Kelly De Sousa

Alaa B Abdellatif

Isabelle Giscos-Douriez

Tchao Meatchi

Laurence Amar

Fabio L Fernandes-Rosa

Sheerazed Boulkroun

MD Maria-Christina Zennaro
email: maria-christina.zennaro@inserm.fr

Colocalization of Wnt/β-Catenin and ACTH Signaling Pathways and Paracrine Regulation in Aldosterone-producing Adenoma

Keywords: PA, primary aldosteronism, APA, aldosterone producing adenoma, Aldosterone, Mineralocorticoids, Endocrine Hypertension, Primary Aldosteronism, Aldosterone producing adenoma, Adrenal Cortex, signalling pathway, paracrine regulation, mast cells, vessels

come

Introduction:

Aldosterone producing adenomas (APA) and bilateral adrenal hyperplasia are the main causes of primary aldosteronism (PA) [START_REF] Funder | The Management of Primary Aldosteronism: Case Detection, Diagnosis, and Treatment: An Endocrine Society Clinical Practice Guideline[END_REF]. PA is the most frequent form of secondary arterial hypertension with a prevalence of 5% of hypertensive patients in primary care and up to 10% of those seen in reference centers [START_REF] Monticone | Prevalence and Clinical Manifestations of Primary Aldosteronism Encountered in Primary Care Practice[END_REF][START_REF] Hannemann | Prevalence of primary aldosteronism in patient's cohorts and in population-based studies--a review of the current literature[END_REF][START_REF] Brown | The Unrecognized Prevalence of Primary Aldosteronism[END_REF]. Hypertension, increased aldosterone levels with suppressed plasma renin, and in many cases hypokalemia are the main characteristics of the disease. Patients with PA are at excess risk for cardiovascular events when compared to patients with primary hypertension [START_REF] Savard | Cardiovascular complications associated with primary aldosteronism: a controlled cross-sectional study[END_REF][START_REF] Monticone | Cardiovascular events and target organ damage in primary aldosteronism compared with essential hypertension: a systematic review and meta-analysis[END_REF].

Different somatic mutations in APA and germline mutations in familial PA were discovered using whole exome sequencing approaches. These mutations affect genes coding for ion channels (KCNJ5, CACNA1D, CACNA1H, CLCN2) or ATPases (ATP1A1, ATP2B3) [START_REF] Fernandes-Rosa | Genetic and Genomic Mechanisms of Primary Aldosteronism[END_REF]. They lead to autonomous aldosterone production by increasing the expression of CYP11B2, coding for aldosterone synthase. The prevalence of somatic mutations is estimated between 88 and 96% by immunohistochemistry-guided next-generation sequencing (NGS) [START_REF] Nanba | Targeted Molecular Characterization of Aldosterone-Producing Adenomas in White Americans[END_REF][START_REF] Nanba | Genetic Characteristics of Aldosterone-Producing Adenomas in Blacks[END_REF][START_REF] Sousa | Genetic, Cellular, and Molecular Heterogeneity in Adrenals With Aldosterone-Producing Adenoma[END_REF][START_REF] Ono | Histological Characterization of Aldosteroneproducing Adrenocortical Adenomas with Different Somatic Mutations[END_REF][START_REF] Nanba | Prevalence of Somatic Mutations in Aldosterone-Producing Adenomas in Japanese Patients[END_REF]. Other autonomous aldosterone producing lesions were described in normal adrenals as well as in peritumoral tissue in adrenals with APA. Indeed, somatic mutations in CACNA1D, ATP1A1 and KCNJ5 have been described in APCC (aldosterone producing cell clusters, also called aldosterone producing nodules [START_REF] Williams | International Histopathology Consensus for Unilateral Primary Aldosteronism[END_REF]) and pAATL (possible APCC to APA translational lesions) [START_REF] Sousa | Genetic, Cellular, and Molecular Heterogeneity in Adrenals With Aldosterone-Producing Adenoma[END_REF][START_REF] Nishimoto | Aldosterone-stimulating somatic gene mutations are common in normal adrenal glands[END_REF][START_REF] Nishimoto | Case Report: Nodule Development From Subcapsular Aldosterone-Producing Cell Clusters Causes Hyperaldosteronism[END_REF]. The recurrence of somatic mutations in APA driver genes and the metabolic profile of APCC suggested that they may induce APA development [START_REF] Nishimoto | Aldosterone-stimulating somatic gene mutations are common in normal adrenal glands[END_REF].

In addition to genes coding for ion channels and pumps, mutations in genes related to adrenal development, maintenance of the zona glomerulosa (ZG) and steroidogenesis were also described in APA. Particularly, somatic mutations in CTNNB1 coding for β-catenin are found in 2% to 5% of cases [START_REF] Scholl | Novel somatic mutations in primary hyperaldosteronism are related to the clinical, radiological and pathological phenotype[END_REF][START_REF] Akerstrom | Activating mutations in CTNNB1 in aldosterone producing adenomas[END_REF], possibly causing a proliferative advantage in adrenal cells and an abnormal activation of WNT signaling pathway. More recently, somatic mutations in GNAQ/GNA11 were identified in APA carrying somatic CTNNB1 mutations in patients presenting with PA in puberty, pregnancy or menopause [START_REF] Zhou | Somatic mutations of GNA11 and GNAQ in CTNNB1-mutant aldosterone-producing adenomas presenting in puberty, pregnancy or menopause[END_REF]. Somatic mutations in PRKACA (catalytic subunit of protein kinase A) are rare findings in APAs and their direct involvement in APA development is still unclear [START_REF] Rhayem | PRKACA Somatic Mutations Are Rare Findings in Aldosterone-Producing Adenomas[END_REF]. The Wnt/β-catenin pathway plays a role in the identity and function of ZG cells, whereas the ACTH/cAMP pathway is involved in the differentiation of ZG cells into zona fasciculata (ZF) cells by inhibiting the Wnt/β-catenin pathway [START_REF] Drelon | Adrenal cortex tissue homeostasis and zonation: A WNT perspective[END_REF] as well as in regulating glucocorticoid biosynthesis. We have previously reported that in APA the Wnt/β-catenin pathway was activated mainly in areas expressing aldosterone synthase [START_REF] Sousa | Genetic, Cellular, and Molecular Heterogeneity in Adrenals With Aldosterone-Producing Adenoma[END_REF], supporting its role in maintaining ZG cell identity and function [START_REF] Pignatti | Beta-Catenin Causes Adrenal Hyperplasia by Blocking Zonal Transdifferentiation[END_REF]. The observed intratumoral heterogeneity in APA suggested that the interplay between ACTH/cAMP and Wnt/β-catenin pathways may be involved in the transdifferentiation of ZG cells into ZF cells within the APA.

Aldosterone production is regulated by the renin-angiotensin system, potassium concentrations and, to a lesser extent, by the adrenocorticotropic hormone (ACTH) [START_REF] Connell | The new biology of aldosterone[END_REF]. When binding to its receptor (melanocortin type 2 receptor-MC2R), ACTH activates adenylate cyclase (AC) and protein kinase A (PKA), which phosphorylates CREB (cAMP response element binding protein) resulting in increased StAR (steroidogenic acute regulatory protein) expression [START_REF] Hattangady | Acute and chronic regulation of aldosterone production[END_REF].

In addition, paracrine regulation of aldosterone production is mediated by factors released by components of the APA microenvironment, i.e. chromaffin cells, endothelial cells, nerve fibers and immune cells [START_REF] Duparc | Mast cell hyperplasia is associated with aldosterone hypersecretion in a subset of aldosterone-producing adenomas[END_REF][START_REF] Ehrhart-Bornstein | Intraadrenal interactions in the regulation of adrenocortical steroidogenesis[END_REF][START_REF] Wils | The neuropeptide substance P regulates aldosterone secretion in human adrenals[END_REF][START_REF] Lopez | Role of Mast Cells in the Control of Aldosterone Secretion[END_REF]. Serotonin (5-HT) released by perivascular mast cells is known to induce aldosterone production. Different signals may stimulate mast cell degranulation such as neurotransmitters, neuropeptides and hormones [START_REF] Theoharides | Neuroendocrinology of mast cells: Challenges and controversies[END_REF]. However, the control of mast cell degranulation in the adrenal gland is not well clarified [START_REF] Duparc | Mast cell hyperplasia is associated with aldosterone hypersecretion in a subset of aldosterone-producing adenomas[END_REF][START_REF] Hinson | The relationship between adrenal vascular events and steroid secretion: the role of mast cells and endothelin[END_REF]. A peculiar feature of the adrenal gland is also the very high expression of VEGF, even in adulthood, despite the absence of active angiogenesis [START_REF] Thomas | Role of adrenocorticotropic hormone in the development and maintenance of the adrenal cortical vasculature[END_REF][START_REF] Feige | Angiogenesis in adrenocortical physiology and tumor development[END_REF]. ACTH controls the coordinated development of vessels and endocrine cells. In this context, the role of VEGFA, whose expression is controlled by ACTH, is to maintain a high density of stable fenestrated microvessels [START_REF] Thomas | Role of adrenocorticotropic hormone in the development and maintenance of the adrenal cortical vasculature[END_REF][START_REF] Feige | Angiogenesis in adrenocortical physiology and tumor development[END_REF]. The combined secretion of angiogenic factors by endocrine cells and trophic factors by endothelial cells allows the maintenance of a "symbiosis" between these cellular compartments.

The aim of this study was to investigate the relationship between different signaling pathways and components of the microenvironment in adrenals with APA to better understand the mechanisms driving the development of aldosterone producing structures and intratumoral heterogeneity. We performed detailed morphological investigations of 11 adrenals with APA and one with micronodular hyperplasia using multiplex immunofluorescence multispectral image analysis. In addition, CYP11B2 IHC guided RT-qPCR was performed on RNA extracted from formalin-fixed paraffin-embedded (FFPE) tissues in 7 adrenals. Results were correlated with the APA mutation status.

