Gauthier Berthomieu
email: gauthier.berthomieu@univ-brest.fr

Vincent Koehl

Mathieu Paquier

Directional Loudness of Low-Frequency Noises Actually Presented Over Loudspeakers And Virtually Presented Over Headphones *

Previous studies have revealed that the loudness of low-frequency pure tones increased with the interaural time difference (ITD). This effect accounts for the directional loudness phenomenon at low frequencies, where ITD is the main localization cue. So far, this effect has only been studied for sounds generated and presented directly over headphones, which are not natural listening conditions. The present study aims at investigating this effect on lowfrequency noises stemming from real sources. Twenty subjects assessed the loudness of stimuli that were actually displayed by loudspeakers arranged at various locations within a listening room or that were recorded with a dummy head and virtually reproduced through headphones. Results show that the directional loudness sensitivity (DLS) is in agreement with the previously revealed ITD effect. Moreover, the DLS was higher when stimuli were reproduced over headphones than over loudspeakers, specifically when frontal sources were located at a short distance from the listeners. One hypothesis on this effect relies on visual cues that were available to the listeners only when sounds were reproduced over loudspeakers, providing information about the source distance. Listeners were also aware that sounds were reproduced on loudspeaker or headphones, possibly involving different loudness processings, leading to DLS differences.

INTRODUCTION

Effect of direction and ITD on loudness

The direction of a sound source in relation to the listener affects significantly the loudness of the sounds it produces, especially in the horizontal plane [START_REF] Robinson | The loudness of sound fields[END_REF][START_REF] Sivonen | Directional loudness in an anechoic sound field, head-related transfer functions, and binaural summation[END_REF][START_REF] Sivonen | Directional loudness and binaural summation for wideband and reverberant sounds[END_REF][START_REF] Sivonen | Binaural loudness for artificial-head measurements in directional sound fields[END_REF]. There is growing awareness that this phenomenon, called directional loudness, has to be taken into account for audio reproduction systems, especially for multichannel ones [START_REF] Zacharov | Auditory periphery, HRTF's and directional loudness perception[END_REF][START_REF] Dash | Multichannel Loudness Listening Test[END_REF]. This phenomenon is largely accounted for by at-ear pressures, that are highly dependent on the position of the source with respect to the listener. More precisely, the filtering applied by the head, torso and ears of the listener on a sound that reaches his/her ears depends on the direction from which the sound comes [START_REF] Zacharov | Auditory periphery, HRTF's and directional loudness perception[END_REF]. This filtering leads to a variation of the at-ear sound pressure level, which is the main factor involved in the loudness sensation. Consequently, directional loudness was mainly expected to occur for high-frequency stimuli, since the filtering effect of the body is rather small for low frequencies [START_REF] Moore | Space perception[END_REF]. Nevertheless, directional loudness has been observed for low-frequency narrow-band noises [START_REF] Sivonen | Directional loudness in an anechoic sound field, head-related transfer functions, and binaural summation[END_REF]. Furthermore, binaural loudness models that take at-ear pressures as input tend to underestimate directional loudness effect in comparison with experimental data [START_REF] Moore | A loudness model for time-varying sounds incorporating binaural inhibition[END_REF][START_REF] Sivonen | Directional loudness in an anechoic sound field, head-related transfer functions, and binaural summation[END_REF]. These observations suggested that at-ear sound pressure modifications could not fully explain the directional loudness phenomenon, especially for low-frequency stimuli.

This assumption was confirmed by previous studies that highlighted an effect of the interaural time difference (ITD) on the loudness of pure tones. A small but significant loudness increase (+1.5 dB) was reported for low-frequency (200 and 400 Hz), low-level (40 phon) pure tones whose ITD reached 772 µs [START_REF] Koehl | Loudness of low-frequency pure tones lateralized by interaural time differences[END_REF]. This ITD value corresponded to a 90 • incidence angle according to Kuhn's low-frequency model [START_REF] Kuhn | Model for the interaural time differences in the azimuthal plane[END_REF]. The loudness increase proved to be caused by the ITD itself rather than by the related localization. This was observed by estimating the loudness of sounds with a fixed ITD whose induced localization was counterbalanced thanks to an Interaural Level Difference (ILD, which is the second binaural localization cue) leading to the opposite ear [START_REF] Koehl | Effects of interaural differences on the loudness of low-frequency pure tones[END_REF]. Another previous experiment focused on the evolution of this effect as a function of the level of the stimulus [START_REF] Berthomieu | Influence of interaural time differences on loudness for low-frequency pure tones at varying signal and noise levels[END_REF]. ITD was reported to significantly enhance (between 1.5 dB and 2 dB) the loudness of pure tones whose loudness level was up to 40 phon at 100 Hz and up to 50 phon at 200 Hz. These results indicate that ITD is involved in the binaural loudness process. In order to control the ITD in these experiments, sounds were presented in an audiometric booth and reproduced over headphones with a fixed ITD applied between the two channels, which constitutes a rather unecological sound presentation.

Effect of ecological validity on loudness

According to Epstein and Florentine [START_REF] Epstein | Binaural loudness summation for speech and tones presented via earphones and loudspeakers[END_REF][START_REF] Epstein | Binaural loudness summation for speech presented via earphones and loudspeaker with and without visual cues[END_REF], the ecological validity of an experiment is likely to affect the binaural loudness summation and should be taken into account in loudness research. This was concluded from results regarding the binaural-to-monaural loudness ratio which is the loudness growth observed when a sound is presented at the two ears compared to at one ear only. Such a comparison can be conveniently achieved by feeding either one channel or two channels of headphones. Assuming that a monaural listening situation was not ecologically valid to the listeners, Epstein and Florentine assessed the binauralto-monaural ratio for speech stimuli displayed whether on loudspeakers, whether on headphones [START_REF] Epstein | Binaural loudness summation for speech and tones presented via earphones and loudspeakers[END_REF], with or without visual cues [START_REF] Epstein | Binaural loudness summation for speech presented via earphones and loudspeaker with and without visual cues[END_REF]. They reported that the binaural-tomonaural loudness ratio decreased as the ecological validity of the presentation increased (that is for loudspeakerreproduced stimuli displayed with visual cues). Although binaural-to-monaural ratio is not directly related to directional loudness, they are both involved in binaural loudness summation and one could wonder if ecological validity could have an effect on directional loudness. Furthermore, Sivonen reported that reverberant sounds yielded to smaller directional loudness effects than anechoic ones [START_REF] Sivonen | Directional loudness and binaural summation for wideband and reverberant sounds[END_REF]. Thus, the room effect is also likely to decrease the directional effects observed in an anechoic chamber.

