 No differences in ethanol profiles are noticed at the pre-vaporization zone in Fig. 2 for dry air. This is expected since droplet and gas compositions are the same in this region. However, far into the reaction zone, ethanol emerges in both flames. Differences between both cases in dry air are justified by the late injection of the remaining ethanol by MC droplets (see S C 2 H 5 OH profile in Fig. 4), which do also penetrate farther into the flame (see Fig. 3).

When comparing both scenarios, deviations in humid air are much more evident than those of dry air. Except for Y C 2 H 5 OH and Y H 2 O profiles, the general behaviors seen for dry air are maintained for humid air. Both ethanol and water profiles change in the pre-vaporization zone between approaches because of the interaction of the hydrophilic droplets with the air humidity when en- abling the MC model. Accordingly, the ethanol mass fraction and gas and droplet temperatures reaching the flame are higher with the MC approach. In contrast, water mass fraction arriving at the reaction zone is lower with the MC approach. The most important phenomenon observed in Fig. 4 refers to the higher values of S C 2 H 5 OH in the reaction zone for the MC when compared with the SC approach for both dry and humid air. This shows that water condensation enhances ethanol evaporation, which can be justified by the droplet heat-up and droplet compositions change as depicted in Fig. 3. The intensification of the ethanol evaporation by enabling the MC approach occurs as soon as water starts to be formed in the flame, which coincides with the reaction zone. As a consequence, fuel is directly injected into the high reaction rates region, intensifying them and allowing for an increase in the flame propagation velocity. The alignment between ω C 2 H 5 OH and chemical heat release rate (HRR) profiles presented respectively in Figs. 4 and5 corroborates this rationale. Concerning the scenario with humid air, the HRR profile is slightly anticipated when compared with its counterpart for both flames computed with the MC approach. This occurs because of the higher mass fractions of ethanol reaching the flame front when water condensation occurs already in the pre-vaporization zone. So far, analyses are concentrated for a single value of the overall equivalence ratio, i.e. φ over = 3.0, since deviations among scenarios are more pronounced for rich mixtures. Nevertheless, such discussions are valid throughout the computed span of φ over . To demonstrate this, Figs. 6,7, and 8 present colormaps of selected quantities. Such colormaps were constructed with the computed flames in a grid defined by φ over and the spatial coordinate x.

| X L,k [-] T d [K] s [mm] d/d 0 T d X L,C 2 H 5 OH X L,H 2 O
ω C 2 H 5 OH ω H 2 O S C 2 H 5 OH S H 2 O
In Figs. 6 and 7 selected quantities from flames computed in both scenarios with dry air are presented and compared using deviation plots. To compute such deviations, the following expression is used ψ = ψψ ref , where ψ refers to the compared quantity and subscripts ref to a reference value, i.e. the quantity presented on the left in the colormap figures.

Gas and droplet temperatures and the mass fraction of water show a similar behavior previously noted in profile plots. As the values of φ over increase, droplet penetration increases, and the behavior noticed for gas and droplet temperatures at φ over = 3.0 is replicated. However, the evolution of Y H 2 O do not follow a regular shape throughout φ over . From results achieved for both SC and MC approaches, Y H 2 O profiles depict a monotonic behavior through x up to φ over ≈ 3.0. Around this value of φ over , the mass fraction of water reaches a maximum. But, for mixtures richer than φ over ≈ 3.0, the Y H 2 O reaches a maximum between 0mm and 10mm, then slowly decreases. This occurs due to the high penetration of the droplet into the oxidation zone and the late injection of fuel and absorption of water in MC cases, as noticed through the Y C 2 H 5 OH profiles in Fig. 8 5 .

The remaining key quantities used to justify the flame speed behavior in the different scenarios are presented in Fig. 7. The coupling source terms follow the trend noticed in the profile plots. Throughout the φ over no shape changes are noticed, but values are higher for cases computed with the MC approach. In contrast, the remaining source terms in Fig. 7 do not show such a regular behavior. From the leanest to the highest φ over , the negative peak values of ωC 2 H 5 OH regularly approach to the position 0.0 mm and become more intense. Such a behavior is maintained until φ over ≈ 2.5 is reached. For richer mixtures, a second one appears downstream of the first ωC 2 H 5 OH negative peak, indicating the decomposition of the later released ethanol by droplets into the oxidation zone. Despite this bimodal shape of ωC 2 H 5 OH through x, the HRR profiles become gradually more concentrated and intense as φ over becomes higher until the corresponding value of the maximum laminar flame speed is reached. The HRR slowly decreases for richer mixtures until the quenching point is reached. Altogether, the colormaps presented in Figs. 6 and7 attest the reasoning presented in terms of profile plots to justify the flame speed behavior noticed in Fig. 1 when including or neglecting the MC description of hydrophilic fuels.

This section is closed by discussing the colormaps of selected quantities that are more pertinent when the MC description is enabled, in Fig. 8. The impacts of considering air humidity are clearly noticed in Y C 2 H 5 OH in Fig. 8. As with profile plots, water in the fresh reactants intensifies the pre-vaporization of ethanol. This phenomenon increases with φ over , corroborating the justification given to the increase of the flame speed as the mixture becomes richer. Also, in Y C 2 H 5 OH colormaps, as the pre-vaporization increases, less ethanol is available in the droplets and the amount of ethanol released in the oxidation zone decreases. The corresponding change in droplet composition is reported in terms of the liquid molar fraction of fuel in the second row of Fig. 8. As a droplet moves through the flame, its composition changes from pure fuel to pure water. The presence of air humidity accelerates this process and, in this scenario, droplets interacting with flames have a higher amount of water. Further, droplets in humid air penetrate more into the oxidation zone than droplets in dry air, due to the lowers evaporation rate of water. Regarding X L,C 2 H 5 OH , the variation from lean to rich mixtures is obviously due to the increase in φ over . Very interestingly, we notice that the available ethanol at the flame location is increasing with φ over . It confirms that pre-vaporization is a first source of flame speed increase, as more gaseous fuel is immediately available to feed the flame.

Another important quantity to be tracked in MC scenarios is the coupling source term of water S H 2 O . By comparing humid and dry air scenarios, water starts to condense as soon as droplets are injected into a humid atmosphere. Since no water is available in the pre-vaporization zone with dry air, S H 2 O is zero in this region. However, the more intense values of S H 2 O occur in the reaction zone for both cases, which are focused in Fig. 8. This is more pronounced as φ over increases.

Analysis of hydrous ethanol

Following the investigation of pure hydrophilic fuel droplets interacting with flames, it is a natural choice to analyze how such an interaction evolves for multi-component droplets composed by the hydrophilic fuel and water. Throughout this section, droplets are composed of binary mixtures of ethanol and water, i.e. 92.5% of ethanol and 7.5% of water in mass, following the composition of hydrous ethanol with higher percentage of water specified in [START_REF] Anp | Resoluc ¸ão anp nº 907[END_REF].