Materials and methods:

Patients

Patients included in this study underwent adrenalectomy between 2013 and 2016 at the Hôpital Européen Georges Pompidou and were recruited within the COMETE-HEGP protocol (authorization CPP 2012-A00508-35) and are described in [START_REF] Sousa | Genetic, Cellular, and Molecular Heterogeneity in Adrenals With Aldosterone-Producing Adenoma[END_REF]. Screening and subtype identification of PA were performed according to institutional and Endocrine Society guidelines [START_REF] Funder | Case detection, diagnosis, and treatment of patients with primary aldosteronism: an endocrine society clinical practice guideline[END_REF][START_REF] Amar | SFE/SFHTA/AFCE primary aldosteronism consensus: Introduction and handbook[END_REF][START_REF] Baron | Criteria for diagnosing primary aldosteronism on the basis of liquid chromatography-tandem mass spectrometry determinations of plasma aldosterone concentration[END_REF], 16 adrenals from patients with APA and two adrenal blocs from one patient with multinodular hyperplasia were investigated for a total of 18 samples from 17 patients (Table 1).

All patients gave written informed consent for genetic and clinical investigation. Procedures were in accordance with institutional guidelines. APA mutational status has been described in [START_REF] Sousa | Genetic, Cellular, and Molecular Heterogeneity in Adrenals With Aldosterone-Producing Adenoma[END_REF].

Multiplex immunofluorescence

Multiplex immunofluorescence staining was performed with the Opal 7-color Manual IHC Kit (PerkinElmer) in two separate sets of experiments. Sections were deparaffinised in xylene and rehydrated through graded ethanol before washing with distilled water and TBST (0.1 M Tris-HCl, pH 7.5, 0.15 M NaCl, 0.05 % Tween 20). Sections were re-fixed by 20 min incubation in 4% paraformaldehyde followed by a distilled water wash. The slides were incubated in AR6 buffer (1/10; PerkinElmer) and subjected to microwave treatment for 15 minutes at 20% power for antigen unmasking. Nonspecific staining was blocked with blocking solution (PerkinElmer) for 10 minutes. Given the complexity of the setup of multiplex immunofluorescence either CYP11B1 or CYP17A1 were used to identify ZF cells.

For a first multiplex immunofluorescence, the slides were incubated with a mouse monoclonal antibody against aldosterone-synthase (1/100, hCYP11B2, clone 41-13C, kindly provided by Dr C Gomez-Sanchez, RRID: AB_2650562), rabbit polyclonal antibody against 17α-hydroxylase (1/1000, LSBio #LS-B14227, RRID: AB_2857939), mouse monoclonal antibody against β-catenin (1/400 ; BD Biosciences #610153, RRID: AB_397554), rabbit polyclonal antibody against MC2R (1/200, Abgent #AP5540b, RRID: AB_10820209), and a rabbit monoclonal antibody against pCREB (Ser133) (1/500, Cell signaling technology #9198, RRID: AB_2561044). For a second multiplex immunofluorescence, the slides were incubated with a mouse monoclonal antibody against mast cell tryptase (1/10000, BIO-RAD #MCA1438, RRID: AB_2206190), rabbit monoclonal antibody against S100 protein (1/2, Agilent #GA50461-2, RRID: AB_2811056), antibody against 11β-hydroxylase (1/100, hCYP11B1-80-2-2, kindly provided by Dr C Gomez-Sanchez, RRID: AB_2650563), and a mouse monoclonal antibody against CD34 (1/5000, ThermoFisher #MA1-10202, RRID: AB_11156010) during 1h at room temperature. Sections were washed and incubated with secondary antibody working solution (PerkinElmer) during 10 minutes; for CYP11B1 the slides were incubated with an anti-rat secondary antibody (1/400, ImmPRESS Anti-Rat IgG, Vector Laboratories #MP-7404, RRID: AB_2336531) during 1h at room temperature. Then, slides were incubated for 10 minutes in TSA plus solution (included in the Opal 7-color manual IHC kit to detect antibody staining), prepared according to the manufacturer's instructions: Opal 570 (1/100), Opal 650 (1/100 -1/200 for S100), Opal 690 (1/50), Opal 540 (1/50 -1/100 for CYP11B1), Opal 520 (1/50), Opal 620 (1/200). Microwave treatment was performed to remove primary and secondary antibodies while retaining an intact fluorescent signal. This process was repeated until all targets of interest were detected, using the respective Opal fluorophore for each one. The slides were counterstained with DAPI (PerkinElmer) for 5 minutes.

Immunohistochemistry

Sections were deparaffinised in xylene and rehydrated through graded ethanol. For antigen unmasking, the slides were incubated 30 min at 98°C in Trilogy solution (1/20) (Sigma-Aldrich; St Louis, MO USA) for aldosterone-synthase (CYP11B2) and 11β-hydroxylase (CYP11B1) immunohistochemistry, or in a citrate solution (0.935%, Vector Laboratories; Burlingame, USA) for immunostaining against CD34, mast cell tryptase, pCREB, MC2R and β-catenin. No antigen unmasking was performed for S100 immunostaining. Endogenous peroxidases were inhibited by incubation in 3% hydrogen peroxide (Sigma-Aldrich) for 10 min. Nonspecific staining was blocked with filtered Tris 0.1 M pH 7.4, 10% normal goat serum, 10% bovine serum albumin, and 0.1% SDS for 90 min (for 11 β-hydroxylase staining); filtered Tris 0.1 M pH 7.4, 10% horse serum and 0.5% SDS for 60 min (for aldosterone-synthase staining) or with PBS 1x and 10% normal goat serum for 30 mins (for CD34, mast cell tryptase, S100, β-catenin, MC2R, and pCREB stainings). The slides were incubated overnight at 4°C (aldosteronesynthase, 11β-hydroxylase, and pCREB stainings) or during 1h at room temperature (β-catenin MC2R, mast cell tryptase, S100 protein and CD34 stainings), using the same antibodies and same dilutions described for multiplex immunofluorescence experiments. Sections were washed, incubated 30 min with affinity purified horse anti mouse secondary antibody for aldosterone-synthase, β-catenin, CD34 and mast cell tryptase stainings (1/400, Vector Laboratories #BP-2000, RRID: AB_2687893), rabbit anti rat antibody for 11β-hydroxylase antibody (1/400, Vector Laboratories #BA-4001, RRID: AB_10015300), or an anti-rabbit secondary antibody for MC2R, S100 and pCREB stainings (1/400, Vector Laboratories #BA-1000, RRID: AB_2313606). Slides were washed and incubated with an avidin-biotinperoxydase complex (Vectastain ABC Elite; Vector Laboratories) for 30 min. The slides were developed using diaminobenzidin (Vector Laboratories; Burlingame, USA) and counterstained with hematoxilin (Sigma-Aldrich; St Louis, MO USA).

Analysis and quantification of histological features

Multiplex immunofluoresence and immunohistochemistry images were acquired using a Vectra® automated imaging system and automatically quantified with the InForm® image analysis package (both Perkin Elmer; Waltham, USA). Each monoplex biomarker was used to generate the spectral library required for multispectral analysis. Tryptase positive cells and S100 positive fibers were counted as objects, and CD34 positive vessels as area based on their staining in CYP11B2 expressing and non expressing areas. The quantification of these markers was automatically performed with inForm. Areas in 11 APA were selected to allow the determination of colocalization of aldosterone-synthase (CYP11B2), 17α-hydroxylase (CYP17A1), MC2R, pCREB and cytoplasmic and nuclear staining for β-catenin, which was automatically quantified using InForm® (Perkin Elmer; Waltham, USA).

The distance between mast cells and nerve fibers was measured using the Icy software (http://icy.bioimageanalysis.org/).

RNA extraction and RT-qPCR

RNA was co-extracted with DNA from formalin-fixed paraffin-embedded (FFPE) sections using AllPrep DNA/RNA FFPE kit (Qiagen). Before extraction, APA and aldosterone producing cell clusters (APCC) were identified by CYP11B2 immunohistochemistry (IHC) as described in [START_REF] Sousa | Genetic, Cellular, and Molecular Heterogeneity in Adrenals With Aldosterone-Producing Adenoma[END_REF]. Based on the CYP11B2 IHC, the areas of interest were delineated and isolated for DNA and RNA extraction by scraping unstained FFPE sections guided by the CYP11B2 IHC slide using a scalpel under a Wild Heerbrugg microscope. 250 ng of total RNA were retrotranscribed (iScript reverse transcriptase, Biorad, Hercules, CA).

Primers used for amplification of MC2R (qHsaCEP0054989) and MRAP (qHsaCID0022591) were purchased from BioRad. The sequence of primers used for MRAP2, VEGFA, 18S, and GAPDH can be provided upon request. Quantitative PCR was performed using SYBRgreen (Sso advanced universal SyBr Green supermix, Biorad, Hercules, CA) on a C1000 touch thermal cycler (Biorad CFX96 Real Time System), according to the manufacturer's instructions. Controls without template were included to exclude primer dimer formation or PCR contaminations. RT-qPCR products were analyzed in a post amplification fusion curve to ensure that a single amplicon was obtained. Normalization for RNA quantity, and reverse transcriptase efficiency was performed against two reference genes (geometric mean of the expression of Ribosomal 18S and GAPDH RNA). Quantification was performed using the standard curve method. Standard curves were generated using serial dilutions from a cDNA pool of all samples of each experiment, yielding a correlation coefficient of at least 0.98 in all experiments.

Statistical Analyses

Quantitative variables are reported as mean +/-SEM. Comparisons between groups were done with unpaired t-test when Gaussian distribution or the Mann-Whitney test when no Gaussian distribution. A p value < 0.05 was considered significant for comparisons between 2 groups.

Results

Elements of paracrine regulation of aldosterone biosynthesis in APA

11 adrenals with APA were analysed by multiplex immunofluorescence to study the cellular environment and markers of paracrine regulation: mast cells were labelled with tryptase, nerve cells with S100, and vascular endothelial cells were labelled with CD34. In addition, the Wnt/βcatenin and ACTH/cAMP/PKA pathways involved in the maintenance and function of the adrenal cortex were investigated (Figure 1). These APA carry somatic mutations previously identified by Sanger sequencing and IHC-guided targeted NGS, including 2 KCNJ5 mutations, 3 CACNA1D mutations, 3 ATP1A1 mutations, and 3 ATP2B3 mutations (Table 1).