These findings about binaural and directional loudness both suggest that effects observed under rather unecological conditions could be reduced in more realistic situations. Since the previous results about the effect of ITD on loudness were obtained with pure tones directly generated and displayed over headphones, one may wonder whether the loudness increase reported for headphone-generated stimuli lateralized with the sole ITD still holds under more realistic conditions, namely for real sources located in a room. Besides, stimuli directly synthesized over headphones are often perceived "within the head" rather than coming from a distant source [START_REF] Blauert | Distance hearing and inside-the-head locatedness[END_REF], which could constitute an additional source of disparity between these laboratory presentation conditions and natural ones.

Aim of the present study

The present study has been designed in order to investigate the directional loudness effects for low-frequency noises stemming from loudspeakers located around the subject in a listening room. Contrarily to the previous results about the ITD effect, such stimuli were emitted by real sources in a room that was not anechoic. The stimuli were presented to the listeners by either actually reproducing them over loudspeakers or by virtually reproducing them over headphones, in order to study the influence of the presentation conditions. One should note that reproducing the stimuli either over loudspeakers or headphones is not likely to modify the directional effects as long as visual cues are available to the subjects. According to Sivonen et al., the directional loudness sensitivity of narrow-band noises was the same whether they were directly reproduced through visible loudspeakers located all around the subject in an anechoic room [START_REF] Sivonen | Directional loudness in an anechoic sound field, head-related transfer functions, and binaural summation[END_REF] or reproduced at the same positions with headphones by using individual HRTFs [START_REF] Sivonen | Effect of direction on loudness in individual binaural synthesis[END_REF]. The latter experiment took place in the same anechoic chamber and the loudspeakers were still mounted in the tested directions even if sounds were reproduced over headphones to improve the plausibility of the binaural synthesis. In this specific case, it might not have been possible to distinguish between two identical sounds that were played back over loudspeakers or headphones [START_REF] Langendijk | Fidelity of three-dimensional-sound reproduction using a virtual auditory display[END_REF]. However, in most laboratory experiments, binaural stimuli (whether recorded or synthesized) are not presented with visual representations of the sound sources. This also applies to the present study as no loudspeaker was mounted in the directions under study when sounds were reproduced over headphones. Thus, the presentation conditions under investigation differed not only because of the reproduction system itself (loudspeakers or headphones) but also because of the information they provided about the sound sources, such as visual information.

The effects of direction on loudness were assessed in terms of Directional Loudness Sensitivity (DLS) by comparing directional stimuli to frontal references. As the room effect is likely to alter the directional loudness [START_REF] Sivonen | Directional loudness and binaural summation for wideband and reverberant sounds[END_REF] and as the position of a sound source is likely to evoke a specific room response, several spatial configurations of the sound sources in the listening room were tested so that the observed effects would not be caused by a specific loudspeaker layout within the room. The DLS was also assessed for headphone-reproduced stimuli lateralized with the sole ITD for comparison with previous studies.

Material and methods

The effect of direction on loudness (or DLS) was investigated by matching low-frequency noises emitted by lateral sources with frontal references. Two different presentation conditions were under study: one where sounds were actually played back over loudspeakers and one where these sounds were first binaurally recorded and then virtually reproduced through headphones. For the low-frequency noise under test, the room effect may vary with the source position and thus affect the directional loudness [START_REF] Sivonen | Directional loudness and binaural summation for wideband and reverberant sounds[END_REF]. The DLS was then investigated for four different spatial configurations of the sound sources enabling to elicit and take into account different room responses.

Stimulus

The stimulus that was investigated in this experiment was a narrow-band noise, which bandwidth was set to one Equivalent Rectangular Bandwidth (ERB) so that all the spectral components of this noise were contained in one PAPERS DIRECTIONAL LOUDNESS OF LOW-FREQUENCY NOISES critical band. The center frequency of the noise was 265 Hz since previous experiments reported a predominant effect of ITD on loudness between 200 and 400 Hz [START_REF] Koehl | Loudness of low-frequency pure tones lateralized by interaural time differences[END_REF][START_REF] Berthomieu | Influence of interaural time differences on loudness for low-frequency pure tones at varying signal and noise levels[END_REF]. The ERB was computed according to the following equation by Glasberg and Moore [START_REF] Glasberg | Derivation of auditory filter shapes from notched-noise data[END_REF]:

ERB N = 24.7 × (4.37F + 1) (1)
where F = 0.265 kHz is the center frequency of the ERB. This equation led to a 53-Hz wide ERB. The narrow-band noise was generated according to the procedure described by Edmonds and Culling [START_REF] Edmonds | Interaural correlation and the binaural summation of loudness[END_REF]. The reference level was fixed at 50 phon [START_REF] Berthomieu | Influence of interaural time differences on loudness for low-frequency pure tones at varying signal and noise levels[END_REF] (corresponding to 58.4 dB SPL at 265 Hz according to the ISO 226 standard [START_REF]Acoustics -Normal equal-loudnesslevel contours[END_REF]) at the center of the head of the subject in his/her absence. The duration of each stimulus was 1.6 s, smoothed by onset and offset ramps of 100 ms.

Procedure

Twenty subjects aged from 20 to 25 years took part in the experiment and were payed for their participation. Their hearing thresholds were measured for the noise investigated in this experiment using a standard procedure [START_REF]Methods for manual pure-tone threshold audiometry[END_REF] and had to be ≤ 10 dB HL to go on with the experiment. None of them had experience in laboratory listening tests.

Points of Subjective Equality (PSE, corresponding to the level at which a sound is perceived as loud as a reference sound) were obtained using a two-interval, twoalternative, forced choice paradigm (2I2AFC), following a 1-up 1-down rule [START_REF] Levitt | Transformed updown methods in psychoacoustics[END_REF]. In each trial, a test sound and a reference sound were presented in random order, separated by a 500 ms pause. The test sound was presented by a lateral source (azimuth of -90 • or +90 • ) and the reference sound was presented by a frontal source (0 • ). The task was to indicate whether the first or the second sound was louder, with no other possible option and independently of any other perceived difference. The software was developed and executed on MAXMSP and subjects responded using two buttons on a gamepad. These instructions were indicated orally and a few trials were presented before the beginning of the test in order to familiarize the subjects with the interface and procedure.