Laminar flame speeds are presented in Fig. 9 against φ over , in humid and in dry air. In contrast to Fig. 1, the influence of mixing water with fuel in the liquid phase follows the expected trend: the hydrous ethanol delivers lower flame speed values than the corresponding cases of pure ethanol. However, the influence of air humidity follows the same trends previously noticed for pure ethanol. Figures 10 and 11 present profiles plots for φ over = 3.0 of the same quantities as in Sec. 3.1. In view of the quantities used to justify the flame speed, differences between cases computed with hydrous ethanol in dry and humid air are more pronounced for gaseous mass fractions, liquid molar fractions, reaction rates, and HRR. The intensification of the flame speed values from dry to humid air as seen in Fig. 9 for hydrous ethanol cases can be justified by the higher mass fraction of ethanol arriving at the flame front. The higher release of ethanol vapor into the reaction zone does occur, but is less pronounced than the pre-vaporization of ethanol before reaching the flame. Accordingly, it is expected that, by reducing the droplet injection distance, flame speed values computed in dry and humid atmospheres will approach each other. However, the minimal evaporation of fuel in the pre-vaporization zone and the higher release of fuel vapor straight into the reaction zone shall preserve higher flame speed values for cases computed in humid air.

The composition of the hydrous ethanol droplets, typical for commercial fuels in Brazil, might generate the so-called inversion problem, first documented in [START_REF] Filho | A new robust modeling strategy for multi-component droplet heat and mass transfer in general ambient conditions[END_REF] and where the less volatile component leaves the droplet first. Simulations conducted in [START_REF] Filho | A new robust modeling strategy for multi-component droplet heat and mass transfer in general ambient conditions[END_REF] are performed for single droplets in atmospheres with fixed or varying composition, not modified by the vapor released or collected by droplets. Within that context, it was possible to observe for binary droplets of alcohols and water that water completely left the droplet first. This phenomenon is suppressed by including minimal water vapor in the far-field gas. The required amount depends on the liquid composition, initial gas and liquid temperatures, and VLE and vapor pressure modeling approaches. In the present work and following the procedure applied in [START_REF] Filho | A new robust modeling strategy for multi-component droplet heat and mass transfer in general ambient conditions[END_REF] for a fixed far field gas composition and temperature of 298K at 101.325kPa, the inversion problem is suppressed for the chosen hydrous ethanol composition for a relative humidity higher than 1.5%, i.e. Y H 2 O = 0.0003. Here, the small amount of water released by droplets in the near field of the injection allows a value of Y H 2 O > 0.0003. As a result, the inversion problem is suppressed, and the evolution of X L,H 2 O presented in Figs. 10 and12 show that water is the last component remaining in both conditions dry and humid air. The results presented in Fig. 12 clearly indicate that penetration is farther into the flame for cases computed with humid air. This behavior agrees with the previously reported results for anhydrous ethanol. The water mass fraction and liquid molar fraction colormaps clearly point out that the interaction of droplets and the air humidity in the pre-vaporization zone are the main source of deviation between both scenarios. In humid air simulations, droplets arrive at the flames with more water. Consequently, the overall evaporation rate reduces, and droplets penetrate farther in the oxidation zone. The contour plots of the coupling source term S H 2 O point out the differences between both scenarios. As no humidity is present in the pre-vaporization zone of the dry air simulations, this term is slightly positive for x < 0.0. As droplets start to interact with the flame, strong condensation occurs, since S H 2 O < 0. A rapid inversion to an evaporation mode (S H 2 O > 0) follows as the right temperatures of the gas phase shift droplets temperature to a plateau (see Fig. 10), consequently indicating that both ethanol and water are leaving the droplets. For the colormaps of ωH 2 O and HRR, both depict similar behaviors. Values become more intense and concentrated with φ over in a straight zone from 0.0mm to 1.0mm. Although simulations with dry air allow a larger span of φ over , values of both ωH 2 O and HRR are predominantly more intense for the humid air case. In summary, the results presented in Fig. 8 corroborate the reasoning presented regarding profile plots to justify the higher flame speed achieved in humid rather than dry air.

Conclusions

Flames propagating in droplet mists were simulated with a detailed description of the chemistry and the diffusion transport for different hydrophilic fuel compositions to clearly pose the importance of considering the multi-component description of liquid fuels. Analyses systematically evolved from single to two-phase flows and from single to multi-component modeling approaches.

To rigorously account for the differential diffusion of vapor into the gas flow, the approach in [START_REF] Filho | On the interaction between turbulence and ethanol spray combustion using a dynamic wrinkling model coupled with tabulated chemistry[END_REF] has been applied. Novel and impactful findings have been obtained regarding flame speed, which were carefully justified throughout the manuscript. In addition, a novel justification was presented for the observed higher flame speed values of flames propagating in droplets mists when compared to single phase flames. The results show that the description of a hydrophilic liquid as a singlecomponent substance suppresses the description of important phenomena for reacting two-phase flows.

Results were first concentrated on simulations of flames propagating in sprays of pure hydrophilic fuel. Therein, intriguing findings were noticed. As soon as the multi-component approach is enabled, flame speeds become higher than those values achieved with the single-component approach. Even more intriguing was the inverse behavior of the flame speed values when computations were performed in humid air. Instead of being reduced, as for single phase or in mists with the single component approach, flames propagates faster by including multi-component phenomena. These phenomena could be properly justified by the detailed description of each species' heat and mass transfer mechanisms, as allowed by the chosen modeling strategy.

Then, investigations of flames propagating in droplet mists formed by binary mixtures of ethanol and water are conducted. Typically, behaviors noticed for pure ethanol droplets are reproduced for hydrous ethanol. Nevertheless, flame speeds are lower than those obtained with pure ethanol droplets given a specific atmosphere. Special attention has been paid to the occurrence of the so-called inversion problem, noticed in [START_REF] Filho | A new robust modeling strategy for multi-component droplet heat and mass transfer in general ambient conditions[END_REF]. However, the two-way coupling, included for the first time with the approach proposed in [START_REF] Filho | On the interaction between turbulence and ethanol spray combustion using a dynamic wrinkling model coupled with tabulated chemistry[END_REF], inhibits such a phenomenon for the simulated setups, as water vapor becomes present in the far field.

The present study is an important contribution to the technological development associated with using biofuels and sustainable aviation fuels (SAF). A special focus was given to ethanol due to its increasing usage for transportation. However, other alcohols, such as methanol, and ketones, are expected to demonstrate the same behavior because of their corresponding hydrophilic characteristic. Results indicate that air humidity does influence basic flame characteristics, which may support the development of strategies to control the combustion process better when using this kind of fuels. We highlight that the achieved results are not observed experimentally so far, as it is not a common practice to control air humidity in reacting flow investigations. Therefore, the achieved outcomes can be used as a motivation for subsequent experimental analyses.

-Linha V and Coordenac ¸ão de Aperfeic ¸oamento de Pessoal de Nível Superior -Brasil (CAPES) -Finance Code 001 are also acknowledge.