Multiplex immunofluorescence revealed abundance of tryptase positive mast cells and a dense vascular component in APA independently of the mutational status. Remarkably, in all APA analysed, the majority of mast cells were found in areas expressing CYP11B2, in contrast to areas not expressing CYP11B2 or areas expressing CYP11B1 (p<0.0001) (Figure 2A-B). There was no difference of vascular surface between CYP11B2 expressing and non-expressing areas (p=0.1214) (Figure 2C). APA also contained nerve fibers whose localisation was independent of the expression of CYP11B2 (p=0.6614) (Figure 2D). Remarkably, colocalization of mast cells and nerve fibers, which would suggest innervation of mast cells, was rarely observed (Figure 3A). Indeed, measurement of the distance between mast cells and nerve fibers in the 11 APA included in our study showed a mean distance between immune cells and nerve fibers of 80.27 µm, with important intratumoral heterogeneity (Figure 3B). Multiplex immunofluorescence on selected areas revealed cellular co-expression of CYP11B2 with activated i.e. nuclear and/or cytoplasmic staining of β-catenin in the majority of cells, in contrast to areas expressing CYP17A1, independently of the mutational status of APA, as previously described (10) (Figure 1). Finally, mast cells were found both within the APA and in the adjacent adrenal cortex, often in close proximity to vascular cells (Figure 4).

Expression of components of ACTH signaling and vascularization

Expression of MC2R was more frequently observed in CYP11B2 positive areas in comparison to areas expressing CYP17A1. Among cells expressing CYP11B2, 68% coexpress MC2R; in contrast, only 15% of CYP17A1 positive cells express also MC2R and this pattern is independent of the mutation status (Figure 5A-B). Expression of pCREB in APA was observed in ≈11% of cells and mainly observed in APA with CACNA1D mutations. pCREB does not appear to be co-localized with CYP11B2 nor CYP17A1 in any of the mutational groups (Figure 5C-D). Co-expression of pCREB in cells expressing MC2R was also low (Figure 5E) suggesting that MC2R expression is not correlated to PKA signaling in those cells.

For a better understanding of the control of the ACTH/cAMP signaling pathway in APA and its interaction with the vascular component, the expression of MC2R, MRAP, MRAP2 and VEGFA was investigated by RT-qPCR in five APA included in the multiplex immunofluorescence study. Three APA carried a CACNA1D mutation, one carried an ATP2B3 mutation and in one APA no mutation had been identified; in addition, a nodule not expressing CYP11B2 and not carrying somatic mutations in any of the APA driver genes was included (Table 1, Figure 6A-B). In addition, different areas expressing or not CYP11B2 from two APA carrying KCNJ5 mutations were also analysed by RT-qPCR (Figure 7A).

MC2R mRNA was expressed in three out of four APA included in our study, although at different levels (Figure 6C). Interestingly, in one adrenal gland presenting a small APA and a large nodule not expressing CYP11B2, MC2R was expressed only in the APA, but not in the CYP11B2 negative nodule (Figure 6C). MRAP and MRAP2 are accessory proteins for MC2R signaling [START_REF] Webb | Minireview: the melanocortin 2 receptor accessory proteins[END_REF]. MRAP expression was observed in APA from patients 25 (non-mutated), 42 (CACNA1D mutated) and 56 (ATP2B3 mutated) (Figure 6D), but not in APA from patients 10 and 34 (CACNA1D mutated); MRAP2 was not expressed in any of the samples (data not shown).

Within heterogeneous APA carrying KCNJ5 mutations (Figure 7A), the expression of the MC2R gene was higher in areas expressing CYP11B2 in comparison to areas not expressing CYP11B2 (Figure 7B). MRAP was expressed heterogeneously in APA but independently of CYP11B2 expression (Figure 7C), while again MRAP2 expression was not found (data not shown).

The expression of VEGFA was found in all APA as well as in the CYP11B2 negative nodule of patient 56, independently of the APA mutation status (Figure 6E). Within heterogeneous APA, expression of VEGFA was higher in areas expressing CYP11B2 in comparison to areas not expressing CYP11B2, and grossly followed the pattern of MC2R expression in the majority of zones investigated (Figure 7D).

ACTH and β-catenin signaling pathways and paracrine regulation in other aldosterone

producing lesions from adrenals with APA Within our adrenal samples, several APCC and secondary nodules not expressing CYP11B2 were present, including multiple APCC in one adrenal with micronodular hyperplasia. The mutational status of 13 APCC from three adrenals carrying an APA, and four APCC and one pAATL from one adrenal with micronodular hyperplasia had previously been assessed by CYP11B2 immunohistochemistry-guided NGS [START_REF] Sousa | Genetic, Cellular, and Molecular Heterogeneity in Adrenals With Aldosterone-Producing Adenoma[END_REF]. Three APCC carried KCNJ5 mutations, seven carried CACNA1D mutations and in seven APCC no mutations were identified (Table 1).

Remarkably, all APCC in adrenals with APA or with micronodular hyperplasia showed cytoplasmic and/or nuclear β-catenin coexpressed with CYP11B2, independently of the mutational status; nuclear pCREB expression was also observed, indicating an activation of both signaling pathways in APCC (Figure 8). For technical reasons, in these structures acquisition of MC2R labeling on Opal was not possible, thus MC2R expression in the same APCC was investigated by IHC. MC2R was strongly expressed at the membrane and in the cytoplasm of cells composing the APCC (Figure 9). Nuclear pCREB was also strongly expressed in the APCC, as well as in the ZG, similar to activated β-catenin (Figure 8).

Remarkably, accumulation of mast cells was observed around APCC with a reorganization of the vascular network, where the centripetal capillaries follow the CYP11B2 positive cells (Figure 8); in some cases, mast cells were observed in close proximity to vascular cells (Figure 4). Nerve fibers labeled by S100 were hardly detected in APCC.

Remarkably, in the pAATL the outer part expresses CYP11B2 and the inner part is CYP17A1 positive (Figure 10). Activated β-catenin, a reduced vascular network, nuclear pCREB expression and an abundant number of mast cells were observed in the external part of the structure coexpressed with CYP11B2 (Figure 10). In contrast, the inner part of the pAATL did not express activated β-catenin and pCREB, showed a more organised vascular network and less mast cells. MC2R expression was homogeneous in the pAATL (Figure 10). This differential pattern was observed, although the inner and outer part of the pAATL carry the same CACNA1D mutation (Table 1).

A secondary nodule non-expressing CYP11B2 from patient 56 was also analysed. This nodule, which does not carry a somatic mutation (Table 1), expresses CYP17A1, shows nuclear expression of pCREB and heterogeneous expression of activated β-catenin but no expression of MC2R (Figure 11).

Discussion

The Wnt/β-catenin, ACTH/cAMP/PKA signaling pathways and paracrine pathways play an important role in steroidogenesis and adrenal development [START_REF] Pignatti | Regulation of zonation and homeostasis in the adrenal cortex[END_REF], but their role in the development of APA and other aldosterone producing structures in the context of somatic mutations as well as their interactions remain unclear. Although previous studies have investigated individual components of this pathways independently, here we applied multiplex immunofluorescence and multispectral image analysis to investigate proteins involved in aldosterone (CYP11B2) and cortisol (CYP11B1/CYP17A1) biosynthesis, in addition to markers of Wnt/β-catenin (β-catenin) and ACTH/cAMP/PKA (MC2R, pCREB) signaling, as well as paracrine pathways of the tumor microenvironment (Tryptase, S100) and vascularisation (CD34), in adrenals with APA and with micronodular hyperplasia. Our results show a high abundance of mast cells and dense vascularisation in APA, which is independent of the mutation status. Mast cells were mainly localized in zones expressing aldosterone synthase within the tumour. In cells expressing aldosterone synthase, β-catenin is activated and MC2R is highly expressed and found at the cell membrane; VEGFA expression was more important in areas expressing CYP11B2 suggesting regulation by ACTH signaling. In APCC, β-catenin is activated and co-expressed with aldosterone synthase; a high number of mast cells are observed in these areas with a reorganisation of the blood vessels following the cellular arrangement of steroidogenic cells. Strong nuclear pCREB expression was also observed in these structures, together with MC2R expression.

Our results confirm that mast cells are abundant in APA [START_REF] Lopez | Role of Mast Cells in the Control of Aldosterone Secretion[END_REF]. In addition, our study shows that mast cells accumulate next to CYP11B2 positive cells in APA, supporting their specific contribution to aldosterone biosynthesis. Indeed, several studies have demonstrated that mast cells are able to stimulate aldosterone production through the secretion of serotonin and the activation of intracellular calcium signaling [START_REF] Lefebvre | Production and metabolism of serotonin (5-HT) by the human adrenal cortex: paracrine stimulation of aldosterone secretion by 5-HT[END_REF][START_REF] Boyer | Dysregulation of Aldosterone Secretion in Mast Cell-Deficient Mice[END_REF][START_REF] Hinson | Adrenal mast cells modulate vascular and secretory responses in the intact adrenal gland of the rat[END_REF]. It is well known that the adrenal cortex is richly innervated and contains vasoactive intestinal peptide, substance P and neuropeptide Y peptidergic fibers, which may influence aldosterone synthesis through a paracrine regulation [START_REF] Wils | The neuropeptide substance P regulates aldosterone secretion in human adrenals[END_REF]. Although it has been shown that neuronal mechanisms are involved in mast cell activation [START_REF] Duparc | Mast cell hyperplasia is associated with aldosterone hypersecretion in a subset of aldosterone-producing adenomas[END_REF], supporting the possibility that the sympathetic system can influence the function of a subgroup of APA, colocalization of mast cells and nerve fibers was rarely observed in APA in our study, suggesting that mast cell degranulation is not primarly stimulated by nerve fibers.

These results are in accordance with previous work showing only occasionally contacts between mast cells and nerve terms in APA tissues [START_REF] Duparc | Mast cell hyperplasia is associated with aldosterone hypersecretion in a subset of aldosterone-producing adenomas[END_REF]. However, although we have quantified between 50-100% of the surface of each APA, we cannot exclude that some interactions may have been missed; also local concentrations of neurotransmitters may signal to mast cells at distance.