The test sounds were initially presented at a level randomly set 10 dB above or below the reference sound level. After the subject's response, their level was lowered by a given amount if the subject judged it was louder than the reference sound, whereas it was increased by a certain amount if the subject judged the reference sound was louder. The step size was initially set to ±4 dB and changed to ±1 dB after two reversals in the equalization curve (i.e. when the loudness judgment of the subject changed from one trial to another for the same test sound). A total of eight reversals were collected for each test sound. Then, PSEs were derived from the means of the test sound levels at the six last reversals, relative to the reference sound level. The experiment was split in two sessions, with a 5 min break between them. Each of these sessions consisted of the same task, but under different presentation conditions: one where sounds were actually played back over loudspeakers and one where sounds were virtually reproduced over headphones. Each subject participated in the two sessions in a random order.

Actual presentation

The experiment took place in a sound-attenuated listening room, which had been designed so that its RT60 was 0.3 s at 250 Hz [START_REF]Measurement of room acoustic parameters -Reverberation time in ordinary rooms[END_REF], in compliance with the IEC 60268-13 standard [24] concerning room characteristics for listening tests on loudspeakers. Four loudspeakers were placed at various locations within the room (see Fig. 1) to reproduce both reference and test sounds. As shown in Fig 2, this setup enabled to arrange frontal and lateral loudspeakers in four different spatial configurations within the room to differently elicit its response. In one given configuration, the frontal (0 • ) loudspeaker playing reference sounds, denoted R, was located at either 1 or 2 m from the listening point whereas both distances could be allocated to the lateral loudspeakers (-90 • or +90 • ) playing test sounds, denoted T. The subject sat in a chair that was placed in the room so that the center of his/her head corresponded to the listening point depicted by the dot in Fig. 1. The subject's head was precisely positioned using a headrest and a chin rest and it remained fixed during the procedure. Each spatial configuration was achieved by pointing the subject towards one of the four loudspeakers. The experiment was subsequently divided into four sub-sessions, with respect to the four spatial configurations under test. The sub-session order was randomly chosen for each subject. Each sub-session lasted between 5 and 10 min and subjects were allowed to stand up from the chair between each sub-session. The headrest and the chin rest were maintained in a fixed position during the whole session so that the subject's head could be precisely positioned in the same position at the beginning of each sub-session. Sounds were generated using a RME Fireface 800 sound card and reproduced through Amadeus PMX 4 loudspeakers, powered by Audac DPA154 amplifiers. The four loudspeakers were calibrated so that they produced a loudness level of 50 phon at the center of the head of the subject in his/her absence. In other words, they delivered 58.4 dB SPL [START_REF]Acoustics -Normal equal-loudnesslevel contours[END_REF] at the listening point whatever their location within the room.

Virtual presentation

The stimuli that were presented to the listeners through the actual sources were recorded in order to be played back through headphones in these presentation conditions. In order to provide the listener with the same acoustic stimuli with headphones as with loudspeakers, binaural recordings were carried out. At the frequency range under test, inter-individual variations of head size and shape cause small differences of at-ear pressures and arrival times [25] that are even smaller than the just noticeable differences [26]. Thus, the recordings were carried out with a dummy head (Neumann KU100) that enabled an accurate recording of the sounds at the entrance of the (blocked) ear canal. The dummy head was precisely arranged at the position of a subject's head during the actual presentation (see Fig. 3) and was calibrated by using a Brüel & Kjaer Type 4231 sound calibrator at 1 kHz. Thus, twelve stimuli were recorded this way corresponding to each of the three azimuths (-90 • , 0 • and 90 • ) in each of the four spatial configurations (Fig. 2).

The stimuli were presented over Sennheiser HD650 headphones (circumaural, open). The output level of the system was adjusted by placing the headphones on the calibrated dummy head. The session took place in the same listening room as in the loudspeaker session. Subjects sat in the same chair, but no loudspeaker was mounted in any of the tested directions so that subjects could not match the sounds they heard with an identifiable sound source. Sub- jects were asked to place the test headphones comfortably over their ears and to not modify this position once the test had started as realistic changes in the headphone position can be audible [27]. Subjects had to carry out eight loudness equalizations, corresponding to the two equalizations (one for each test sound) in each of the four spatial configurations of the session 1 (see Fig 2).

In order to compare the effect of the sole ITD on the loudness of pure tones to that of the narrow-band noise used as stimulus in this experiment, one additional equalization was realized in this session. Its reference sound was the narrow-band noise directly synthesized and played back through the headphones (without being recorded by the dummy head) in a diotic presentation, at the same reference level than the previous stimuli (50 phon). The test sound that was to be equalized on this reference sound was the same narrow-band noise directly synthesized with a fixed 772 µs time difference applied between the two channels. This value was also used in the previous experiments on the effect of ITD on loudness [START_REF] Koehl | Loudness of low-frequency pure tones lateralized by interaural time differences[END_REF][START_REF] Koehl | Effects of interaural differences on the loudness of low-frequency pure tones[END_REF][START_REF] Berthomieu | Influence of interaural time differences on loudness for low-frequency pure tones at varying signal and noise levels[END_REF].

These nine equalizations were done in the same session that lasted approximately 30 min. Stimuli appeared in a random order for each subject.

Results

Since the PSE is the level difference for which a test sound is perceived as loud as a reference sound, a negative PSE means that a lower sound pressure level was required for the test sound to match the reference sound in loudness. Thus, when providing both sounds with the same pressure level, the test sound would have been perceived louder than PAPERS DIRECTIONAL LOUDNESS OF LOW-FREQUENCY NOISES the reference sound, indicating a higher loudness sensitivity to directional sounds. The results are subsequently presented as DLS for the rest of the paper:

DLS = -PSE (2)
The outcome of the ninth equalization (involving diotic and dichotic headphone-synthesized stimuli) presented in the same session as the virtual presentation does not properly result from the comparison of real sources located in different directions but from sounds differing in their ITDs only. This loudness match will also be denoted as DLS for sake of clarity.

In order to investigate the effect of the presentation conditions on directional loudness, a repeated-measures analysis of variance (ANOVA) was conducted on the sixteen DLS values obtained in actual and virtual presentations. The spatial configuration (4 levels) and the test sound azimuth (2 levels) were also included as factors of the analysis:

• Presentation conditions (2 levels): actual, virtual.