Appendix A. Explanation about faster flames encountered in spray combustion

Flames propagating in droplet mists show higher maximum values of the laminar flame speeds than flames in mixtures of gaseous reactants. This behavior occurs besides the higher absolute enthalpy of gaseous flames at similar overall equivalence ratios. This phenomenon was early noticed in experimental works (e.g. [START_REF] Hayashi | Propagation velocity and structure of flames in droplet-vapor-air mixtures[END_REF][START_REF] Nomura | An experimental study on flame propagation in lean fuel droplet-vapor-air mixtures by using microgravity conditions[END_REF]) and later reproduced numerically in one-dimensional flames described by detailed reaction mechanisms (e.g. [START_REF] Neophytou | Simulations of laminar flame propagation in droplet mists[END_REF][START_REF] Filho | Numerical analyses of laminar flames propagating in droplet mists using detailed and tabulated chemistry[END_REF]). Although many rationales were used to explain such high flame speeds in the literature, none seems sufficient to justify it.

Different mathematical expressions are available to estimate the laminar flame speed (s l ) of gaseous flames (e.g. [START_REF] Williams | Combustion Theory[END_REF][START_REF] Kuo | Principles of combustion[END_REF][START_REF] Poinsot | Theoretical and numerical Combustion[END_REF]). Kuehne et al. [START_REF] Kuehne | Analysis of sub-grid pdf of a progress variable approach using a hybrid les/tpdf method[END_REF] present an equation which allows the computation of the consumption speed (s c ) in terms of the source term of a reaction progress variable ωpv ,

s c ∝ ∞ -∞ ωpv dx, in which s l = s c -u u (A.1)
and u u refers to the unburnt gas velocity. Such an expression offers an advantage to analyze flames propagating in droplets mists, since according to the composition of the reaction progress variable (Y pv ), a phase coupling term can be avoided in its corresponding transport equation. As a result, a clearer connection between s l and the integral of ωpv is noticed when compared with other expressions based on the integral of the HRR and the reaction rates (e.g. summarized in [START_REF] Filho | Effects of reaction mechanisms and differential diffusion in oxy-fuel combustion including liquid water dilution[END_REF]), which accounts for coupling source terms. Results presented in With this aspect in mind, during the development of the present work, some analyses have been conducted about the evolution of the spray flames in terms of the local mixture fraction (Z) and the reaction progress variable employed in [START_REF] Filho | Investigations of evaporative cooling and turbulence flame interaction modeling in ethanol turbulent spray combustion using tabulated chemistry[END_REF]

, i.e. Y pv = Y CO 2 /M CO 2 + Y H 2 O /2.5M H 2 O + Y CO /1.5M CO .
In contrast to premixed gaseous flames, where only Y pv varies for a fixed Z, there is a simultaneous evolution of Z and Y pv in spray flames, due to the gradual release of vapor across the flame by droplets. This was previously discussed in [START_REF] Filho | Numerical analyses of laminar flames propagating in droplet mists using detailed and tabulated chemistry[END_REF] and is plotted in Fig. A.14 over a Flamelet Generated Manifold (FGM) colored by ωpv . To allow a better approximation of the reaction stages among spray flames and the FGM depicted in Fig. A.14, the considered spray flames in this section do no account for the evaporative cooling effects (see [START_REF] Filho | Numerical analyses of laminar flames propagating in droplet mists using detailed and tabulated chemistry[END_REF]), but are based on the SC approach and the diffusion transport is modeled by the unity Lewis number strategy by enforcing that Sc = Pr = 0.7. The FGM was constructed with premixed gaseous flamelets computed with the mechanism proposed in [START_REF] Marinov | A detailed chemical kinetic model for high temperature ethanol oxidation[END_REF] for φ ∈ [0.47, 1.97] following a similar strategy employed in [START_REF] Filho | On the interaction between turbulence and ethanol spray combustion using a dynamic wrinkling model coupled with tabulated chemistry[END_REF]. The same diffusion transport approach applied for the spray flames are used to compute the premixed gaseous flamelets. As shown in [START_REF] Filho | On the interaction between turbulence and ethanol spray combustion using a dynamic wrinkling model coupled with tabulated chemistry[END_REF], simulations conducted with, virtually, the same FGM table are able to recover the laminar flame speed of flames propagating in droplets By plotting the evolution of flames propagating in a droplet mists over a ωpv manifold on Z and Y pv , it turns out that, according to the vapor release rate across the flame, reaction paths are able to cross a broader region of high values of ωpv when compared to premixed gaseous flames. As droplets mass transfer rates presents larger time scales than combustion reactions (e.g. [START_REF] Myers | Flame propagation in heterogeneous mixtures of fuel drops and air[END_REF][START_REF] Franzelli | Characterizing spray flame-vortex interaction: A spray spectral diagram for extinction[END_REF][START_REF] Filho | A consistent artificially thickened flame approach for spray combustion using les and the fgm chemistry reduction method: Validation in lean partially pre-vaporized flames[END_REF]), it is possible to conclude that reaction paths do also stays longer in regions with high values of ωpv . The results presented in allow an increase of the reaction rate which consequently impacts on the prediction of the flame speed. On one hand, in terms of a valid progress variable, the fuel injection in the carrier phase by the coupling source terms allows further formation of combustion products at high reaction rates, which is revealed by the continuous and distributed values of ωpv throughout the flame. On the other hand, the interaction of droplets and flames adds fuel enthalpy throughout the reaction zone, allowing the enhancement of the heat release rate within the reaction zone. As a result, flame speed is intensified when compared to gaseous combustion. This observation is not restricted to flames neglecting the evaporative cooling and it is not specific to a diffusion transport model.

Figure 1 :

 1 Figure 1: Laminar flame speed by equivalence ratio of single phase (SP) and two-phase freely propagating flames for both humid and dry air. In all mists pure ethanol is injected. SC denotes single component and MC multi component droplet model.

Figure 2 :

 2 Figure 2: Evolution of the gas temperature and the mass fractions of ethanol and water. On the left: dry air; on the right: humid air. SC: black; MC: red.

Figure 3 :

 3 Figure 3: Evolution of the normalized droplet diameter, droplet temperature and the liquid mass fractions of ethanol and water. On the left: dry air; on the right: humid air. SC: black; MC: red.

Figure 4 :

 4 Figure 4: Evolution of reaction source terms ωk and coupling source terms S k for ethanol and water. On the left: dry air; on the right: humid air. SC: black; MC: red.

Figure 5 :

 5 Figure 5: Evolution of the heat release rate (HRR) and the chemical source term of ethanol ω C 2 H 5 OH . On the left: dry air; on the right: humid air. SC: black; MC: red.

Figure 6 :

 6 Figure 6: Colormaps of selected quantities of flames computed with the SC and the MC approaches in dry air. Left: SC; middle: MC; right: deviations between SC and MC approaches. Black line: penetration threshold; green line: droplet injection position; dashed line: penetration threshold for humid air in deviation plots.

Figure 7 :

 7 Figure 7: Colormaps of selected source terms of flames computed with the SC and the MC approaches in dry air. Left: SC; middle: MC; right: deviations between SC and MC approaches.