The Wnt/β-catenin and ACTH/cAMP/PKA signaling pathways are both involved in cell differentiation and function of the ZG and ZF. Although only ≈5% of APA carry CTNNB1 mutations, β-catenin is activated in a majority of them [START_REF] Berthon | WNT/beta-catenin signalling is activated in aldosterone-producing adenomas and controls aldosterone production[END_REF]. In certain cases, CTNNB1 mutations alone, arising in the ZG, may suffice to induce development of APA maintaining the ZG phenotype of the tumor. In other cases, CTNNB1 may contribute to tumor formation in APA carrying other types of mutations, by promoting cell proliferation or nodule formation either as a first hit due to somatic mutations or because of its activation due to mechanisms that need to be identified. The two hit model is supported by the identification of somatic GNAQ/GNA11 mutations in CTNNB1 mutated APA in patients with PA presenting at puberty, pregnancy or menopause [START_REF] Zhou | Somatic mutations of GNA11 and GNAQ in CTNNB1-mutant aldosterone-producing adenomas presenting in puberty, pregnancy or menopause[END_REF], as well as the occurrence of KCNJ5 mutations in adrenals from patients with FAP carrying germline APC mutations [START_REF] Vouillarmet | Aldosterone-Producing Adenoma With a Somatic KCNJ5 Mutation Revealing APC-Dependent Familial Adenomatous Polyposis[END_REF].

Previous studies have shown that the expression of MC2R is higher in APA compared to the normal adrenal gland [START_REF] Ye | G-protein-coupled receptors in aldosterone-producing adenomas: a potential cause of hyperaldosteronism[END_REF]. Our results showed that MC2R was highly expressed in areas expressing CYP11B2 in APA, a result which was confirmed by MC2R gene expression studies of different regions of APA expressing or not CYP11B2. In contrast, expression of pCREB in APA was low and did not show any particular colocalization with either CYP11B2, CYP17A1 or MC2R, suggesting that CREB phosphorylation is independent of MC2R activation in APA.

We further investigated the activity of the ACTH signaling pathway by studying two accessory proteins MRAP and MRAP2 known to initiate or inhibit MC2R activation respectively [START_REF] Novoselova | Melanocortin receptor accessory proteins in adrenal gland physiology and beyond[END_REF].

While we did not observe any expression of MRAP2, the expression of MRAP was heterogeneous and independent of CYP11B2 expression, both across APA and within heterogeneous APA carrying KCNJ5 mutations. Altogether, these results suggest that in APA, ACTH may be involved in the regulation of aldosterone production by signaling through MC2R/MRAP and activation of calcium rather than CREB signaling. Indeed, activation of calcium signaling by ACTH has been previously shown, involving activation, through phosphorylation via PKA, of voltage gated calcium channels [START_REF] Hattangady | Acute and chronic regulation of aldosterone production[END_REF][START_REF] El Ghorayeb | Role of ACTH and Other Hormones in the Regulation of Aldosterone Production in Primary Aldosteronism[END_REF][START_REF] Gallo-Payet | YEARS OF POMC: Adrenal and extra-adrenal functions of ACTH[END_REF].

APA are highly vascularized structures. Although we did not observe intratumoral heterogeneity in vascularization by multiplex immunofluorescence, VEGFA expression was more important in areas expressing CYP11B2 in contrast to areas not expressing CYP11B2.

The increase of VEGFA expression in these areas may be explained by the presence of perivascular mast cells, which are involved in the maintenance of angiogenesis, as shown in pancreatic islet tumors [START_REF] Soucek | Mast cells are required for angiogenesis and macroscopic expansion of Myc-induced pancreatic islet tumors[END_REF], or alternatively by the activation of the ACTH/cAMP pathway via MC2R, as MC2R is highly expressed in these same regions. Indeed, in the adrenal gland, ACTH stimulates the release of VEGF and the stabilisation of its mRNA [START_REF] Lefebvre | Role of ACTH in the Interactive/Paracrine Regulation of Adrenal Steroid Secretion in Physiological and Pathophysiological Conditions[END_REF]. Furthermore, it has been suggested that changes in the vascular supply of the adrenal cortex, due to phenomena of atherosclerosis or high blood pressure, may influence the function of the adrenal cortex, resulting in compensatory adrenal cortex hyperplasia and eventually nodulation [START_REF] Sasano | Adrenal Cortex[END_REF].

Remarkably, investigation of APCC revealed similar patterns of expression as observed in APA, although with some peculiar features. We observed abundant mast cells in APCC, supporting a role for paracrine regulation of autonomous aldosterone production in these structures. The localization of mast cells close to blood vessels and within CYP11B2 positive areas suggest that they may influence mineralocorticoid production directly and/or via the blood flow. Furthermore, all APCC in adrenals with APA or with micronodular hyperplasia showed nuclear and/or cytoplasmic β-catenin coexpressed with CYP11B2, independently of the mutational status. In contrast to APA, strong nuclear pCREB expression was also observed, together with MC2R expression, suggesting ACTH signaling via PKA/pCREB in APCC.

MC2R was previously identified as a highly expressed gene in APCC [START_REF] Nishimoto | Aldosterone-stimulating somatic gene mutations are common in normal adrenal glands[END_REF]. These results indicate that in APCC both ACTH/cAMP as well as Wnt/β-catenin signaling are activated, suggesting that APCC may be intermediary structures in terms of cell lineage between the ZG and the ZF. This hypothesis is supported by previous work showing characteristics of both ZG and ZF within the same structures [START_REF] Boulkroun | Aldosterone-producing adenoma formation in the adrenal cortex involves expression of stem/progenitor cell markers[END_REF]. The presence of mast cells in these structures may contribute to the activation of PKA signaling pathway via serotonin/5HT4 signaling (50) and be involved in the autonomous aldosterone production. The additional activity of the calcium signaling pathway in regulating CYP11B2 expression and aldosterone production in APCC is supported by the presence of somatic mutations in APA-driver genes that have been previously shown to activate calcium signaling. These finding suggests that different signalling pathways are involved in the development and maintenance of APCC.

Remarkably, in a nodule non expressing CYP11B2 from an adrenal with APA, mast cells were present but localized to the areas not expressing CYP11B1 either. This is consistent with previous studies showing that mast cell proliferation is observed in a deoxycorticosteronesecreting tumor and APA but not in cortisol-secreting adenomas (51), suggesting that mast cells may preferentially favour proliferation of glomerulosa cells [START_REF] Duparc | Mast cell hyperplasia is associated with aldosterone hypersecretion in a subset of aldosterone-producing adenomas[END_REF] and mineralocorticoid secretion.

In conclusion, our results show that aldosterone producing structures in adrenals with APA share common molecular characteristics and cellular environment, despite different mutation status, suggesting common developmental mechanisms. In particular, mast cells appear to be closely associated with cells expressing aldosterone synthase, both in APA and APCC, and their degranulation seems not to be regulated by innervation. In these same areas, activation of ßcatenin indicates a zona glomerulosa cell identity. Activation of PKA signalling was heterogeneous in aldosterone producing structures, suggesting different signalling pathways activated by ACTH and serotonin to drive aldosterone biosynthesis.

Figure 1 .

 1 Figure 1. Signaling pathways and cellular environment in APA. A, Colocalization of

Figure 2 .

 2 Figure 2. Distribution of components of the microenvironment in different regions of

Figure 3 .

 3 Figure 3. Interaction between nerve fibers and mast cells in APA. A. The distance between

Figure 4 .

 4 Figure 4. Perivascular localization of mast cells in APA. APA tissues from three patients

Figure 5 .

 5 Figure 5. Expression of components of PKA signaling in APA. Automatic quantification of

Figure 6 .

 6 Figure 6. Expression of genes involved in ACTH/cAMP signalling and vascularization. (A)

Figure 7 .

 7 Figure 7. Expression of genes involved in ACTH/cAMP signaling and vascularization and

Figure 8 .

 8 Figure 8. Expression and activation of signaling pathways and paracrine pathways in

Figure 9 .

 9 Figure 9. Comparison between IHC and multiplex immunofluorescence in APCC. For

Figure 10 :

 10 Figure 10: Expression and activation of signalling pathways and paracrine pathways in

Figure 11 :

 11 Figure 11: Wnt/β-catenin and ACTH/cAMP signaling in a nodule not expressing

Table 1 . Samples analyzed in this study.

 1

	559
	Patient ID	Structure	CYP11B2 staining	Mutation	Multiplex Immunofluorescence study	Gene expression study
	1	APA	Yes	ATP2B3	Yes
	4	APA	Yes	CACNA1D	Yes
		APCC3	Yes	CACNA1D	Yes
		APCC4	Yes	KCNJ5	Yes
		APCC5	Yes	Neg	Yes
		APCC6	Yes	Neg	Yes
		APCC7	Yes	Neg	Yes
	8	APA	Yes	CACNA1D	Yes
		APA	Yes	CACNA1D		Yes
		APA	Yes	ATP1A1	Yes
		APA	Yes	Neg		Yes
		APA	Yes	ATP1A1	Yes
		APA	Yes	CACNA1D		Yes
		APA	Yes	ATP2B3	Yes
		APA	Yes	KCNJ5
		APA zone 1	No	KCNJ5		Yes
		APA zone 2	Yes	KCNJ5		Yes
		APA zone 3	Yes	KCNJ5		Yes
		APA zone 4	No	KCNJ5		Yes
		APA	Yes	CACNA1D	Yes
		APCC1	Yes	Neg	Yes
		APCC2	Yes	CACNA1D	Yes
		APCC4	Yes	CACNA1D	Yes
				CACNA1D	Yes
				CACNA1H	Yes
		APCC5	Yes	KCNJ5	Yes
		APA	Yes	CACNA1D		Yes
		APA	Yes	KCNJ5	Yes
		APA zone 1	No	KCNJ5		Yes
		APA zone 2	Yes	KCNJ5		Yes
		APA	Yes	KCNJ5	Yes
		APCC2	Yes	CACNA1D	Yes
		APCC4	Yes	KCNJ5	Yes
		APCC1	Yes	Neg	Yes
		APCC3	Yes	Neg	Yes
		APA	Yes	ATP1A1	Yes
		APA	Yes	ATP2B3	Yes	Yes
		Nodule	No	Neg	Yes	Yes
	48 bloc1	APCC1	Yes	CACNA1D	Yes
		APCC2	Yes	Neg	Yes
		APCC3	Yes	CACNA1D	Yes
		APCC6	Yes	CACNA1D	Yes
	48 bloc4	pAATL B2+	Yes	CACNA1D	Yes
		pAATL B2-	No	CACNA1D	Yes

Acknowledgments

The authors wish to thank CE Gomez-Sanchez (University of Mississippi Medical Center, Jackson, MS) for providing antibodies against CYP11B1 and CYP11B2.