• Spatial configuration (4 levels): configurations a, b, c, d.

• Azimuth (2 levels): -90 • , +90 • .
Results of this ANOVA are given in Table 1. As this study primarily focuses on the effects of the presentation conditions on the DLS, the significant effects involving this factor will be discussed first. Other significant effects, namely the "spatial configuration" effect and its interaction with the sound source azimuth are caused by the room effect. The main consequences of this room effect is that the DLS values themselves are not consistent with the loudness gain provided by the lateralization of a sound source in one given spatial configuration within the room, leading to an inconsistent pattern across the configurations identifiable on Fig. 4 and Fig. 5. However, the room effect is likely to be cancelled when averaging DLS values across the spatial configurations, and it did not have any influence on the presentation conditions effects since it was globally the same whether the sounds were reproduced over headphones or loudspeakers, and was therefore present in a similar way in the actual and virtual presentation conditions.

Presentation conditions effects

One of the main results regarding this analysis is that the presentation conditions proved to have significant effects on the DLS. These effects were dependent on the spatial configuration and on the test sound azimuth, as indicated by the significant "presentation conditions × spatial configuration × azimuth" interaction. Bonferroni posthoc tests revealed a significant difference between the two presentation conditions in the spatial configuration c when the test sound was located at -90 • (p < .001) or at +90 • (p = .007). In this configuration and for these two azimuths, DLS was larger in the virtual presentation than in the actual presentation, as shown in Fig. 4.

Presentation conditions effects also appeared to depend on the spatial configurations when combining the test sound azimuths as the "presentation conditions × spatial configuration" interaction proved to be significant. Thus, the effect of the presentation conditions on DLS was not the same for all spatial configurations of the sound sources. Bonferroni post hoc tests revealed a significant difference between the two presentation conditions in the spatial configurations c (p < .001) and d (p = .016) only. In these two configurations, DLS was larger in the virtual presentation than in the actual presentation, as shown in Fig. 5. As depicted in Fig. 2, the configurations c and d were similar in the way that the reference sound source was at a distance of 1 m from the subject, whereas it was at a distance of 2 m in configurations a and b. Then, the fact that DLS did not significantly depend on the presentation conditions in the configurations a and b whereas they did significantly depend on the presentation conditions in the configurations c and d is likely to be caused by the distance of the frontal sound source.

To summarize about these two interactions :

• DLS was similar whether the sound sources were actual or virtual when the frontal sound source was located at 2 m from the subjects. • Virtual sound sources yielded to larger DLS than actual ones when the frontal sound source was located at 1 m from the subjects, for each of the two azimuths in the configuration c and when combining the two azimuths in the configuration d.

Finally, the presentation conditions proved to have a significant effect when combining all spatial configurations and azimuths, as shown by the significance of the "presentation conditions" simple effect. As indicated in the left part of Fig. 6, DLS was significantly larger with the virtual presentation of the sounds than with the actual one. The right part of the figure depicts the DLS obtained for the noise synthesized and directly reproduced over headphones with a fixed 772 µs ITD between the two channels. A t-test revealed that this DLS is significantly larger than zero (t(19) = 5.296, p < .001) and is about 1.5 dB, which is in agreement with the previous findings on the effect of ITD on loudness for pure tones [START_REF] Koehl | Loudness of low-frequency pure tones lateralized by interaural time differences[END_REF][START_REF] Koehl | Effects of interaural differences on the loudness of low-frequency pure tones[END_REF][START_REF] Berthomieu | Influence of interaural time differences on loudness for low-frequency pure tones at varying signal and noise levels[END_REF]. In addition, independent-samples t-tests revealed that neither the DLS obtained in virtual (t(29.949) = 1.5011 , p = .144) nor actual (t(178) = -.531, p = .596) presentation conditions is significantly different from the DLS of the stimulus with a fixed ITD. The DLS was also significantly larger than zero in both virtual (t(159) = 13.677, p < .001) and actual (t(159) = 11.433, p < .001) presentation conditions.

At the frequencies under investigation, the fact that the DLS is larger than zero is likely to be accounted for by the ITD. Then, the average time difference between the two channels of the dummy head was measured for each test sound (two azimuths and four spatial configurations) in order to be compared to the fixed 772 µs ITD.

Spatial configuration effects

The ANOVA also revealed that the spatial configuration had significant effects on the DLS values. In other words, the loudness ratio between lateral and frontal sound sources was not the same depending on the spatial configuration of the sound sources in the listening room. Since this room was not anechoic, these effects are likely to be caused by sound pressure variations at the ears of the listeners and of the dummy head even though the four loudspeakers were calibrated to deliver the same level at the center of the subjects heads and of the dummy head. Therefore, atear SPL variations affecting frontal and lateral sources will also affect the DLS values resulting from the comparison of these two sources, as indicated by the "spatial configuration" simple effect and by the "spatial configuration × azimuth" interaction. As an example, a spatial configuration for which the reference sound pressure level is lower than that of the reference sound in another spatial configuration would lead to higher overall DLS values. In order to verify this hypothesis, the reference sound pressure levels were measured on each ear of the dummy head in each spatial configuration and averaged over the two ears, before being compared to the overall DLS value in each spatial configuration. The results are depicted on Fig. 7, and show a good match between the two patterns. These SPL variations (Fig. 7 right) appear to partially account for the DLS dependency on spatial configuration (Fig. 7 left), although one should keep in mind that the SPL of the lateral test sound is also involved in DLS. It should be emphasized that the Y-axis of the right figure is reversed since reference sound pressure level and DLS values are anticorrelated. The 0 dB in this figure is the level delivered by the reference sources (50 phon) at the center of the head.

The DLS value in each spatial configuration may then per se not be representative of the directional loudness effect in a given configuration because of these SPL variations. On one hand, if a loudspeaker delivered a lower SPL than its neighbour at the ears of the listeners and of the dummy head, this results in a higher DLS value in the spatial configuration in which it is the reference source. On the other hand, the DLS value in the spatial configuration where its neighbour is the reference (see Fig. 1 and Fig. 2) will be proportionally lower. Thus, the room effect is likely to be averaged over the four spatial configurations. This is supported by the good match between the averaged DLS obtained with the room acoustic and the DLS obtained with ITD only (Fig. 6) since at the frequencies under investigation, directional loudness is expected to be mostly accounted for by ITD.

