Michiel Postema

Philippe Marmottant

Charles T Lancée

Michel Versluis

Sascha Hilgenfeldt

Nico De Jong

Ultrasound-induced Coalescence of Free Gas Microbubbles

When gas bubbles collide, the following stages of bubble coalescence have been reported: flattening of the opposing bubble surfaces prior to contact, drainage of the interposed liquid film toward a critical minimal thickness, rupture of the liquid film, and formation of a single bubble. During insonification, expanding contrast agent microbubbles may collide with each other, resulting in coalescence or bounce.

In this study, we investigate the validity of the film drainage formalism for expanding free bubbles, by subjecting rigid-shelled contrast agent microbubbles to ultrasound, in order to release gas, and photograph the coalescence of these free gas bubbles. As with colliding bubbles, bubble surface flattening is related to the Weber number. Only inertial film drainage between free interfaces explains the observed coalescence times. In accordance with theory, smaller bubble fragments coalesce on very small time scales, while larger bubbles bounce off each other.

I. INTRODUCTION

When two gas bubbles collide or are driven into each other, coalescence into a single bubble may result. The following stages of bubble coalescence have been identified (cf. Figure 1): flattening of the opposing bubble surfaces prior to contact, drainage of the interposed liquid film toward a critical minimal thickness, rupture of the liquid film, and formation of a single bubble. If the critical thickness is not reached during collision, the bubbles bounce off each other instead.

Free gas bubble coalescence after collision has been studied extensively [START_REF] Marrucci | A theory of coalescence[END_REF], [START_REF] Dimitrov | Hydrodynamics of thin liquid films. On the rate of thinning of microscopic films with deformable interfaces[END_REF], [START_REF] Ivanov | Generalized equations of thin films hydrodynamics and their application to the calculations of the thinning rate of films with non-deformed surfaces[END_REF], [START_REF] Lin | Thinning of a liquid film as a small drop or bubble approaches a fluid-fluid interface[END_REF], [START_REF] Chesters | Bubble coalescence in pure liquids[END_REF], [START_REF] Duineveld | Bouncing and coalescence of two bubbles in water[END_REF]. With ultrasound contrast agents, microbubble coalescence has been observed during ultrasound insonification, when expanding microbubbles come into contact with each other [START_REF] Postema | Optically observed microbubble coalescence and collapse[END_REF], [START_REF] Postema | Ultrasound-induced microbubble coalescence[END_REF], [START_REF] Postema | Medical Bubbles[END_REF]. With the aid of highspeed photography, we previously investigated the coalescence times of insonified soft-shelled microbubbles. We compared observed coalescence times to calculated film drainage times, based on the Reynolds equation [START_REF] Reynolds | On the theory of lubrication and its application to Mr. Beauchamp Tower's experiments, including an experimental determination of the viscosity of olive oil[END_REF] for no-slip interfaces and on the drainage equation for free interfaces. We concluded that the bubbles behaved as if they had free interfaces like free gas bubbles [START_REF] Postema | Ultrasound-induced microbubble coalescence[END_REF]. However, to support this conclusion, we should investigate the validity of the drainage equations for expanding bubbles. In this study we do so, by subjecting rigid-shelled contrast agent microbubbles to ultrasound, in order to release gas, and investigate the coalescence of these free gas bubbles. We compare these times to the computations.

Previously, we reported on ultrasound-induced gas release from contrast agent microbubbles [START_REF] Postema | Optically observed microbubble coalescence and collapse[END_REF]. This so-called sonic cracking has been observed with microbubbles with rigid encapsulations.

II. THEORY

Flattening of the opposing bubble surfaces occurs in case of colliding bubbles with constant volumes, if the bubble system has a Weber number We 0.5 [START_REF] Chesters | Bubble coalescence in pure liquids[END_REF]. If We 0.5, the bubbles will coalesce without the prior formation of an interposed film. The Weber number for a fluid containing two bubbles with radii R 1 and R 2 , respectively, is given by the inertial force relative to the surface tension force:

We = ρ u 2 σ R m , ( 1
)
where u is the relative approach velocity, ρ is the fluid density, σ is the surface tension, and R m is the mean bubble radius for which holds:

2 R m = 1 R 1 + 1 R 2 . ( 2
)
We propose to extend this criterium to approaching walls of expanding bubbles. Because the radius and with it the approach velocity of oscillating bubbles change during a cycle, so does the Weber number. The approach velocity for expanding bubbles with a constant center-to-center distance is

u = Ṙ1 + Ṙ2 . ( 3
)
If the Weber number is low, bubble coalescence will always occur, without flattening of the adjacent surfaces prior to contact [START_REF] Chesters | Bubble coalescence in pure liquids[END_REF]. In the high Weber number regimen, coalescence is determined by a second step, after flattening: film drainage.

When the expansion time is less than the time needed for film drainage, the bubbles bounce off [START_REF] Chaudhari | Coalescence of gas bubbles in liquids[END_REF].