Funding

This work was funded through institutional support from Inserm, the Agence Nationale de la Recherche (ANR-15-CE14-0017-03), and the Fondation pour la Recherche Médicale (DEQ20140329556).

Data availability

Some or all datasets generated during and/or analyzed during the current study are not publicly available but are available from the corresponding author on reasonable request.

Declaration of interest

The authors have nothing to disclose

Declaration of interest

The authors have nothing to disclose


Thibaut Divoux

Eric Bertin

Valérie Vidal

Jean-Christophe Géminard

Intermittent outgassing through a non-Newtonian fluid

Keywords: numbers: 05.45.-a, 05.40.-a, 47.57-s, 83.60.Rs, 91.40.Hw

We report an experimental study of the intermittent dynamics of a gas flowing through a column of a non-Newtonian fluid. In a given range of the imposed constant flow rate, the system spontaneously alternates between two regimes: bubbles emitted at the bottom either rise independently one from the other or merge to create a winding flue which then connects the bottom air-entrance to the free surface. The observations are reminiscent of the spontaneous changes in the degassing regime observed on volcanoes and suggest that, in the nature, such a phenomenon is likely to be governed by the non-Newtonian properties of the magma. We focus on the statistical distribution of the lifespans of the bubbling and flue regimes in the intermittent steady-state. The bubbling regime exhibits a characteristic time whereas, interestingly, the flue lifespan displays a decaying powerlaw distribution. The associated exponent, which is significantly smaller than the value 1.5 often reported experimentally and predicted in some standard intermittency scenarios, depends on the fluid properties and can be interpreted as the ratio of two characteristic times of the system.

I. INTRODUCTION

A large number of physical systems driven far from equilibrium exhibit an intermittent behavior, where quiet phases (off -state) randomly alternate with periods of strong activity (on-state). Experimental examples in physical systems include electronic devices [1], spin-wave instabilities [2], plasma produced by a gas discharge [3], liquid crystals [4,5], and nanoscopic systems such as single molecules [6], nanocrystal quantum-dots [7], or nanoparticles diffusing through a laser focus [8]. Intermittency has also been reported in other disciplinary fields, like in the example of the sleep-wake transitions during sleep [9]. A standard characterization of the intermittency phenomenon is the distribution of time spent in the off-state. Interestingly, in most of the experimental studies reported so-far [1][2][3][4][5][6][7][8], this distribution exhibits a power-law regime with an exponent close to 1.5, with a cut-off at large times. This value of the exponent is wellunderstood theoretically through the so-called scenarios of on-off intermittency [10][11][12] and type-III intermittency [13,[START_REF] Schuster | Deterministic Chaos[END_REF], which both predict a power-law distribution with an exponent 3/2.

A Newtonian fluid flowing through a non-Newtonian material is alike to present different escaping regimes [START_REF] Zoueshtiagh | [END_REF] as well as an intermittent activity, as previously observed both in physical [16,17] and geophysical [18,19] contexts. In the laboratory, experiments have been conducted in the case of air emission through an immersed granular layer [16]. These studies evidenced different airoutgassing regimes through the non-linear medium at a constant flow rate. In particular, it has been observed that gas emitted at the bottom of an immersed granular layer can cross the whole system through temporary channels, which later spontaneously collapse [16,17]. In a geophysical context, volcanologists reported observations of the degassing process which interestingly exhibits similar temporal patterns [18]. In this case, the gas, released by magma during its rise toward the free surface, plays the role of the Newtonian fluid and magma the role of the non-Newtonian material [20,21]: inside the volcano conduit, dissolved gas gives birth to bubbles, which ascend and burst intermittently at top of the volcano vent [19]. What remains puzzling is the existence of spontaneous changes between different activities (e.g. discrete bursts or continuous puffing [22]) for which the non-Newtonian properties of magma could play an important role [19,23,24].

At the laboratory scale, two kinds of experiments have been previously conducted in order to model the volcanic degassing-activity. On the one hand, experiments were designed to account for the potential effects of the geometry of an underlying magma-chamber [25]. These studies were limited to the case of Newtonian fluids and, besides, did not consider the issue of the time spent in each of the regimes. On the other hand, recent laboratory experiments performed on real rhyolitic melts close to their natural conditions have revealed that during their rise, bubbles deform and coalesce under shear [26] leading to channel-like bubble networks [27]. Those structures were proposed as a key ingredient in the magma degassing process at depth [27], but not directly related to the non-Newtonian rheology of magma.

In this paper, we report an experimental study of the intermittent dynamics of a gas rising through a column of a non-Newtonian fluid. We unravel that this outgassing process can be considered as a two-states process : either it occurs through bubbles rising independently (the bubbling regime, on-state), or through a gas channel which crosses tortuously the whole system (the winding-flue regime, off-state). Let us emphasize here that such an intermittent process, defined in terms of a two-states process (bubbling or channel-like regime), is different from the intermittent regime reported in purely Newtonian fluids, as described in [28]. Indeed, a Newtonian solution cannot sustain the formation of a flue (in contrast to non-Newtonian fluids [29]) and, in this case, intermittency can be related to the formation of antibubbles [28]. Here, we report statistical data concerning the irregular oscillations between the bubbling and the winding flue regimes. Specifically, we measure the statistics of the time spent in both the bubbling and flue regimes. We observe that the lifespan of the flue is characterized by a power-law distribution with an exponent significantly smaller than the often reported exponent 3/2. This non-standard exponent turns out to depend slightly on the rheological properties of the fluid. Using a simple stochastic two-states model, we relate this exponent to the ratio of two characteristic times of the system, that we estimate from the experimental data.

These results might be of interest to the geophysics community as the magma, charged with bubbles, exhibits a flow-threshold and a shear-thinning behavior [19][20][21]30]. Indeed, non-Newtonian rheological properties are likely to explain the existence of different outgassing processes (including bubble networks) and to govern the associated nontrivial statistics.

II. EXPERIMENTAL PROCEDURES A. Experimental setup

The experimental setup (Fig. 1) consists of a vertical plexiglass tube (inner diameter 74 mm, height 270 mm) filled with a non-Newtonian solution. Air is injected at the bottom of the fluid column through an air tank, partially filled with water. The system thus makes it possible to tune the inner free volume V of the tank (ranging from 60 to 800 cm 3 ) by changing the inner amount of water and to inject humid air. Besides, above the fluid column, a small container filled with water maintains a saturated humidity level at the free surface. This way, one avoids any significant drying of the sample during the experimental time. A mass-flow controller (Bronkhorst, Mass-Stream series D-5111) introduces air inside the tank at a constant flow rate Q (from Q min = 0.17 cm 3 /s to Q max = 1.74 cm 3 /s). Air is then injected at the bottom of the fluid column through a nozzle (diameter d = 2.0 mm). Rigid tubes (typical diameter, 8.0 mm) insure the connection between the tank and the column. We measure the variation of the overpressure δP inside the chamber with the help of a low-pressure differentialsensor (Honeywell S&C, 176PC28HD2) connected to a multimeter (Keithley,196). A C++ program records the pressure data (to within 5 Pa) through the GPIB interface over long time-durations (typically a few days) at 5 Hz. As we will see, monitoring the pressure in the tank chamber makes it possible to probe the degassing activity while direct visual observation is obstructed as the gel solution progressively fills up with bubbles (Sec. II C).

The fluid consists in a diluted solution (10% in mass of distilled water, unless otherwise specified) of a commercial hair-dressing gel (Gel coiffant, fixation extra forte, FIG. 1: Sketch of the experimental setup -Air, from a mass-flow controller F , is injected, at a constant flow rate Q, in a chamber (volume V ) connected to the bottom of the fluid column (height h). By means of a presure sensor P , we measure the overpressure δP inside the chamber as a function of time. In the picture on the right-hand-side, one can notice that the density of bubbles trapped into the gel strongly depends on the altitude (The scale is given by the inner diameter of the plexiglass tube, 74 mm.)

Auchan). This choice is mainly justified by the fact that one can easily be supplied with large quantities of fluid, reproducible mixtures are rather easy to prepare [31] and they are stable in time if well prevented from drying. Some of the non-Newtonian rheological properties of the fluid are reported in the appendix A. In particular, the solution, when free of bubbles, is shearthinning and we estimated the viscoelastic characteristic time τ c = 1/ γc ≃ 1700 s, compatible with the ratio of the viscosity at low shear-rate η 0 ≃ 6.10 4 Pa.s to the estimated flow threshold σ c ≃ 35 Pa.

B. Preliminary observations

The gel solution is poured inside the tube and a constant flow is imposed. Qualitatively, one observes that the solution starts filling up with small-sized bubbles. These small bubbles, which remain trapped because of the fluid threshold, are further advected by the large bubbles subsequently emitted at the nozzle and progressively a vertical gradient pointing toward the top of the column takes place (Fig. 1). After this transient regime, whose duration depends on the flow rate Q, the fluid column reaches a constant height h, significantly larger than the initial height h 0 . We observe that there exists a flow rate Q b which can be experimentally defined as the most effi-cient flow rate to fill the solution with trapped bubbles. The transient which lasts a few hours for Q ≃ Q b can last days to weeks if Q significantly differs from Q b . Special attention has been paid to the characterization of the bubble gradient and of the associated fluid rheology. Details are reported in the appendix A. Finally, note that all the data reported in this article were obtained after the bubble gradient was established.