In addition, these at-ear SPL differences were present in the two presentation conditions because of the binaural recording method employed for creating virtual sound sources. Inter-individual SPL variations may have resulted from the coupling between the headphone and each individual listener's ears, but the average at-ear SPLs were assumed to follow a similar pattern as the one measured by the dummy head and depicted on the right of Fig. 7. In conclusion, these SPL differences are not likely to account for the observed effects of the presentation conditions on the DLS.

Discussion

The results of the experiment show that:

• The loudness of a low-frequency narrow-band noise was higher when it was located at the side of a listener than when it was located at the front, for the two presentation conditions under investigation. • This increase was not different, for both presentation conditions, from the increase observed with ITD only. • The increase was inferior in the actual presentation (sounds stemming from actual loudspeakers) than in the virtual presentation (binaural recording of the loudspeaker-reproduced stimuli, with no loudspeakers mounted in the tested directions) when the frontal sound source was at a distance of 1 m from the subject. • The increase was the same in both presentation conditions when the frontal sound source was at a distance of 2 m from the subject. • For the positions were the frontal sound source was at a distance of 1 m, this increase occurred for each of the two lateral source azimuths in configuration c whereas it occurred only when combining the two azimuths in configuration d.

Effect of the presentation conditions

The overall DLS obtained in the actual presentation conditions was lower than the DLS obtained in the virtual presentation conditions. This result is in agreement with those obtained by Epstein and Florentine [START_REF] Epstein | Binaural loudness summation for speech and tones presented via earphones and loudspeakers[END_REF][START_REF] Epstein | Binaural loudness summation for speech presented via earphones and loudspeaker with and without visual cues[END_REF], who measured a lower binaural-to-monaural ratio when increasing the ecological validity of their experiments by displaying stimuli through loudspeakers rather than through headphones and by adding visual cues to their stimuli. As a result, binaural or directional loudness investigations achieved under controlled laboratory presentation conditions are likely to highlight isolated phenomenons that affect binaural loudness summation but whose observed magnitude could be higher than when observed in real life. Comparatively, experiments designed using real sound sources along with visual cues are likely to highlight closer to natural magnitude effects.

According to the results of the present study, the distance of the frontal sound source (displaying the reference sound) had a different effect on DLS in the two presentation conditions. Since both auditory [29] and visual [30] distance cues were reported to affect loudness, these distance cues could account for the variation of DLS with distance. Fig. 6. DLS as a function of the presentation conditions (left) and for headphone-synthesized stimuli (right), with 95% confidence intervals.

Auditory cues

Since the SPL was fixed at a same listening point for the four loudspeakers, it did not vary whether the sound sources were at 1 or 2 m from the subjects and could not account for DLS variations. On the other hand, other acoustic characteristics of the sound could be affected by the distance of the sources (i.e., direct-to-reverberant ratio, spectral energy distribution. . . ) [START_REF] Moore | Space perception[END_REF]. Those characteristics were similar in the two presentation conditions thanks to the binaural recording used in the virtual presentation. Some differences might however have resulted from the differences between the subjects' individual HRTFs (that filtered the sounds in the actual presentation) and the dummy head HRTFs (that filtered the sounds in the virtual presentation). Yet, HRTFs depend on source distance only in proximal space (< 1 m and even closer at the frequencies under investigation) [31,32]. Then, even if a different filtering oc-Fig. 7. DLS as a function of the spatial configuration (left) compared to the average SPL between the two ears of the dummy head for the reference sound (right) in each spatial configuration. curred in the actual and virtual presentation conditions, the differences should remain the same whether the source is at 1 or 2 m from the subjects.

Furthermore, it could be considered that the DLS dependency on source distance was not determined by the auditory distance cues themselves but by the resulting perceived distance. Then, a potential effect of visual cues to distance should also be discussed since visual estimates of distance are better than auditory estimates [33].

Visual cues

The visual cues to distance were not the same in the two presentation conditions. In the virtual presentation, neither frontal nor lateral sound sources were visible and subjects had little if any clue to physical sources that may have reproduced the sounds they heard. In the actual presentation, visual cues for the frontal sound sources were available to the subjects during the whole procedure, which was not the case for the lateral sound sources because of the headrest and chin rest that their in a fixed position. Thus, subjects did not have the same access to visual information according to the presentation conditions and to the azimuth of the sources.

When the frontal sources were visible and close to the subject is in the actual presentation conditions in the spatial arrangements c and d, see Fig. 2), DLS was significantly lower than when they were not visible (that is in the virtual presentation conditions). This decrease means that the loudness of the reference and test sounds tended to get closer. Since DLS was positive (i.e., test sounds were perceived louder than reference sounds), the DLS lowering could be due either to an increase in loudness of the reference sound or to a decrease in loudness of the test sound. In each spatial configuration of the sources, DLS was assessed on both 1 and 2 m distant lateral test sounds. Thereby, if the distance of the lateral sound source affected DLS in any way, its effect would be canceled in each spatial configuration because of the assumed left/right symmetry of directional loudness [START_REF] Koehl | Loudness of low-frequency pure tones lateralized by interaural time differences[END_REF]. Thus, the observed DLS differences between the two presentation conditions are more likely to be accounted for by the loudness of the frontal reference sounds. Following this hypothesis, the loudness of sounds that come from visible and close sources would be higher than the loudness of sounds that come from invisible or farther sources at a same physical level delivered to the listener. Such an effect was reported for visible sources in an anechoic room: the loudness related to a loudspeaker located at 3.75 m was less than when at 2.25 m, even though the sound pressure level was fixed at the position of the listener [30]. This explanation could also account for the fact that no DLS difference was observed between the loudspeaker and headphone presentation conditions investigated by Sivonen et al. [START_REF] Sivonen | Directional loudness in an anechoic sound field, head-related transfer functions, and binaural summation[END_REF][START_REF] Sivonen | Effect of direction on loudness in individual binaural synthesis[END_REF] since visual cues were provided in the two conditions.