Figure 8 :

 8 Figure 8: Colormaps of selected quantities of flames computed with the MC approach in dry and humid air. Left: dry air; middle: humid air; right: deviations between flames in dry and humid air. Black line: penetration threshold; green line: droplet injection position; dashed line: penetration threshold for humid air in deviation plots.

Figure 9 :Figure 10 :

 910 Figure9: Laminar flame speed by equivalence ratio of single phase (SP) and two-phase freely propagating flames for both humid and dry air. In all mists the MC approach is applied.

Figure 11 :

 11 Figure 11: Evolution of selected source terms. Black: dry air; red: humid air.

Figure 12 :

 12 Figure 12: Colormaps of selected quantities of flames computed with hydrous ethanol in dry and humid air. Left: dry air; middle: humid air; right: deviations between flames in dry and humid air. Black line: penetration threshold; green line: droplet injection position; dashed line: penetration threshold for humid air in deviation plots.

  Fig. A.13 demonstrates that the proportionality presented for gaseous flames in Eq. A.1 does also hold for flames propagating in droplets mists. Specifically, results presented in Fig. A.13 do not coincide with the previous ones presented throughout this manuscript due to the diffusion transport model chosen for the analysis presented in this section, as explained in what follows.

Figure A. 13 :

 13 Figure A.13: Laminar flame speed and ∞ -∞ ωpv dx by equivalence ratio of single phase (SP) freely propagating flames and flames propagating in droplets mists with d 0 d = 25µm and d 0 d = 50µm. Gray: SP; black: d 0 d = 25µm; red: d 0 d = 50µm.

Figure A. 14 :

 14 Figure A.14: Flame paths ploted over a Flamelet Generated Manifold colored by ωpv . Black line refers to the fastest gaseous flame while magenta to flame propagating in droplet mists. Dashed line: d 0 d = 25µm and dotted line: d 0 d = 50µm.

  Fig. A.15 corroborates this rationale.

Figure A. 15 :

 15 Figure A.15: Development of ωpv and HRR throughout the spacial coordinate x for the three flames traced over the FGM in Fig. A.14. Gray: SP; black: d 0 d = 25µm; red: d 0 d = 50µm.

  .

		0.150 0.180					Y C 2 H 5 OH Y H 2 O T	1800 2100			0.150 0.180					Y C 2 H 5O H Y H 2O T	1800 2100
		0.120							1500			0.120					1500
	Y k [-]	0.090							1200	T [K]	Y k [-]	0.090					1200	T [K]
		0.060							900			0.060					900
		0.030							600			0.030					600
		0.000							300			0.000					300
		-2	0	2	4	6	8	10	12			-2	0	2	4	6	8	10	12
					s [mm]									s [mm]

In[START_REF] Santos | The general formulation of the energy equation and the impact of enthalpy diffusion on multi-component droplet heat and mass transfer[END_REF], it has been shown that this mode degenerates to the one of Abramzon and Sirignano[START_REF] Abramzon | Droplet vaporization model for spray combustion calculations[END_REF]. In this way, a single approach is sufficient to conduct simulations for both multi-and single-component scenarios.

The flame front position is where the gas temperature is increased by 200 K compared to the inlet temperature.

It must be remembered that the mixture's absolute enthalpy differs between SP and spray cases. The evaporating cooling induced by the spray has been shown to decrease the flame speed in[START_REF] Filho | Numerical analyses of laminar flames propagating in droplet mists using detailed and tabulated chemistry[END_REF], and this trend must be kept in mind in the comparison between gaseous and spray cases.

In the SC approach, the droplet composition is fixed to a single species.

Notice that colormaps of the MC computation in humid air are plotted in both Figs.

and 8.

Acknowledgements

We acknowledge the financial support from São Paulo Research Foundation (FAPESP -grant # 2021/14245-1). The support of Fundac ¸ão de Desenvolvimento da Pesquisa -Fundep, Rota 2030


Naomi Truan
email: n.a.l.truan@hum.leidenuniv.nl.

How and why choosing the wrong form of address may make you look like a boomer

Keywords:

, the V-form and the T-form become objectified, they also become metapragmatically linked to stereotypic personae. As this third-order index becomes visible, using the formal V-form Sie and engaging on a metapragmatic debate on its necessity on social media becomes indexed and re-enregistered with two interrelated yet distinct personae: the boomer and Karen.

Introduction

In T/V languages, address choice is a highly sensitive communicative choice. Even when nominal forms of address such as first names can easily be avoided, pronouns remain a topic of contention. The metapragmatic debate around the decision of the social media team of the Deutsche Bahn (DB), the German railway company, to address their customers with the informal pronoun of address du (T-form) on Twitter (now: X) 1 is illustrative of the tensions between two poles: "contesting the DB's decision, or endorsing it-but nothing in-between" (Truan 2022: 228).

To understand how such metapragmatic debates arise, let us unpack the two main stances regarding the use of T or V pronouns in German on social media: On the one hand, users in favor of the V-form foreground the commercial relationship, arguing that the interactions between a company and its customers, unknown adults, takes place in the V-form in standard German. In this line of reasoning, the hierarchies offline prevail over digital communicative norms. On the other hand, opting for the T-form is not merely constructed as a matter of personal preference, but as the only way to display appropriate behavior online. For users pro T-form, the move to the T-form is indeed regarded as complying with implicit communicative norms on social media [START_REF] Truan | When) Can I say Du to You? The metapragmatics of forms of address on German-Speaking Twitter[END_REF].

People who argue that using the T-form is unmarked thus do not merely adhere to what they believe is the widespread communicative norm on social media. Rather, users pro T-form also consider that using the T-form is an indicator of competence and, conversely, that sticking to the V-form indexes age (being old) and/or stiffness, thus forming the complex antithetic persona of the unfitted and/or pretentious Internet user-basically the boomer. Both these characteristics (inadequacy due to age and/or unnecessary formality) then merge into the negative figure of Günther, Jürgen, Norbert, or Birgit, who become stereotypical figures of the White, late-middle aged, rigid, old-fashioned stereotypical German and will be called 'boomer' or 'Karen' depending on the social and linguistic characteristics they exhibit. By contrast, users pro T-form build their online persona on appropriateness and thus register-based competence, but also on their ability to navigate complex-because heterogeneous, changing-settings, whereas the users insisting on the V-form are deemed inappropriate.