The radial velocity of the liquid in the film is a combination of a plug flow driven by the motion of the interfaces, and a laminar velocity profile (analogous to Poiseuille flow) driven by the radial pressure gradient [START_REF] Klaseboer | Film drainage between colliding drops at constant approach velocity: experiments and modeling[END_REF], [START_REF] Young | A Brief Introduction to Fluid Mechanics[END_REF]. If the bubble surfaces consist of a high concentration of surfactant, on our working scales the interfaces are to be considered immobile (no-slip) [START_REF] Van Wijngaarden | The mean rise velocity of pairwise-interacting bubbles in liquid[END_REF]. In the case of no-slip interfaces, the interfacial tangential velocity is zero, so the plug flow contribution is zero [START_REF] Klaseboer | Film drainage between colliding drops at constant approach velocity: experiments and modeling[END_REF]. In the case of free interfaces, the Poiseuille contribution to the drainage flow becomes negligible [START_REF] Van Wijngaarden | The mean rise velocity of pairwise-interacting bubbles in liquid[END_REF], [START_REF] Klaseboer | Film drainage between colliding drops at constant approach velocity: experiments and modeling[END_REF]. The film drainage time for free radial surfaces is approximated by the equation [START_REF] Kirkpatrick | The influence of approach velocity on bubble coalescence[END_REF], [START_REF] Hagesaether | Coalescence and break-up of drops and bubbles[END_REF]:

τ d ≈ R f ρ 8 p log h i h c , ( 4
)
where η is the viscosity of the fluid, ρ is the density of the fluid, R f is the film radius, h i is the initial thickness, h c is the critical film thickness, at which the film ruptures, p and is the pressure difference between film and surrounding fluid which is taken

p = σ 1 R 1 + 1 R 2 . ( 5
)
In our computations, we take η = 0.001 Pa s, ρ = 998 kg m -3 , σ = 0.072 N m -1 , and h c = 10 nm .

(

) 6
Flattening takes place when:

Ṙ1 + Ṙ2 dh dt , (7)
whereas the flat film drainage happens in the next stage, when

Ṙ1 ≈ Ṙ2 ≈ 0. (8)
Thus, during drainage, on our timescales, we may take p and R f constant over time [START_REF] Postema | Ultrasound-induced microbubble coalescence[END_REF]. Repeated coalescence and fragmentation has been reported [START_REF] Postema | Ultrasound-induced microbubble coalescence[END_REF]. Fragmentation is the fission of a bubble into smaller bubbles. It occurs around peak contraction, when the bubble collapse is driven by inertial forces, since the inward acceleration continues to increase as the bubble approaches its minimum radius and suddenly changes sign as the bubble begins a rebound [START_REF] Chomas | Threshold of fragmentation for ultrasonic contrast[END_REF]. The number of fragments into which a bubble breaks up has been related to the dominant spherical harmonic oscillation mode n [START_REF] Brennen | Fission of collapsing cavitation bubbles[END_REF], [START_REF] Postema | Medical Bubbles[END_REF]. The estimated number of fragments N is

N ≈ n 3 . ( 9
)
Transducer Contrast agent Container Microscope Fig. 2. Overview of the experimental bubble-system.

III. EXPERIMENTAL METHODS

Our experimental setups for taking pictures of insonified contrast bubbles were as described in [START_REF] Chin | Brandaris 128: a 25 million frames per second digital camera with 128 highly sensitive frames[END_REF] and in [START_REF] Postema | Ultrasoundinduced encapsulated microbubble phenomena[END_REF]. An overview of the bubble-system is shown in Fig. 2. A 200 µm capillary tube, through which contrast agent was flowing, was fixed in the focal area of a V389-SU 500 kHz or a V397-SU 2.25 MHz single-element transducer (Panametrics Inc., Waltham, MA). The optical observations of the insonified ultrasound contrast agent were recorded with the Brandaris-128 system, operating at speeds up to 15 MHz.

The free gas bubbles were released from PB127 (POINT Biomedical Corporation, San Carlos, CA). PB127 consists of bilayered microspheres encapsulating nitrogen bubbles with a mean diameter of 4 µm. The outermost layer is albumin and the inner layer is composed of a biodegradable polymer. The content of a PB127 vial was resuspended in 5 ml of deionized water, and shaken gently for 20 seconds before further dilution. Diluted PB127 was inserted through the capillary tube using a syringe pressed by hand. It was insonified by 6 or 8 cycles of 500 kHz (period T p =2 µs), or by 8 cycles of 1.7 MHz (T p =0.6 µs) ultrasound at acoustic pressures corresponding to mechanical indices between 0.3 and 1.9.

IV. RESULTS AND DISCUSSION

The same stages of coalescence described for colliding bubbles could be distinctly observed with expanding free gas microbubbles and soft-shelled microbubbles. Examples of softshelled microbubble coalescence were shown in [START_REF] Postema | Optically observed microbubble coalescence and collapse[END_REF], [START_REF] Postema | Ultrasound-induced microbubble coalescence[END_REF], [START_REF] Postema | Simulations and measurements of optical images of insonified ultrasound contrast microbubbles[END_REF].