Other factors

In the present experiment, listeners were aware that the sounds they heard were displayed whether by loudspeakers or by headphones in the corresponding test sessions. This awareness could have had an effect on the loudness processing of the sounds [START_REF] Epstein | Binaural loudness summation for speech presented via earphones and loudspeaker with and without visual cues[END_REF], independently from physical changes in the heard stimuli, and the exact same sounds could somehow have led to different DLS judgments according to the presentation conditions. Distance perception could also have interacted with other high level factors, for example the externalization of the sound sources. Even though relations between externalization of a sound source (i.e., perceiving a sound as coming from the exterior of the head) and perceived distance are not fully established yet [34], it could be hypothesized that sound externalization played a role in the observed loudness summation. Sounds are likely to be internalized (i.e. perceived as coming from "inside" the head) when they are reproduced over headphones, especially when displayed at the front (0 • ) than at the side (±90 • ) of a listener [35,36]. On the other hand, sounds reproduced over actual sound sources are reported to be externalized whatever their location with respect to the listener [37]. Then, the degree of externalization could not have been the same for reference (located at 0 • ) and test sound (located at ±90 • ) sources in the virtual presentation conditions, while it should have been the same for all sound sources in the actual presentation conditions. This could have had an effect on the perceived sound sources distance, and as a consequence on the resulting DLS.

Conclusion

The results of this experiment extended the previously highlighted effect of ITD on loudness of stimuli displayed under unrealistic listening conditions to that of stimuli reproduced with natural binaural cues in a listening context with stronger ecological validity.

The directional loudness effect was found to be dependent on the presentation conditions in which the sounds were perceived. More precisely, the loudness of sounds was PAPERS DIRECTIONAL LOUDNESS OF LOW-FREQUENCY NOISES increased by a higher amount when they were side-located and heard in virtual presentation conditions with no visible sound source than when they were presented by actual sound sources located at the side of the listener. This only occurred when the frontal sound source, used as a reference, was located at the closest studied distance (1 m) from the subject. One hypothesis accounting for these observations is that for a same sound pressure level, sounds produced by frontal sources could have been perceived louder when the sources were located at 1 m from the subject than when they were located at 2 m from the latter, provided the sound sources were visible. This condition was only fulfilled in the actual presentation conditions. These DLS differences could also be accounted for by other parameters that varied between the two presentation conditions, such as the HRTFs used, or more globally by high level processes that rely on the presentation conditions themselves rather than on their effects on the stimuli.

Fig. 1 .

 1 Fig. 1. Loudspeakers arranged around the listening point (dot) in the test room.

Fig. 2 .

 2 Fig. 2. Loudspeakers arrangement for each of the four spatial configurations. Sources denoted R display the reference sounds, sources denoted T display the test sounds.

Fig. 3 .

 3 Fig. 3. Position of the dummy head, maintained by the headrest and chin rest, during the recording of the stimuli.

Fig. 4 .Fig. 5 .

 45 Fig.[START_REF] Sivonen | Binaural loudness for artificial-head measurements in directional sound fields[END_REF]. DLS as a function of the azimuth of the test sound in each spatial configuration for the two presentation conditions, with 95% confidence intervals.

Table 1 .

 1 These eight ANOVA results. measurements led to a slightly higher average ITD than 772 µs (µ = 859 µs, σ = 19 µs), but should not lead to a significantly different DLS[28].

	Source

J. Audio Eng. Soc., Vol. ?, No. ?, ? ?

J. Audio Eng. Soc., Vol. ?, No. ?, ? ?

corrected due to a violated assumption of homogeneity of variances.J. Audio Eng. Soc., Vol. ?, No. ?, ? ?

Acknowledgments

The authors wish to thank the staff from the "Image & Son" department of the University of Brest and the ticipants of this experiment.

This work was supported by the ANR-13-CORD-0008 EDISON 3D project, funded by the French National Agency of Research (http://www. agence-nationale-recherche.fr/).

PAPERS

vol. 65, pp. 589-599 (2017b), doi:https://doi.org/10.17743/ jaes.2017.0018.

[37] W. M. Hartmann, A. Wittenberg, "On the externalization of sound images," J. Acoust. Soc. Am., vol. 99, no. 6, pp. 3678-3688 (1996), doi:https://doi.org/10.1121/ 1.414965.

THE AUTHORS

Gauthier


Philipp Gruner

Yousr Skhiri

Benoît Semin

Quentin Brosseau

Andrew D Griffiths

Valérie Taly

Jean-Christophe Baret

Benoit Semin

Microfluidic Approaches for the Study of Emulsions: Transport of Solutes

published or not. The documents may come   L'archive ouverte pluridisciplinaire

INTRODUCTION

Droplet-based microfluidic systems are promising platforms for high-throughput screening applications [START_REF] Theberge | Microdroplets in microfluidics: An evolving plat-form for discoveries in chemistry and biology[END_REF][START_REF] Guo | Droplet microfluidics for highthroughput biological assays[END_REF]. The versatile encapsulation of various types of biomaterials, such as proteins, nucleic acids, single genes, or cells makes droplets perfectly suitable as a tool for miniaturized and automatized enzymatic assays, cell screening, cancer diagnostics, or drug screening platforms [START_REF] Agresti | Ultrahigh-throughput screening in drop-based microfluidics for directed evolution[END_REF][START_REF] Miller | High-resolution doseresponse screening using droplet-based microfluidics[END_REF][START_REF] Baret | Quantitative cell-based reporter gene assays using droplet-based microfluidics[END_REF]. The success of the technology relies on the very high-throughput of each individual step of droplet manipulation, which reaches several kHz for droplet production, reinjection, splitting, or fusion [START_REF] Seemann | Droplet-based microfluidics[END_REF]. The droplets are used as microcontainers behaving in principle as independent, miniaturized and closed reacting vessels that can be actuated on demand for the steps required in a typical biological assay [START_REF] Theberge | Microdroplets in microfluidics: An evolving plat-form for discoveries in chemistry and biology[END_REF].

In practice, droplets are produced in microchannels and stabilised against coalescence by surfactant molecules, resulting in an emulsion, i.e. a dispersion of one phase into another, stabilised by surfactant molecules [START_REF] Bibette | Emulsions: basic principles[END_REF]. From a fundamental perspective, emulsions are systems out of equilibrium as they only correspond to a local minimum of the free energy landscape and the final equilibrium state where the two phases are separated in two compartments of macroscopic size will eventually be reached. The typical time-scale for this process is linked to the ageing mechanism of the emulsion, involving floculation, coalescence and molecular transport between droplets [START_REF] Bibette | Emulsions: basic principles[END_REF].

The first relevant step for the use of droplet as microreactor is the stabilisation of the droplets by the surfactant, which is achieved by formulation and optimisation of surfactant concentration and additives. This side is well established and microfluidic systems have proven very efficient tools to study the underlying mechanisms in the stabilisation of emulsions by surfactants [START_REF] Bremond | Decompressing emulsion droplets favors coalescence[END_REF][START_REF] Baret | Kinetic Aspects of Emulsion Stabilization by Surfactants: A Microfluidic Analysis[END_REF].