C. Experimental protocol

We pointed out that small bubbles remain trapped in the fluid, which might lead to an evolution of the rheological properties through time (aging). Thus, in order to ensure the reproducibility of the experiment, we chose the following experimental protocol : the gel solution, initially free of bubbles, is poured inside the tube; the flow rate is set to the smallest accessible value, Q min ; the overpressure δP is then recorded for, at least, 3 days. Subsequently, the flow rate is increased by steps of amplitude δQ up to the maximum value, Q max . For each value of the flow rate Q, the pressure P is again recorded for, at least, 3 days. Then, the same process is applied to decrease the flow rate Q down to Q min . The whole process will be referred to as a flow rate cycle. For all the experiments reported here, we chose δQ ≃ Q min , corresponding to about ten data points over the experimental range of Q.

III. EXPERIMENTAL RESULTS

A. Overall behavior of the system

We now turn to the study of the pressure recorded inside the tank-chamber. We report δP , the variations of the pressure around its mean value, high-pass filtered at 1 mHz. One immediately notices that the pressure exhibits two distinct behaviors (Fig. 2), which emphasizes rest and activity periods.

Thus, a first crucial result is the following: for a given flow rate, the system spontaneously alternates, in an irregular manner, between two states. Either cusped-like bubbles are emitted at the bottom of the gel column, rise through it and burst at the top independently from one another (the bubbling regime); the corresponding pressure variation δP exhibits successive rises and drops, the latter corresponding to the formation of the bubbles. Or, a channel, previously reported as a 'bubble sausage' [29], connects the bottom air-entrance to the column top (winding flue regime); the corresponding δP is almost constant.

The formation of the flue is linked to the non-Newtonian properties of the hair-gel solution and, as we shall see, to the thixotropy. A rising bubble produces a shear which locally leads to a decrease of the fluid resistance to flow, thus creating an easy path through

τ b (i) τ b (i+1) τ f (i) τ f (i+1) τ f (i+2)
FIG. 2: Typical pressure variation δP (t) vs time t -At a constant flow rate, the typical signal from the pressure sensor exhibits a spontaneous alternation between rest and activity periods. Rapid drops of the overpressure mark the emission of successive bubbles at the bottom of the column whereas an almost-constant overpressure corresponds to a flue connecting the injection hole to the free surface. The analysis consists of measuring the lifespan τ b (resp. τ f ) of the bubble (resp. flue) regime. The figures from top to bottom display the signal at different time scales (h0 = 70 mm, V = 800 cm 3 and Q = 0.35 cm 3 /s).

the fluid column [32]. This process takes place if the time-difference between two successive bubbles is shorter than the typical relaxation time scale of the fluid. Once formed, the flue, subjected to a creep flow under the effect of gravity, slowly deforms and eventually collapses, leading the system back to the bubbling regime. These two mechanisms explain why the system switches quickly between two very different states.

As a first global result, we report the fraction of time, Φ b , spent by the system in the bubbling state at a given flow rate (Fig. 3). Below a certain threshold Q * , the system experiences the bubbling-regime, whereas above Q * the system naturally alternates between the bubbling and winding-flue regimes (We note that Q * ≃ Q b , which is discussed in the appendix B). We point out that the two regions, above and below the transition, are not symmetric: indeed, for Q < Q * , we only observe the bubbling regime (the system is unable to form a flue) whereas, in the case Q > Q * , even for the largest flow rate, the flue always eventually tweaks and collapses (finite lifespan). The critical flow rate Q * is independent of the column height h 0 and of the chamber volume V but depends on the rheological properties of the fluid. and we assessed Q * ≃ 0.3 cm 3 /s for 10% of added water and Q * ≃ 1 cm 3 /s for 15% (Fig. 3). Finally, note that, even if the channel can always collapse at large flow rate, one can identify a flow rate Q + ≃ 1.5 cm 3 /s above which the emission of a single bubble leads to the formation of a new channel (flow rate Q above the gray region in Fig. 3).

From now on, because of the binary behavior of gel column at a given flow rate Q, we shall account for the complex dynamics of the system by considering the overpressure signal as a temporal sequence {τ

(1) f , τ (1) b , τ (2) f , τ (2) b , ..., τ (n) f , τ (n)
b } of the successive flue-(resp. bubbling-) regime lifespans, τ f (resp. τ b ). We aim at estimating the probability distributions p b (τ b ) and p f (τ f ). To do so, we display estimates of the corresponding cumulative probability distributions F b (τ b ) (Fig. 4) and F f (τ f ) (Fig. 6), defined as

F x (τ x ) ≡ ∞ τx p x (τ ) dτ (1)
where x stands for b or f . We sort the sequence {τ

(i) x } into {τ ′(j) x } such that τ ′(1) x > τ ′(2) x > . . . > τ ′(n) x (2)
and plot j/n versus τ ′(j) x [33].

B. Bubbling regime

From the temporal sequence {τ (n) b }, we deduce that there exists a characteristic time, τ * b , to build a flue from the bubbling regime. Indeed, the cumulative probability distribution F b (τ b ) decreases almost exponentially for increasing values of τ b (Fig. 4). Thus, the lifespan τ b of the bubbling regime presents an almost-exponential probability distribution. We report the associated characteristic time τ * b as a function of the flow rate Q for different values of the chamber volume V (Fig. 5). First, τ * b decreases drastically when the flow rate is increased above Q * (Note that τ * b is not defined for Q < Q * as the system is constantly in the bubbling regime and that, for Q > Q + , the measurements are difficult to perform because of the small number of channel collapses during the experimental time.) Second, we observe that τ * b is almost independent of V . In contrast, τ * b depends on the distribution of the small bubbles in the fluid. Indeed, τ * b increases slightly when the fluid column is stirred each time the flow rate is set to a new value (Fig. 5), which reveals the sensitivity of the phenomenon to the rheology of the fluid.

The existence of a characteristic time τ * b associated with the lifespan of the bubbling regime is quite intuitive but the mechanism leading to the formation of the channel is complex. A full description of the phenomenon, which would deserve an extensive study, is beyond the scope of the present article. However, we propose a simple heuristic argument (Appendix B) which suggests to describe the experimental data by the following fitting function (Fig. 5):

τ * b ≃ -τ 0 ln Q c 1 Q * - 1 Q . (3)
The key ingredients are a decrease of the flow threshold (yield stress) due to the shear imposed by the rising bubbles and the thixotropy of the fluid charged with bubbles. Interestingly, the rheological measurements reported in the appendix A point out that the small bubbles enhance the thixotropy and thus play here an important role. From the interpolation of the experimental data, we obtain τ 0 ≃ 65 s, Q c = 0.35 cm 3 /s and Q * ≃ 0.29 cm 3 /s (added-water content 10%, V = 530 cm 3 and V = 800 cm 3 , h 0 = 70 mm). Interestingly, requiring τ * b > 0 in the equation ( 3), we obtain a maximum flow rate 3 /s, which roughly corresponds to the upper limit in figure 3. In order to define this upper limit properly, one must consider instead the flow rate for τ * b to equal the typical time of a bubble emission. We estimate, in this case, that the channel forms immediately, after the emission of a single bubble, for Q > 1.5 cm 3 /s. Thus, even if this rough model must be considered with caution, the proposed mechanism accounts for the existence of a characteristic lifespan τ * b of the bubble regime in a finite range ]Q * , Q + ] of the imposed flow rate, τ * b decreasing when the flow rate Q is increased.

Q + ≡ Q c Q * /(Q c -Q * ) ≃ 1.7 cm

C. Winding flue regime

From the temporal sequence {τ

(n) f }, we observe that, for Q ∈ ]Q * , Q + ], the cumulative distribution F f (τ f ) of the winding-flue lifespan τ f presents a power-law behav- ior, F f (τ f ) ∝ τ -α f for τ f ∈ [τ 1 , τ 2 ]
with τ 1 ∼ 10 s and τ 2 ∼ 1000 s (Fig. 6) and a rapid decay beyond the cut-off time τ 2 . We report in the figure 7 the experimental values of α obtained for flow rates in the gray region defined in the figure 3. We estimate that α = 0.18 ± 0.02, this latter value being independent of Q and V . However, α depends on the spatial distribution of the small bubbles which alter the rheological properties of the fluid (Appendix A). This conclusion is drawn by using a slightly different protocol: in an experimental series, we stirred the solution after each increment in the flow rate and estimated an even smaller value α ≃ 0.1 in this latter case (Fig. 7). We thus observe that α is always significantly lower than the usual value α = 0.5, often reported in experimental observations [1][2][3][4][5][6][7][8] and also expected from some of the theoretical intermittency scenarios, like the on-off intermittency [10][11][12]. Note that such a small value of the exponent (α < 1) imposes a cutoff at long times, τ 2 , which is necessary for the average τ f to exist. Experimentally, the data correspond to an acquisition time of 4 days, which is significantly larger than τ 2 , so that we expect the system to have reached a stationary state [34] and the cut-off not to be due to the finite experimental time. In some sense, τ 2 corresponds to the largest memory time scale during which the stresses in the fluid at rest remain correlated, which is compatible with the viscoelastic time of the fluid, that is to say τ 2 ∼ τ c , thus of the order of 10 3 s (Appendix A).

Hence, the flue lifespan does not exhibit any characteristic timescale in a temporal window between τ 1 and τ 2 in which a power-law distribution with a small exponent is observed. These observations, which lie at the core of the present article, are thoroughly discussed in the section IV. The cumulative probability distribution F f (τ f ) of the time spent in the flue regime exhibits a power-law behavior, up to a large-time cutoff τ2. Curves have been vertically shifted for clarity, and the slope 1/2 characterizing standard on-off intermittency is shown for comparison. Note that the data correspond to an acquisition time of 4 days, which is significantly larger than τ2, so that we expect the system to have reached a stationary state [34] and the cut-off not to be due to the finite experimental time [(Symbol, Q cm 3 /s).