Beyond the phenomenon at stake here, the practices analyzed in this paper combine two sociolinguistic phenomena that have often been considered rather separately until now. It first draws on the pragmatics and sociolinguistics of forms of address, exemplifying empirically that communicative norms always need to be assessed for specific communities of practice. While this claim may not sound particularly original, social meaning-based approaches to the construction of Internet personae [START_REF] Agha | The social life of cultural value[END_REF][START_REF] Agha | Voice, Footing, Enregisterment[END_REF][START_REF] Bogetić | Metalinguistic comments in teenage personal blogs: Bringing youth voices to studies of youth, language and technology[END_REF][START_REF] Squires | Enregistering internet language[END_REF][START_REF] Ilbury | U Ok Hun?: The digital commodification of white woman style[END_REF][START_REF] Heyd | First names and sociolinguistic enregisterment: Digital tropes of linguistic mobility[END_REF] have not shown yet how the ideological link between address forms and typical personae works. In this regard, this paper makes a decisive contribution to both the literature on the metapragmatics of address forms and personae from a sociolinguistic perspective. I propose that address choice and its metapragmatics play a crucial role for the construction of characterological figures. Specifically, I show that through a process of enregisterment [START_REF] Agha | The social life of cultural value[END_REF][START_REF] Agha | Voice, Footing, Enregisterment[END_REF], address forms become metapragmatically linked to stereotypic personae.

The paper is structured as follows. I first briefly review the literature on address choice in German with a focus on pronouns (T/V forms) and social media. In order to understand how address choice may be linked with certain sociolinguistic personae, it is then necessary to present the concept of persona in sociolinguistics. Section 4 focuses on the corpus, showing how tweets following the announcement of the DB to address their customers informally have been selected. The data analysis is handled in Sections 5 and 6. The qualitative analysis focuses on how users pro T-form refer to users pro V-forms through two main strategies: (1) being on a firstname basis with the detractors, thus actively provoking users resisting the T-form; (2) calling the detractors 'boomers' or 'Karen', thus exhibiting digital competence while shutting down the discussion. Ultimately, I argue that the stereotypic personae of users not mastering digital norms relies on the re-enregisterment [START_REF] Watts | Language, the Singer and the Song: The Sociolinguistics of Folk Performance[END_REF] of the global figures of the boomer and Karen, and how they become locally interpreted in the German context.

Address choice in German

Address choice in German relies on the distinction between formal (V, from French vous) and informal (T, from French tu) pronominal forms to refer to the addressee(s). The opposition between those two sets of forms gives rise to three pronominal forms of address: 1) second person singular du (sg. T-form), which can be seen as the informal form of address to refer to a single individual;

2) second person plural ihr (pl. T-form), which is the informal form used to address a group of addressees that would be addressed as Du if they were singled out, but also within mixed groups (Hickey 2003: 409;Kretzenbacher 2010: 15); 3) third person plural Sie (pl. V-form), which is the honorific form of address to address either a single person or a group of people formally.

The distinction may be read as an opposition between "power and solidarity" [START_REF] Brown | The pronouns of power and solidarity[END_REF], but several authors have noted the "fuzzy boundaries in actual usage" (Bruns & Kranich 2021: 8) or "fuzzy edges" (Kretzenbacher 2011a: 71). Indeed, while the plural V-form Sie is considered to be unmarked between two adults who do not know each other, especially in professional contexts, many specific communities such as sports clubs, political parties, in particular the communist and socialist ones, smaller religious communities (Spillner 2014: 177), or students (Kretzenbacher 2010: 13), favor the singular T-form du.

More specifically, in the online context we are looking at in this paper, it has been shown that address choice is a highly disputed matter. Studies on the early days of the Internet have shown that the T-form du was usual (Kretzenbacher 2011b: 879; cited by Kretzenbacher & Schüpbach 2015: 37), and still remains "unmarked" between individual users (Kretzenbacher & Schüpbach 2015: 37). On the one hand, Kretzenbacher's (2005: 10-12) exploration of the German language websites of Ikea in Germany, Switzerland and Austria has shown that what is considered appropriate has more to do with reciprocal address rather than with specific forms.

On the other hand, [START_REF] Truan | When) Can I say Du to You? The metapragmatics of forms of address on German-Speaking Twitter[END_REF] investigation of the metapragmatic stances following the switch to the T-form du by the German railway company have been met with both indignation and indifference or agreement.

The overall picture is that German-speaking adults who have never met usually employ the plural V-form Sie for a first or work-related encounter, but that speakers may use or be open to the T-form du on social media. The picture becomes more complex from the moment on a brand (here, the German railway company Deutsche Bahn) offers a shift that may seem to align with the conventions on a specific platform (Twitter), while potentially disregarding that for some users, the customer-client relationship prevails. In those cases, the choice of an address form not only becomes an object of contention, but also a symbol of the persona of the user opting for the V-form or the T-form. To better grasp how address forms may index specific personae, I now turn to the notions of enregisterment, characterological figures, and personae on the Internet.

Enregisterment, characterological figures and personae on the Internet

The concept of enregisterment was first coined by Agha as (2003: 231) "processes through which a linguistic repertoire becomes differentiable within a language as a socially recognized register of forms". Drawing on the Bakhtinian concept of voice [START_REF] Bakhtin | The Dialogic Imagination. Four Essays[END_REF][START_REF] Bakhtin | Problems of Dostoevsky's Poetics[END_REF], Agha shows that specific ways of speaking (or utterances) index typical personae. The idea is that people may use different forms to signal different ways of being according to the context: Patterns that are seen as contrastive (differing between people) then index distinct personae (Agha 2005: 38).

Different ways of expressing things then become linked with "social types of persons, real or imagined" (Agha 2005: 38). As more and more people use specific linguistic forms while aligning with the persona that stand behind the use of these forms, a form may be seen as representative or typical of certain types of people and then becomes enregistered (Agha 2005: 57).

Going further, 'the Internet language' has become "differentiable within a language as a socially recognized register of forms" [START_REF] Agha | The social life of cultural value[END_REF]: 231), and, as Bogetić (2016: 249) underlines, "one that is ideologically linked to specific social personae, in this case youth". In other words, the ways we speak online tend to be homogenized as one way of speaking (or one register) that would be typical for how young people speak. But as the ways the youth expresses itself is often seen as deviating from the standard or deficient, the Internet language, as it is associated with the youth, also becomes subject to critique per extension.

Through a process of iconization (Irvine & Gal 2000: 37), linguistic features that index social groups or activities are perceived as a "social's group inherent nature or essence". Then, it not only the Internet discourse, but also its users, that are "characterized as 'uncareful,' 'sloppy' or 'irresponsible'" (Bogetić 2016: 249). While the popular metadiscourse on language and new technologies resort to 'classical' ideological frameworks such as standard ideology [START_REF] Milroy | Language ideologies and the consequences of standardization[END_REF]), concerns about the Internet language use also specifically involve the youth [START_REF] Thurlow | From Statistical Panic to Moral Panic: The Metadiscursive Construction and Popular Exaggeration of New Media Language in the Print Media[END_REF].

Interestingly, as I will show, metapragmatic comments about the use of certain address forms on Twitter are not only linked with a supposedly 'young' communicative behavior, thus showing that people resort to new indexical links when it comes to assess the appropriateness of address forms.

Another line of research focuses on the construction of personae online through a wide range of semiotic means. An example is the 'Hun', a British woman who uses variant spellings and specifically feminine discourse features whose taste and multimodal elements index workingclass despite her best attempts to travel, show she is enjoying her life, etc. (Ilbury 2022). Another example is 'Lisa aus Australien' (Lisa from Australia), a German girl in her early twenties who has spent time abroad and comments on her English language skills without noticing how her language proficiency ties up with tropes of social mobility and privilege [START_REF] Heyd | First names and sociolinguistic enregisterment: Digital tropes of linguistic mobility[END_REF]. Both personae exemplify how using specific linguistic forms become associated with stereotypical figures, and which crucial role names can play in the process, as they enable the (real or imagined) persona to become embodied and personified.