In the following, we will focus on the description of a second ageing mechanism which is crucial to be controlled, for most of the bio-assays, namely, the exchange of chemicals between droplets. Here the practical background is linked to storage and screening of chemicals and potential drugs in droplet-based microfluidics. This approach has already been demonstrated for various systems [START_REF] Miller | High-resolution doseresponse screening using droplet-based microfluidics[END_REF][START_REF] Baret | Quantitative cell-based reporter gene assays using droplet-based microfluidics[END_REF], for example for screening of new drugs. Here, from a fundamental perspective, gradients in chemical potential between droplets will eventually level out, even if the absence of coalescence maintains the integrity of the reactors. The time scale of this process must be determined, in this somehow unusual emulsion system, where virtually all droplets can contain materials varying from droplet to droplet by composition or concentration (Figure 1).

EXPERIMENTS

We designed microfluidic systems to address the specificity of molecular transport in fluorinated oils and showed the role of the surfactant solubilised in the oil phase on the time scale of the exchange and rationalize the effect of water soluble additives on the exchange rate.

Finally, we also demonstrate that the droplet packing influences the exchange rate through the number of first neighbours [START_REF] Skhiri | Dynamics of molecular transport by surfactants in emulsions[END_REF].

Microfluidic method

We use standard lithography techniques to produce microfluidic chips for the formation of mixed emulsions made of monodisperse droplets of aqueous phases in fluorinated oils [START_REF] Xia | Soft lithography[END_REF][START_REF] Anna | Formation of dispersions using flow focusing in microchannels[END_REF]. Droplets of high dye concentration (typically 10 µM) are produced in one flow focussing junction and droplets without dye are produced in a second junction. The droplets are stabilized by block copolymer surfactants (PEG-PFPE, home made according to standard synthesis schemes [START_REF] Holtze | Biocompatible surfactants for water-in-fluorocarbon emulsions[END_REF]) to prevent coalescence. We interface the outlet of the chip with an incubation chamber, externally controllable for the loading of the emulsion, the storage from minutes to several hours and the droplet reinjection (Figure 2). As a model system, we use fluorescent compounds. The concentration of the dyes in the droplet directly relates to their concentrations. Using a laser induced fluorescent setup, we measure the fluorescence of every droplet of the emulsion for quantitative analysis of concentration over millions of droplets. Kinetic measurements are achieved by controlling the reinjection speed over several hours. [START_REF] Skhiri | Dynamics of molecular transport by surfactants in emulsions[END_REF])

RESULTS AND DISCUSSIONS

Effect of the surfactant on transport

In a first set of experiments, we used resorufin in PBS buffer and monitor the exchange kinetics. The distribution of the droplet fluorescence at short time-scale (a few minutes) reveals to peaks, corresponding to the two types of droplets and as time increases the two concentrations tend to equilibrate.

A quantitative measurement of the exchange kinetics is performed by measuring the difference of concentration of the two populations as a function of time (Figure 3). The kinetic is affected by the concentration of the surfactant present in the oil phase: an increase of surfactant concentration leads to a decrease of the equilibration time-scale (increase of rate). The time scale of exchange is obtained by rescaling the time of all experiments by a single time scale, which turns out to be a linear function of surfactant concentration. The shape of the relaxation itself is a universal master curve showing an initial exponential relaxation asymptotically reaching a power-law in the late kinetic. 2012) [START_REF] Skhiri | Dynamics of molecular transport by surfactants in emulsions[END_REF])

Effect of chemistry and the role of additives

The solubility of the dyes in the acqueous phase are known to influence the exchange [START_REF] Woronoff | New Generation of Amino Coumarin Methyl Sulfonate-Based Fluorogenic Substrates for Amidase Assays in Droplet-Based Microfluidic Applications[END_REF]. As an example, we observed exchange rates of the order of one hour for resorufin, several days for fluorescein and a few seconds for coumarine. It is also known that additives such as the protein BSA (Bovine Serum Albumine) solubilised in the water droplet slows down the exchange kinetics [START_REF] Courtois | Controlling the Retention of Small Molecules in Emulsion Microdroplets for Use in Cell-Based Assays[END_REF] which we also observed (Figure 3d). However, the underlying mechanisms are not clear. One of the proposed mechanism is the creation of a layer of proteins at the water -oil interface that would create a kinetic barrier slowing down the exchange. In order to test this hypothesis, we have produced a mixed emulsion in which all droplets contain the same resorufin concentration. As the chemical potential of resorufin is in principle the same in all droplets, the concentration of resorufin should remain constant.

Figure 4: Comparison of the exchange process for an emulsion initially containing two different concentration of resorufin showing that concentrations equilibrate (a) and for an emulsion initially containing the same resorufin concentration but different concentration of the additive BSA showing that resorufin concentrates in BSA containing droplets (b). Reprinted with permission of the Royal Society of Chemistry (original publication: Y. Skhiri, P. Gruner et al.

Soft Matter (2012) [START_REF] Skhiri | Dynamics of molecular transport by surfactants in emulsions[END_REF])

Here, we introduced BSA in half of the droplets and incubated and reinjected the emulsion. At short time scales, the fluorescence signal is the same in all droplets but the signal splits in two indicating that the BSA containing droplets and the non-BSA containing droplet contain different concentration of resorufin. There is therefore an exchange of dye and this exchange should not occur if BSA was only providing a kinetic barrier to exchange. BSA modifies the chemical potential of resorufin in the droplets (and therefore partition coefficient between the oil-surfactant mixture and the water) which impacts the kinetics of exchange in a process controlled by thermodynamic properties. Such an effect relates to the ability of BSA to bind a wide range of small molecules, such as potential drugs [START_REF] Peters | All about Albumin: Biochemistry, Genetics and Medical Applications[END_REF].