IV. DISCUSSION

As explained above, our main result is the experimental observation that the probability density function of flue lifespans displays a power-law behavior over a broad time window, with a non-standard exponent 1 + α ∼ 1.2, which slightly depends on the rheological properties of the fluid. This result is of particular interest, since in standard intermittency scenarios, the exponent takes a universal value, independent of the details of the dynamics. For instance, in the on-off intermittency scenario, the exponent 1+α = 3/2 is directly related to the first return time probability of a random walk (or a "chaotic walk" in the deterministic case) [12]. In purely deterministic scenarios, like type-I, type-II and type-III intermittency scenarios [13,[START_REF] Schuster | Deterministic Chaos[END_REF], the exponents are related to the classification of bifurcations in dynamical system theory [12][13][START_REF] Schuster | Deterministic Chaos[END_REF]. The corresponding values of the exponent 1 + α in these scenarios (1/2 for type-I intermittency, 2 for type-II and 3/2 for type-III [12,[START_REF] Schuster | Deterministic Chaos[END_REF]) all differ significantly from our experimental values.

In the present experiment, due to both its nonstandard value and its observed dependence on the experimental conditions, α is likely to be related to some rheological or physical properties of the system, rather than to some generic theoretical property. It is thus interesting to relate the measured value of the exponent α to some properties of the gel. A full analysis of this issue is well beyond the scope of the present article, but in order to get some first insights, we propose to describe the data with a simple stochastic model with two states, namely bubble or flue. In such a framework, we write that, after having spent a time τ b in the bubble regime, the system has a probability per unit time (or transition rate) r b (τ b ) to switch to the flue regime. Similarly, we assume that after a time τ f in the flue regime, the transition rate to the bubble regime is r f (τ f ). In the bubble regime, the exponential distribution, F b (τ b ), with the characteristic time τ * b means that the transition rate r b is constant, independent of τ b , and equal to r b = 1/τ * b . In contrast, in the winding-flue regime, the observed powerlaw distribution F f (τ f ) implies that the transition rate r f (τ f ) is not a constant, and thus that a more complex dynamics is at play, even in this phenomenological de-scription. From the relation

dF f dτ f = -r f (τ f ) F f (τ f ), (4)
a power-law behavior F f (τ f ) ∝ τ -α f is found to correspond to r f (τ f ) = α/τ f . Still, the power-law behavior is observed only in a window τ 1 τ f τ 2 , which suggests that, as a first approximation, r f could be taken as a constant outside this window. A simple parameterization of r f (τ f ) leading to such a behavior is given by

r f (τ f ) = 1 τ 0 (1 + τ f /τ 1 ) + 1 τ 2 (5)
provided α = τ 1 /τ 0 and τ 1 ≪ τ 2 . The resulting distribution

F f (τ f ) = e -τ f /τ2 (1 + τ f /τ 1 ) α (6)
behaves as a power law for τ larger than τ 1 , with an exponential cut-off at τ 2 . In the opposite limit τ f ≪ τ 1 , F f (τ f ) can be expanded as

F f (τ f ) ≃ 1 -τ f /τ 0 . (7)
This linear decay of F f (τ f ) at short time can thus be used to evaluate the time scale τ 0 . In addition, the time scale τ 1 can be estimated from the crossover between the linear and power-law behavior. From the experimental data, we assess τ 0 ∼ 30-40 s and τ 1 ∼ 5-8 s. These values lead to a ratio τ 1 /τ 0 in the range 0.12-0.27, compatible with the experimental value of α. We can thus consistently interpret the exponent α as the ratio of two characteristic time-scales: the time τ 1 beyond which the winding flue starts to age (roughly the time for the flue to reach its stationnary shape) and the time τ 0 typically needed for the flue to collapse in the early stationary regime. Finally, note that the time τ 0 is of the same order of magnitude as the time needed for the yield stress of the fluid to relax to its asymptotic value σ c after the shear induced by the rise of a single bubble (see appendix B).

V. CONCLUSION AND OUTLOOKS

We have shown that the flow of a Newtonian fluid into a non-Newtonian one can exhibit an intermittent activity, namely between a bubbling and a winding flue regime. The distribution of the off-state lifespan displays a powerlaw behavior with an exponent about 1.2, which significantly differs from the standard exponent 3/2. A simple stochastic two-states model suggests that this nonstandard exponent could be directly related to the ratio of two timescales characterizing the experimental system.

Our results also contain relevant conclusions in a geophysical context, even if we do not claim at any direct interpretation. We propose that the volcanic intermittent activity observed on the field, which has been hitherto explained in terms of constriction of the magma chamber [25] or by changes in gas flux and/or magma flow rate at depth [18,35], could be (partly) the results of the non-Newtonian properties of magma. Indeed, our simple laboratory experiment demonstrates that, even if a constant gas flow is imposed, one can observe an intermittent activity on top of the fluid column.

A more detailed understanding of this non-standard intermittency phenomenon would certainly be desirable, both from practical and fundamental viewpoints. An extensive study of the dependence of the exponent α on the physical properties of the fluid (rheological properties, surface tension [36], . . . ) is in progress. Moreover, we are also currently investigating a two-dimensional experiment, similar to the present three-dimensional one, in which one can monitor the evolution and the collapse of the flue. We aim at relating the overall dynamics of the system to the local dynamics.

Finally, we proposed that the minimum ingredients necessary for a channel to form and stabilize, and thus for the intermittency to be observed, are a shear-thinning and thixotropic fluid. However, a detailed study of the mechanisms at stake in the flue formation and collapse remains to be performed. ter the rheological properties of the fluid.We report here measurements of the size and density of the small bubbles along the fluid column when the system has reached a steady state.

During the first cycle of Q, the state of the column evolves as it fills up with small bubbles which get trapped. However, after having switched Q twice to Q * during the increase and the decrease of the flow rate, the aspect of the column remains qualitatively the same, and one can assume that the vertical bubble gradient has reached a steady state (We give several indications of such an assertion in Sect. III.) In order to characterize the vertical bubble gradient which takes place along the column height in the steady-state regime, we perform the following experiment: from a 15 cm high column which has experienced 5 flow rate cycles, we carefully extract 7 slices, 2 cm thick, corresponding to different altitude z; For each slice, we measure the size of a thousand bubbles using a macroscope (Leitz, Laborlux) and assess the fluid density. The corresponding rheological properties shall be reported in the section A 3.

Let us denote as p n (r) the probability distribution of the bubble size r in the slice n. In each slice, the cumulative probability distribution of the bubble size r, defined as F n (r) ≡ ∞ r p n (r ′ ) dr ′ is exponential (Fig. 9). Thus, the bubble size, in each slice, is exponentially distributed. The corresponding characteristic radius, r * n = (0.58 ± 0.04) mm, is almost constant over the column height h (Fig. 10a). In order to assess the associated bubble concentration, we measured the density of material in each slice (Fig. 10b). The fluid density decreases roughly linearly from the density of the fluid free of bubbles at the bottom to ρ ≃ 750 kg/m 3 at the free surface, corresponding to a maximum gas fraction of about 25%. The measurements confirm the visual observation of a bubble gradient inside the fluid. We estimate that the bubble concentation, which equals 0 at the bottom, is about 300 bubbles per cm 3 at the top.

Rheological properties in presence of bubbles

Using the same experimental protocol as in the section A 1, we determined, for each slice, the rheological properties of the fluid, charged with bubbles. We observe that the bubbles lead to the appearence of a significant mem- ory effect (Fig. 11): the shear stress does not reach the steady-state value instantaneously but after a significant characteristic time, τ 0 , which we estimate from the experimental data to be about 1 min for the largest bubble density (at the top of the column). In contrast, we observe that the shear-thinning properties of the fluid are not qualitatively altered (Fig. 11, inset). Note finally that the yield stress σ c ≃ 25 Pa is roughly constant along the column (Fig. 10d), and smaller that the estimated value for the free bubble gel solution (σ c ≃ 35 Pa). In order to account, at least at a rough estimate, for the observation of a characteristic time of the bubbling regime, we propose that a channel can form and remain stable if the shear-stress imposed by the inner gas flow at the channel walls exactly balances the yield stress. Initially, the yield stress is large and the gas emission at the nozzle necessitates a large overpressure which leads to the formation of a bubble once the fluid starts flowing. The rise of successive bubbles leads to a decrease in the yield stress which allows the emission of gas at a small overpressure and, thus, the formation of a thin channel in the fluid. Moreover, once the channel has formed, there is no flow of the fluid at the walls and the yield stress increases back to its maximum value, which tends to stabilize the structure.

On the one hand, between two successive bubbles, the fluid is at rest and the yield stress, σ y , relaxes toward its asymptotic value σ c over the characteristic time τ 0 according to

τ 0 σy + σ y = σ c . (B1)
where τ 0 is an intrinsic property of the fluid. On the other hand, due to the large shear stress imposed by the rise of the bubble, σ y tends to vanish according to

τ b σy + σ y = 0. (B2)
where τ b is here not an intrinsic property of the fluid. Indeed, τ b characterizes the destructuration of the fluid under stress and, for instance, might depend on the risingbubble size. Hence, τ b ≤ τ 0 [37].

Considering the typical time, τ ≡ V b /Q, between two successive bubbles (V b denotes the volume of the bubble) and the duration of the shear by a rising bubble, t b , according to equations (B2) and (B1), one can estimate that, after the rise of n successive bubbles:

σ y ≃ σ c -σ c t b τ τ 0 τ b 1 -exp -n τ τ 0 (B3)
where we assumed that t b ≪ τ ≪ τ b and only kept the exponential dependence on n.

When the yield stress has reached a small enough value, the gas emission can occur in a gentle manner, a thin gas finger growing from the nozzle. We can estimate that the growth of the finger will lead to a stable channel provided that the shear stress applied to the wall by the inner gas flow does not exceed the yield stress. Assuming a Poiseuille flow inside, one can estimate the shear stress at the wall σ p = 4η a Q/(πr 3 c ) where η a = 1.6 × 10 -5 Pa.s denotes the dynamic viscosity of air and r c the radius of the channel. In this framework, the condition σ p = σ y leads to:

τ * b = -τ 0 ln 1 - τ t b τ b τ 0 1 - σ p σ c (B4)
where we defined τ * b ≡ nτ . This latter equation can be rewritten :

τ * b ≃ -τ 0 ln Q c 1 Q * - 1 Q (B5)
where, by definition,

Q c ≡ τ b τ 0 V b t b and Q * ≡ Q c 1 + Q c /Q + (B6)
with Q + ≡ πr 3 c σc 4ηa . Note that τ * b (> 0) is thus predicted to be defined in a finite range Q ∈ ]Q * , Q + ] of the flow rate and, in agreement with the experimental observations, not to depend on the height of the fluid column.