Similar processes are at work when users pro T refer to detractors as 'boomers' or 'Karen', yet little has been shown on the relationship between address forms and personae in social media yet. This is especially true when it comes to linking address forms to the indexical order, although precisely the T/V distinction was mentioned in [START_REF] Silverstein | Indexical order and the dialectics of sociolinguistic life[END_REF] liminal work.

One of Silverstein's arguments is that no single instance of T or V can index by itself a relationship of power or solidarity, as [START_REF] Brown | The pronouns of power and solidarity[END_REF] postulated. This kind of interpretation, which can be paraphrased as "the V-form is polite" or "the T-form is rude", resorts to a layperson's understanding of how linguistic forms work (Silverstein 2003: 208). For Silverstein (2003: 206), however, "[r]educing the problem to the psychological decision of a single individual to say 'T' or 'V' is, as we can see, already a highly ideologically positioned view of the matter". Thus, a first-order of indexicality equating the T-form with solidarity and, conversely, the V-form with power, offers only a very partial and inconclusive explanation of "whatever is going on here" (Silverstein 2003: 206). Rather, he pursues, we must look at how users metapragmatically imbue T/V forms with social meaning, thus moving from the first-order index to the second-order index that looks at how forms become noticed and commented on.

In this paper, I argue that address forms function as a first-order index, through which a linguistic form (T-form or V-form) indexes the persona of someone compliant to an unmarked, deferent way of addressing others (users of the V-form), or, on the contrary, of someone adhering to more relaxed Internet communicative norms (users of the T-form). When those usages become noticed and metapragmatically linked to one or the other persona, a second-order index is established-which is what happens when Twitter users comment on the reactions following the tweet from the Deutsche Bahn. Finally, when, through a process of enregisterment, the V-form and the T-form become objectified, they also become metapragmatically linked to stereotypic personae. As this third-order index becomes visible, the use of the V-form on social media becomes linked with boomers. This paper thus focuses on how Twitter users, and specifically those in favor or the T-form, metapragmatically take up the comments of the users pro V-form. In doing so, users pro T establish a third-order index that links the use of the V-form with the persona of the stereotypical boomer, while implicitly portraying the users of the T-form as the ideal (because competent) Internet user.

Data collection

In June 2020, the German's railway company Deutsche Bahn announced on Twitter that they would use the T-pronoun du for a three-month test phase. The public reactions were of two kinds: replies, which appear below the initial tweet of the DB and are visible by everyone scrolling down below the DB's tweet, and quoted tweets, that add a comment and show up in the users' timeline. Replies can furthermore be divided into two types: main replies, i.e. direct answers to the DB's initial tweet, and subreplies that are grouped by sub-conversations, for instance when users engage in a side interaction. As they cannot be analyzed content-wise, likes and retweets are not taken into account.

There were 290 main replies, 943 subreplies, and 143 quoted tweets. The 290 main replies and 143 quoted tweets had previously been coded according to their stance (pro T-form, pro V-form, unclear/unexpressed) by two research assistants and myself [START_REF] Truan | When) Can I say Du to You? The metapragmatics of forms of address on German-Speaking Twitter[END_REF]. I could show that the metapragmatic comments are in favor of the T-form in 61% of the cases and 67% of the expressed positions. In this study, particular attention is paid to the reactions of users pro T-form, in particular when they respond to users pro V-form who are scandalized by the DB's decision. The responses to particular users mostly come in form of subreplies, which had not been coded previously. For this paper, I am concentrating on the interactions between Twitter users rather on their exchange with the social media team of the Deutsche Bahn. I am conducting a qualitative analysis of selecting tweets. Indeed, the tweets are sarcastic or contextdependent (replying to a specific user), and coding needed to rely on too many subcategories to be conclusive. For instance, when replying to a user called Birgit, users may call her Birgit, birgit (with small caps), birgie, etc. Each pattern then amounts to only a few occurrences, which is quantitatively not particularly insightful. Instead, by looking at tweets as part of a longer thread (chain of tweets which follow one another), we come at a better understanding of how, for instance, 77 users react to Philip (also: Fipsi, Bro, Boomer), a journalist an author with a big Twitter account (39.4 followers as of October 2023) with similar discourse strategies (see (1) and following examples).

I have identified two main discursive strategies that users pro T-form put forward to ridicule their opponents: (1) ironically fostering a friendly rapport with those who oppose the Tform by using their first name or any variation of it without their consent; (2) referring to these detractors as 'boomers' or 'Karen' to assert digital proficiency while showing the impossibility to conduct a fruitful discussion. I now delve into the two strategies in sections 5 and 6, respectively.

Playing the competent language user, or how to provoke people resisting the informal you

The first strategy can be summed up as 'be on a first-name basis' with users who expressly requested not to be called by their first name. Here, users pro-T reverse the expectations of users who demand to be addressed with the V-form by forcing the use of their first name upon them.

A typical example is the chain of reactions after Philip's tweet:

(1) Wie wäre es, wenn die Bahn sich darauf konzentriert, dass -die Züge pünktlich fahren, -die Züge sauber sind, -die Preise halbwegs reell sind, statt die Kunden peinlicherweise zu duzen? Wir sind nicht per Du.

How about the railroad focusing on ensuring that -the trains run on time, -the trains are clean, -the fares are halfway decent, instead of embarrassing the customers by being on a first-name basis?

We are not on a first-name basis.

Philipp here addresses several consensual and recurring points of concern regarding the German railway company, which, however, conflate the offline and online worlds. The initial tweet of the Deutsche Bahn indeed did not aim at enforcing a generalized use of the T-pronoun Du in trains, but solely on Twitter. Linguistically, the users pro V-form are characterized by a standard use of orthography and punctuation. Consider how in (1), despite the enumeration in form of a list with bullets, Philip introduces commas at the end of each line. By contrast, users pro T-form employ linguistic features deemed typical for online communication:

(2) Heul heul schluchz schluchz sob sob

(3) dU bIsT jA kOmIsCH yOu aRe weird Example (2) exhibits a typical German form: two inflectives (or, as Freywald (2015: 908) argues, "uninflected verbs [which] actually [are] bare verb stems without the otherwise obligatory infinitive suffix -en") combined with reduplication to imitate boomer tears sarcastically and thus characterize their emotional reaction as illegitimate 2 . Although inflectional constructions should not be seen as instantiations of an 'Internet language' that, in fact, does not exist [START_REF] Dürscheid | Netzsprache -ein neuer Mythos[END_REF], they still seem to be used as a means to linguistically mark the mastering of digital norms.