Effect of packing and number of first neighbors during incubation

The shape of the master curve also provides additional information on exchange mechanisms. Indeed, in a simple permeation model, two compartments would equilibrate with an exponential decay of the concentration difference [START_REF] Zwolinski | Diffusion and membrane permability.1[END_REF]. The time scale is then given by partition coefficient, diffusion constant in the permeable layer and the spacing between the compartments. Our experiments display a more complex behaviour. In order to understand the shape of the master curve, one consider a regular array of droplets all separated by a permeable membrane (Figure 5). Under these conditions, the concentration is given by a discrete diffusion equation. The eigenmode and eigenvalues of the Laplace equation can be analytically derived with periodic boundary conditions. In this case, we find that the fastest relaxing mode is the one where droplets alternate one by one. This relaxation mode has an eigenvalue given by the timescale obtained for a pair of droplets. All the other modes relax slower. In the limit of random position of the filled and empty droplets, the kinetic of relaxation is analytically solved by the summation of all the eigenmodes. This operation leads to an exponential decay in the early kinetic, with a time scale equal to half of the fastest mode. The same operation is performed for the late kinetics where the summation leads to a power law behaviour, with an exponent depending on the dimension of the system. Droplets along a line display a power-law of ½, on a square lattice of 1 and on the nodes of a square 3d lattice 3/2,as observed in our experiments (Figure 3c).

Towards other exchange mechanisms: water transport

In all the previous experiments, we used equal buffer concentrations to prevent the transport of water between droplets (Ostwald rippening [START_REF] Bibette | Emulsions: basic principles[END_REF][START_REF] Boitard | Monitoring single cells bio-energetics via the coarsening of emulsion droplets[END_REF]). But our microfluidic approach is equally usable to study this other transport problem in emulsion, namely the transport of the dispersed solvent between droplets. This other ageing mechanisms is a key to be controlled to guarantee the general stability of the emulsion. In addition, as it is also the basis of novel analytical platforms, where the change of relative size of droplets reveals metabolic processes down to the single cell level [START_REF] Boitard | Monitoring single cells bio-energetics via the coarsening of emulsion droplets[END_REF] it becomes critical to understand such processes. In a set of preliminary experiments, we consider the change of droplet sizes in droplet dispersed in fluorinated oils as a function of salt concentration differences. We observed that the time-scale of exchange is not affected by the surfactant concentration which indicates the the solubilization of water and organic molecules follow different mechanisms. The difference in behaviour of organic molecules and water transport relates in principle to the nature of the surfactant supramolecular assembly in the oil. The structure of the micelles solubilized in the oil will determine the affinity of the different compounds for the micelles impacting the exchange process. Experiments are currently on-going to determine these structure for a deeper insight into the microscopic details of the exchange processes.

CONCLUSIONS

Permeation processes in emulsions determine the long-term stability of the emulsion and are a key to be understood and controlled for applications of droplet-based microfluidics. For example, it must be ensured that all reagents and products in assays remain in the droplets for times sufficiently long compared to the time scale of the reaction considered. For storage of drugs in the form of emulsions, it must also be considered that the compounds do not diffuse across the whole emulsion. We identified here a major mechanism by which surfactants promote transport. In addition, we propose guidelines to decrease the exchange rates in emulsions: (i) optimisation of surfactant concentrations to minimize the exchange rate as the rate of exchange is linear with surfactant concentration (ii) formulation principles based on solubility alteration by additives such as BSA, as we have shown that BSA favors the partitioning of the solutes into the water phase therefore reducing exchange rates (iii) optimisation of packing and storage conditions as the exchange rates decrease with number of nearest neighbours and dimension of the system.

Figure 1 :

 1 Figure 1: Droplet-based microfluidics provides tools to produce calibrated emulsion. They are used to determine the exchange rate of compounds. Example of an emulsion of 100 microns droplets containing sulforhodamine (bright droplets) or buffer (dark droplets).

Figure 2 :

 2 Figure 2: Sketch of the microfluidic chip for emulsification of mixed emulsion. Droplets containing a fluorescent dye (resorufin) are produced at one nozzle and droplet without the dye at the second nozzle. The droplets are stored in a reservoir for incubation and slowly reinjected for on-chip fluorescence measurement. Millions of droplets are measured over several hours for kinetic measurement of the exchange process. Reprinted with permission of the Royal Society of Chemistry (original publication: Y. Skhiri, P. Gruner et al. Soft Matter (2012)[START_REF] Skhiri | Dynamics of molecular transport by surfactants in emulsions[END_REF])

Figure 3 :

 3 Figure 3: (a) Distribution of fluorescence in the emulsion as a function of time. Asymptotically, the droplet all contain the same concentration of dye. (b) Variation of the concentration in each population of droplets as a function of time and surfactant concentration: surfactant favors the exchange process. (c) Rescaling of the concentration difference on a master curve. The power law at late time is the result of the random distribution of the droplets in the emulsion. (d) Evolution

Figure 5 :

 5 Figure 5: (a) Model for relaxation of concentration differences by permeation on a square lattice. (b) With periodic boundary conditions, the eigenmodes of the discrete diffusion equation are expressed analytically. The fastest relaxation mode (alternating droplets in both direction) decays exponentially with a time-scale linked to the exchange time scale of isolated pairs. Other modes relax slower. For a random distribution of position of filled and empty droplets, the early time relaxation is an exponential decay with a time scale twice the fastest time scale and the long time limit shows a dimension dependent power law recovered analytically. Reprinted with permission of the Royal Society of Chemistry (original publication: Y. Skhiri, P. Gruner et al. Soft Matter (2012) [11])

Figure 6 :

 6 Figure 6: Measurement of water transport in water in oil fluorinated emulsions. Salt droplets are marked with fluorescein. The droplet volume is monitored as well as fluorescence signals. In this case, the time scale of the process in independent of surfactant concentration.

ACKNOWLEDGMENTS

We thank D. Pekin, L. Mazutis, V. Goust, F. Kleinschmidt, A. El Harrak, J. B. Hutchison, E. Mayot, J.-F. Bartolo, C. Rick, C. Ben Salem and Z. El Harrak and A.D. Griffiths for their contributions as well as B. Maury, S. Herminghaus, J. Bibette and N. Bremond for helpful discussions. The authors acknowledge the financial support of Region Alsace, the 'Fondation d'Entreprise EADS' and the European Commission Framework Program 6 (MiFem). Financial support from the Max-Planck Gesellschaft and the Deutsche Forschunggemeinschaft through the Sonderforschungbereich 755 (Nanoscale Photonic Imaging) are also acknowledged.

The authors also thank the Royal Society of Chemistry for granting permission to reuse figures published in the Soft Matter Special edition 'Soft Matter Principles of Microfluidics' (Skhiri, Gruner et al. Soft Matter (2012) [11]).