From the interpolation of the experimental data (Fig. 5), Q c ≃ 0.35 cm 3 /s, Q * ≃ 0.29 cm 3 /s and τ 0 ≃ 65 s. First, we observe that τ 0 is found to be in reasonable agreement with the estimation obtained in the rheology experiment. Second, from the time difference between successive bubbles in the pressure signal (Fig. 2), we obtain the typical bubble-volume V b ≃ 2 cm 3 and, accordingly, the typical radius r b ≃ 0.8 cm. We estimate the rise time of the bubble along the whole column height (8 cm) to be about 1 s and, thus, t b ≃ 0.2 s (about 2r b /v b , the diameter divided by the rise velocity, v b ≃ 8 cm/s). With this latter value of t b and the experimental Q c , we obtain τ b ≃ 2.3 s, which is a reasonnable value if one considers that the shear rate imposed by the rising bubble is large, of about 1/t b = 5 s -1 (Note, in addition, that the imposed stress is of about ρgr b ∼ 80 Pa where ρ denotes the density of the fluid and g the acceleration due to the gravity.) From Q + ≃ 1.7 cm 3 /s and σ c ≃ 25 Pa (Fig. 10), one can estimate the channel radius r c ≃ 0.1 mm, which is also in agreement with the experimental observation of a very thin channel, a fraction of millimeter in diameter. At last, it would be interesting to understand the mechanism that selects the channel radius (competition between the elasticity and the surface tension?) but the problem is out of the scope of this appendix.

From the proposed mechanism, one can also understand why the small bubbles quickly invade the system when Q is about Q * (i.e. Q b ≃ Q * , Sec. II B). Indeed, on the one hand, in the bubbling regime, the pinch-off of the bubble emitted at the nozzle [38], the coalescence of two bubbles in the bulk ( [39], Sec. III) and the bursting of a bubble at the free surface [31] are likely to leave a small satellite (bubble) [40]. We can thus guess that each rising bubble leaves one or two small bubbles. On the other hand, in the flue regime, the number of small bubbles left by the channel collapse is about the column height divided by the wavelength that develops (Rayleigh instability [42]). In our experimental conditions, we estimate from direct visual observation that the wavelength is about 1 cm (much larger than the channel diameter) and, thus, that each collapse of a channel produces about 10 small bubbles. The channel collapse is thus much more efficient in the production of small bubbles. By definition of Q * , at the transition, the channel is marginaly stable and then frequently collapses. As a conclusion, Q b ≃ Q * .

FIG. 3 :

 3 FIG. 3: Fraction Φ b vs. imposed flow rate Q -The fraction of time spent in the bubbling regime, Φ b , clearly exhibits a transition at a given flow rate Q * which drastically depends on the fluid rheology. Fitting curves, sigmoids, are given as eye leads. The gray area marks the range, Q ∈ ]Q * , Q + ], in which the duration of the bubbling regime can be defined (associated with •, only) [(symbol: height h0 mm, volume V cm 3 ). Added-water content 10 %: (•: 70, 530); (•: 130, 530); (⊗: 70, 800). Added-water content 15 %: ( : 70, 530)].

FIG. 4 :

 4 FIG. 4: Cumulative probability distribution F b (τ b ) -The time τ b spent in the bubbling regime exhibits an exponential distribution with a characteristic time τ * b (Fig. 5). We report data obtained when increasing and decreasing the flow rate Q [(symbol, Q cm 3 /s). Top: (×, 0.347); (•, 0.521); ( , 0.695); (△, 0.869); ( , 1.04); Middle: (♦, 1.22); ( , 0.782); (⋄, 0.608); (1, 0.434). Bottom: (×, 0.347); (•, 0.521); ( , 0.695); ( , 1.04). (Added-water content 10%, V = 530 cm 3 , h0 = 70 mm)].

FIG. 5 :

 5 FIG. 5: Time τ * b vs. flow rate Q -Values of τ * b obtained for both increasing and decreasing flow rates are reported. The closed symbols denote the values deduced from the data reported in the figure 4. The open symbols correspond to data obtained when the fluid column is stirred after each change in the flow rate ( , V = 530 cm 3 ). The continuous line corresponds to the equation (3) with τ0 ≃ 65 s, Qc = 0.35 cm 3 /s and Q * ≃ 0.29 cm 3 /s. The horizontal dashed line denotes the characteristic time of emission of a single bubble, about 1 s. The grey region corresponds to Q ∈ ]Q * , Q + ] [(Symbol, V cm 3 ) : (•, 530); ( , 800). (Added-water content 10%, h0 = 70 mm)].

FIG. 6 :

 6 FIG.6: Cumulative probability distribution F f (τ f ) -The cumulative probability distribution F f (τ f ) of the time spent in the flue regime exhibits a power-law behavior, up to a large-time cutoff τ2. Curves have been vertically shifted for clarity, and the slope 1/2 characterizing standard on-off intermittency is shown for comparison. Note that the data correspond to an acquisition time of 4 days, which is significantly larger than τ2, so that we expect the system to have reached a stationary state[34] and the cut-off not to be due to the finite experimental time [(Symbol, Q cm 3 /s). Top: (•, 0.521); ( , 0.695); (△, 0.869); ( , 1.04). Middle: (⋄,1.22); ( , 0.782); (⋄, 0.608); (1, 0.434). Bottom: (×, 0.347); (•, 0.521); ( , 0.695); ( , 1.04). (Added-water content 10%, V = 530 cm 3 , h0 = 70 mm)].

  FIG.6: Cumulative probability distribution F f (τ f ) -The cumulative probability distribution F f (τ f ) of the time spent in the flue regime exhibits a power-law behavior, up to a large-time cutoff τ2. Curves have been vertically shifted for clarity, and the slope 1/2 characterizing standard on-off intermittency is shown for comparison. Note that the data correspond to an acquisition time of 4 days, which is significantly larger than τ2, so that we expect the system to have reached a stationary state[34] and the cut-off not to be due to the finite experimental time [(Symbol, Q cm 3 /s). Top: (•, 0.521); ( , 0.695); (△, 0.869); ( , 1.04). Middle: (⋄,1.22); ( , 0.782); (⋄, 0.608); (1, 0.434). Bottom: (×, 0.347); (•, 0.521); ( , 0.695); ( , 1.04). (Added-water content 10%, V = 530 cm 3 , h0 = 70 mm)].

FIG. 7 :

 7 FIG. 7: Exponent α vs. flow rate Q -The values of α obtained for increasing and decreasing flow rates (respectively closed and open symbols) are almost the same and significantly smaller than 1/2. Stirred samples (crosses) lead to even smaller values of α (added-water content 10%, V = 530 cm 3 and V = 800 cm 3 , h0 = 70 mm).

FIG. 8 :

 8 FIG. 8: Fluid viscosity η vs shear-rate γ -The fluid is shear-thinning. The vertical gray line indicates the characteristic shear-rate γc. Inset: Fluid viscosity η versus shear stress σ -The measurements clearly point out the existence of a flow threshold σc ≃ 35 Pa [Open symbols correspond to stress-controlled experiments whereas solid symbols correspond to shear-controlled experiments. Gap e = 750 µm : ( , ∆t = 25 s); (♦, ∆t = 1 s); (•, ∆t = 10 s)].

FIG. 9 :

 9 FIG.9: Bubbles size and density -Left: Cumulative probability distribution Fn of the bubble size r in the slice n (The grayscales are uniformely distributed from light gray at the bottom to black at the top.) The distribution Fn is exponential (linear fit, dotted black-line.) We denote r * n the associated characteristic radius. Right: The pictures, from bottom to top, correspond respectively to the slices, z ∈ [0.5, 2.5] cm, z ∈ [8.5, 10.5] cm and z ∈ [12.5, 14.5] cm, respectively.

FIG. 10 :

 10 FIG. 10: Fluid column properties -We report (a) the mean bubble size r * n , (b) the density ρ, (c) the viscosity η0 in the limit of low shear-rate γ, and (d) the fluid-threshold σc along the column height z. Each point corresponds to an average over one slice (thickness 2 cm, horizontal dashedlines).

FIG. 11 :

 11 FIG.11: Viscosity η vs shear stress σ -The rheological properties depend on the altitude z because of the variation of the density of the bubbles trapped in the fluid along the column height. Moreover, we observe that the data obtained for increasing and decreasing shear rate (arrows) do not superpose: the presence of the bubbles leads to a significant memory effect. Inset: Fluid viscosity η vs shear-rate γ -The measurements clearly point out the memory effect (The symbols, from light gray to black, correspond respectively to the slices, z ∈ [0.5, 2.5] cm, z ∈ [3.5, 5.5] cm, z ∈ [8.5, 10.5] cm and z ∈ [12.5, 14.5] cm, where z denotes the altitude. Imposed shear-rate, equilibration time ∆t = 15 s).

  APPENDIX B: ESTIMATE OF τ * b

Acknowledgments

The authors appreciated remarks from J.-F. Palierne and numerous enlightening discussions with S. Vergniolle. T.D. and V.V. have also greatly benefited from the IAV-CEI General Assembly which took place in Reykjavik in late August 2008.

The rheological properties of the solution, free of bubbles, have been measured using a rheometer (Bohlin Instruments, C-VOR 150) equipped with parallel plates (PP-60, gap e = 750 and 1000 µm). Sand paper was glued to the plates in order to prevent any sliding of the fluid at the walls; At 25 • C, we performed both steadyshear and steady-stress experiments with an equilibration time ∆t ranging from 1 to 25 s (Fig. 8). The solution is shear-thinning and we estimated the associated characteristic time τ c = 1/ γc ≃ 1700 s, compatible with the ratio of the viscosity at low shear-rate η 0 ≃ 6 × 10 4 Pa.s to the estimated flow threshold σ c ≃ 35 Pa (Fig. 8).

Bubbles size and density

During the experiments, the small bubbles that remain trapped in the fluid column, due to the yield stress, al-