In the same vein, the subreply 'yOu aRe weird' in (3) does not only comment on the reactions of 2 Freywald (2015: 936) argues that reduplication of uninflected verbs can be interpreted as durative while not involving intensification. It is difficult, based on a single example, to see whether it applies here, but my impression is that intensification is also present in this case, as the idea is that boomers are making a big fuss out of something completely normal and unmarked on social media. It may thus be argued that the (reduplicated) sobbing is both continuous and intense-thus triggering this parodic imitation. users pro V-form content-wise, but adds a stylistic twist to it through the use of alternating caps.

While alternating caps often are used as sarcastic devices3 , the utterance in (8) should be interpreted literally. The sarcastic dimension does not apply to the propositional content of the utterance 'you are weird', but to the whole situation which deserves, according to users pro-T, to be (dis)regarded with contempt.

Also consider the following reactions to Philip's tweet:

(4) Philip, locker bleiben! Ich weiß, Akademiker im fortschreitenden Alter gehören häufig zu der Gruppe Menschen, für die das Inet immernoch #Neuland ist, aber in soz. Netzwerken zu Siezen gilt im allgemeinen eher als Bruch mit der Etikette.

LG 😘 P.S. den Kritiken stimme ich zu! Philip, take it easy! I know, academics in advancing age often belong to the group of people for whom the Inet [Internet] is still #NewTerritory, but saying Sie [V-form] in soc. networks is generally considered rather as a break with etiquette. Cheers 😘 P.S. I agree with the critiques!

(5) Mein Gott, Fipsi, nimm doch endlich mal den Stock aus dem Arsch. For God's sake, Fipsi, take that stick out of your ass for once. boomer which index a certain generation (old-ish) and stiffness ("take it easy!", "take that stick out of your ass for once"). Whether boomer and Karen actually are (fictive) forms of address in ( 7) may be debated, as we may argue that these utterances work as prefabricated units of speech where the vocatives become imbued with a larger meaning related to the pattern ok + boomer/Karen (often without punctuation mark at the end) (see next section).

What holds true for the forms of address, however, is that they all undermine the straightforward request "We are not on a first-name basis" by jokingly twisting the user's desired V-reciprocity. Because Twitter interactions do not happen only between both interlocutors, however, but in front of an "imagined audience" [START_REF] Marwick | I tweet honestly, I tweet passionately: Twitter users, context collapse, and the imagined audience[END_REF] of known mutuals and unknown people, we may see these tweets as directed at the other users as well in order to perform 'digital nativeness' and a witty spirit for anyone following the exchange. The ironic use of Diggah or Bro as in ( 6) is even more salient in this subreply, which combines the rejected form of address with a formal one and a heart as a sign of closeness:

( 4)-( 7), thus showing that the point is not so much to answer to Philip, but to demonstrate how inadequate him sticking to the V-form is on social media. Most reactions revolve around very few users who become the targets of a small-scale shitstorm-thus the concentration on very few first names such as Günther or Birgit, who match real Twitter profiles. Shitstorms, also known as online firestorms, have been defined as "the sudden discharge of large quantities of messages containing negative word-of-mouth and complaint behavior against a person, company, or group in social media networks" (Pfeffer, Zorbach & Carley 2014: 118). Although the parodic or ironic comments analyzed here do not pertain to online aggression, they do create, as a repeated measure by several single users targeting the same person, a community of practice against the individual person being scrutinized.

In conclusion, the presented examples illustrate four distinct strategies employed to address Twitter users exhibiting a pro-V inclination, involving the use of real names, diminutive forms, informal addresses, and variations around phrases like Ok boomer, which we will now turn to. These strategies, while ostensibly humorous, collectively subvert the straightforward request for a formal address, thus highlighting the inadequacy of adhering to the V-form on social media.

These observations shed light on the complex dynamics of online discourse and the ways in which humor and linguistic choices are leveraged to navigate social media interactions while apparently inadvertently piling up the key features of the stereotypic persona of the boomer. We will now consider what exactly being a boomer online entails.

6. "Ok, Boomer" and "Ok, Karen": The V-form as an index for old-fashioned and

entitled language users

Illuminating for our study is how the user's metapragmatic assessment of forms of address becomes attributed to a characterological figure with socio-economic characteristics that do not match the reality. In the friendly yet ironical message in (4), Philip is indirectly portrayed as the boomer-combining a generational gap making him unaware of social media norms with an academic background.

As he is deemed to be of one those "academics in advancing age", Philip combines two main characteristics: belonging to a certain social class (having an academic background, i.e.

having studied) and belonging to an older generation. While the stiffness of academics may be a

German cliché (see the discussion around doctor titles in Truan 2022: 236), the age typically hints to the boomer, the afterwar generation born between 1946 and 1964. But… Philip is not a real boomer. As the big accounts concentrating most subreplies are the ones of public figures, it is quite easy to retrace their birth year: Philip, journalist and author, was born in 1979, and Birgit, author as well, in 1975. So, maybe unsurprisingly, none of them are actually boomers. We may hypothesize that the users calling them boomers mistakenly thought they were older, but this is in fact a relatively unplausible explanation. Rather, we see how boomer functions as an identity label ascribed by others. [START_REF] Scheff | Being Mentally Ill: A Sociological Study[END_REF], cited in Lisboa & Spink (2016: 228), suggests that explicit labels are attached to acts that are seen as norm violations, such as terms like 'drunk' or 'drug addict'. This also applies to implicit or unnamed norms known as residual norms, which are not designated with specific labels. I propose that the answer ok boomer is an attempt at labelling the person using the 'wrong' norms on social media by insisting on transposing address behavior from their offline practices. Described as "the symbol of a generational war" (Lim & Lemanski 2020: 1), it has become a way to cut people off in conversation through the ironic sense of agreement ok seems to convey4 .

In the heated debate on T/V forms of address, the boomer does not activate, or not only, the representation of an old-ish person. More so, the idea is that this person does not master the unwritten social norms on the Internet, with age being a possible explanation factor (they grew up with no contact to social media, thus (still) do not know how things go 'over there'). The characterological figure of the boomer is imbued with a sense of inadequacy and inappropriateness more than with an age-related variable. Because they refuse to adjust to social media norms promoting the use of the T-form, Philip and Birgit, despite their actual date of birth, become symbols of inappropriateness. By labeling the boomer and not the language use per se, social media users demonstrate the importance of forms of address in displaying social competence.

Next to the now phraseological unit ok boomer, Karen is also present in the data. Similar to the boomers, users would not call themselves Karen-it is an "attributed identity" (Garcés-Conejos Blitvich 2022: 16) that is not "enregistered" [START_REF] Agha | The social life of cultural value[END_REF][START_REF] Agha | Voice, Footing, Enregisterment[END_REF] prior to interaction. This means that the traits typical for the figure of Karen become salient as the Twitter conversational thread unfolds. The figures of the boomer and the one of Karen, respectively, point out to interrelated personae, but they do not fully overlap. Despite the limited number of tweets, the data shows a clear gender divide: Users with male names such as Philip,

Günther and Malte are being called boomers, while Birgit is being referred to as Karen. This matches previous findings, as Karen is used as a label for women in 84% of the analyzed incidents in Garcés-Conejos Blitvich (2022: 27). Karen is "stereotypically middle-aged and white" (Garcés-Conejos Blitvich 2022: 14). Thus, in the general perception, she is younger than boomers, and a perceived ethnicity comes into the picture as well. Crucial for both figures, however, is a "sense of entitlement" (Garcés-Conejos Blitvich 2022: 16) that becomes obvious only once the person performing the condemned reaction is publicly being labeled Karen.

Interestingly, one of the most salient features of Karen, her "perceived racism" (Garcés-Conejos Blitvich 2022: 27), is irrelevant for the discussion on T/V forms in German. Similarly, Karen as "the type of person to go over someone's head and resolve conflict by invoking some higher authority e.g. store managers or the police" (Kosse 2021: 7) also plays no role in the German indexical field [START_REF] Eckert | Variation and the indexical field[END_REF]) around forms of address: There is no "higher authority" users pro-V could appeal to. Moreover, as users pro V-form argue, the negotiation of forms of address is situated and specific to the interaction: It cannot indistinctly be applied to all participants. What then, constitutes the core of Karen's persona, the one that becomes reenacted in the German context?

The (real) Birgit users react to is well-known for her traditional, anti-feminist, and transphobic positions. While her political positioning may explain or contribute to conservative language ideologies, racism does not play a role in her unwillingness to transition to more informal forms of address with a customer service on social media. The formula ok Karen here works as a case of "re-enregisterment", "in which a register begins to generate new and possibly very different social stereotypes" (Watts & Morrissey 2019: 278). By conflating the personae of the boomer and Karen, we reduce them to their smallest common denominator: inadequacy and entitlement. The trope of digital gap due to the inadaptation of the boomer generation is relegated into the background, while the summative value of ok gets reinstantiated in a new context. In both cases, the comment marks the final reaction and aims at shutting off the discussion, while pretending to agree. Not quite coincidentally, the ironical dimension of ok also contributes to the anti-figure of the boomer and Karen: the opposite types-those who know how to behave and use T-forms on Twitter-are funny, subtle, relaxed.

Altogether, the personae of the boomer and Karen have lost their central characteristics in the German discourse: They neither refer to old persons, nor to racist ones, either fictively or in reality. Rather, the formulaic expression ok + first name or person-referring noun works as a reference to digital culture to reinforce the trope of users pro T-forms being digitally competent.

In turn, the digital competence of opponents to Philip, Birgit, and similar users, is threefold: 1)

They use the 'right' form of address; 2) They use linguistic forms common on social media; 3) They point to tropes of digital culture known internationally, while allowing for their "reenregisterment" [START_REF] Watts | Language, the Singer and the Song: The Sociolinguistics of Folk Performance[END_REF] in the German local context.

Conclusion

The analysis demonstrates that the use of a specific address form on social media has become enregistered. Specifically, this study concentrated on the metapragmatic appropriation by Twitter Using the V-form then becomes metapragmatically associated with the sense of entitlement and inadequacy-the common denominator reuniting users pro V-form regardless of their generation, gender, and ethnicity.

The role played by forms of address and their metapragmatic evaluation in enacting stereotypical personae is crucial. Here, we see clearly that using a form of address deemed inappropriate has far-reaching consequences: The users resisting change are mocked publicly, consistently, and become the embodied representation of well-known fictive characterological figures. The conflation of the personae of the boomers and Karen is particularly illuminating of how digital tropes [START_REF] Heyd | First names and sociolinguistic enregisterment: Digital tropes of linguistic mobility[END_REF]) become re-instantiated for a local, particular debate. Altogether, the metapragmatic debate on the use of T/V forms in German is an excellent symbol of how apparently global norms prevailing on social media as well as widely shared cultural references find their way in specific communities of practice through a local twist.

( 6 )

 6 Diggah das ist Twitter und keine verfickte Bewerbung. Diggah this is Twitter and not a fucking job application. (7) a. Ok boomer b. Ok Karen Here again, the user pro T-form in (4) demonstrates digital competence through a wide range of linguistic features: abbreviations (Inet for 'Internet' or soz. for 'sozial', LG for 'Liebe Grüße', translated as 'Cheers'), hashtags (#Neuland), and emojis. The examples moreover showcase four ways of addressing the users pro-V: (1) using the person's real name based on their Twitter handle or profile (Philip); (2) using a diminutive, colloquial form of that first name (Fipsi); (3) using a very informal, generic form of address such as Diggah or Bro; (4) variations around Ok

  users, particularly those advocating for the T-form, of comments made by proponents of the Vform. In this process, proponents of the T-form establish a third-order index that connects the usage of the V-form with the persona of the stereotypical boomer, implicitly presenting users of the T-form as the epitome of Internet proficiency due to their competence. Twitter users pro Vform are constructed as inadequate, entitled, and conservative social media users. Digital competency is linguistically marked with a T-form despite nonreciprocity. Precisely because users pro V-form explicitly express their discomfort in being called on a first-name basis, they get reactions purposely violating what they express being comfortable with. Social media users get ascribed 'boomer features' between the lines, as (self-described) competent users display linguistic features typical for the digital world.Ultimately, as the V-form and T-form undergo enregisterment[START_REF] Agha | The social life of cultural value[END_REF][START_REF] Agha | Voice, Footing, Enregisterment[END_REF], a process that results in the objectification of the users pro T-or V-form, they concurrently acquire metapragmatic associations with stereotypical personae. The manifestation of this thirdorder index becomes evident when the utilization of the V-form on social media platforms becomes associated with individuals categorized as boomers. With explicit metapragmatic assessments such as ok boomer or ok Karen, the embodiment of characterological figures goes a step further. Through re-enregisterment[START_REF] Watts | Language, the Singer and the Song: The Sociolinguistics of Folk Performance[END_REF], typical characteristics of boomers or Karen such as age and race are downplayed while others become foregrounded.

  8) Ach bro oder eher gesagt Herr Werwolf, wenn du Probleme an der Arbeit und Co. hast, stehe ich dir immer für ein Gespräch zur Verfügung <3

	Oh bro, or rather Mr. Werewolf, if you [T-form] have problems at work and the like, I'm
	always available for a chat <3
	Interestingly enough, Wulf or Mr. Werwolf belongs to the very few users who received
	much attention, together with Philip or Birgit, who are both big accounts on Twitter (39.6K and
	73.1K followers, respectively, as of November 2023). Philip alone gets 77 subreplies pertaining
	to the same genre as (

See for instance how the user-generated Urban Dictionary explains the phrase: "The texting way of being sarcastic." (https://www.urbandictionary.com/define.php?term=aLtErNaTiNg%20CaPs,, accessed on 8 November 2023).

See again the Urban Dictionary: "When a baby boomer says some dumb shit and you can't even begin to explain why he's wrong because that would be deconstructing decades of misinformation and ignorance so you just brush it off and say okay." (https://www.urbandictionary.com/define.php?term=Ok%20boomer, accessed on 8 November 2023).