As with encapsulated bubbles, coalescence and bounce were regularly observed. For the interacting free gas microbubbles with flattened interfaces observed in the optical images, We 1. We obtained 9 image sequences where free bubble coalescence times and the bubble dimensions could be measured. The times between flattening of the free bubble surfaces and coalescence are less than 0.3 µs, for expanded gas bubbles with diameters between 3 and 5 µm. Figure 3 shows an example of gas release from a PB127 bubble. Each frame corresponds to a 23×23 µm 2 area. Four PB127 bubbles are in the field of view. After ultrasound arrival (frame 13) the bubbles contract. During expansion, gas escapes from the 3 µm upper bubble [START_REF] Hagesaether | Coalescence and break-up of drops and bubbles[END_REF][START_REF] Chomas | Threshold of fragmentation for ultrasonic contrast[END_REF][START_REF] Brennen | Fission of collapsing cavitation bubbles[END_REF][START_REF] Chin | Brandaris 128: a 25 million frames per second digital camera with 128 highly sensitive frames[END_REF]. The free gas is seen detached in frame 21. It expands (22-25) and starts to contract (26). Close to its minimum, the free gas bubble splits up into multiple fragments (27). During expansion, the fragments appear to have coalesced into two separate bubbles (28-29). These bubbles collide during expansion (30). The Weber number, calculated from the bubble wall velocity (29-30) u 2 µm 0.1 µs , is We > 20 0.5 , which agrees with the flattening of the bubble surfaces. Computing equation ( 4) with R 1 = 3.9 µm, R 2 = 3.4 µm, and R f = 2.1 µm yields τ d = 0.6 µs ≈ T p . [START_REF] Reynolds | On the theory of lubrication and its application to Mr. Beauchamp Tower's experiments, including an experimental determination of the viscosity of olive oil[END_REF] This long drainage time accounts for the observed bounce (30-32). Close to maximal contraction (33), the two bubbles fragment. During expansion, the fragments are seen to coalesce (35-37) into two bubbles of perpendicular orientation. Again, these bubbles bounce (38-39), fragment (40), and coalesce into two bubbles perpendicular to their mother bubbles (41). This process repeats itself, until insonification ends (66).

The two remaining free gas bubbles still pulsate, and collide while doing so. These collisions may possibly be attributed to secondary radiation forces. In frame 82, the bubbles coalesce. This coalescence is induced by the pressure field exerted by the bubbles themselves. The remaining bubble has a maximum of 3.8 µm. It pulsates at 1.7 MHz. Hence, the pulsations may be attributed to reflections. Note that the radii of the bubble fragments after a fission event are all: R i < 1 µm. From equations ( 4)-( 6), using the empirical relation [START_REF] Postema | Ultrasound-induced microbubble coalescence[END_REF]:

R f ≈ 2 3 R i , (11)
it follows that the drainage times, and with it the fragment coalescence times are:

τ d < 0.1 µs, (12)
consistent with the observed fast coalescence of fragments in the space of an inter-frame distance (0.1 µs). The bouncing bubbles in Fig. 3 might be considered as an n = 2 spherical harmonic mode system. This is supported by the alternating perpendicular orientations observed. The estimated number of fragments (N ≈ 2 3 = 8) cannot be verified by these observations, because right after fragmentation, the fragments are too small to be observed.

V. CONCLUSIONS

Expanding gas bubble coalescence has been observed with released gas. Bubble surface flattening is observed to be consistent with the Weber number criterium for colliding bubbles.

Calculated drainage times from an inertial drainage model assuming clean, stress-free interfaces are consistent with the observations: For large (fully expanded) bubbles the drainage times are too large (larger than a bubble oscillation cycle) to allow for film drainage and coalescence. Smaller microbubble fragments, however, easily coalesce on very short timescales. Gas release at 1.7 MHz from PB127 microbubbles, captured at 10 Mfps. Each frame corresponds to a 23×23 µm 2 area. Spontaneous coalescence of free gas microbubbles takes place in frames 81-83.

Fig. 1 .

 1 Fig. 1. Schematic representation of colliding bubbles or droplets: approach (a-b), flattening of the interposed film (c), drainage to a critical thickness (d), film rupture (e), and formation of a single bubble (f).

  Fig. 3.Gas release at 1.7 MHz from PB127 microbubbles, captured at 10 Mfps. Each frame corresponds to a 23×23 µm 2 area. Spontaneous coalescence of free gas microbubbles takes place in frames 81-83.

Michiel Postema e-mail: m.postema@erasmusmc.nl

ACKNOWLEDGMENTS

This work has been supported by the Technology Foundation STW (RKG.5104). We are indebted to Andrea Prosperetti for very helpful discussions and thank POINT Biomedical Corporation for supplying PB127.


Yvon Haradji

Mathieu Schumann

Jérémy Albouys

Nicolas Sabouret

Christian Inard

SMACH : Multi-Agent Simulation of Human Activity in Households

Keywords: Jérémy Albouys, Nicolas Sabouret, Agent-Based Simulation, Energy Consumption, Simulation Of Human Activity, Buildings

come

Introduction

In the context of energy consumption reduction, studying and understanding the residential sector appears as a key factor. Indeed, 57% of the final energy consumption in Europe is used for space heating [START_REF] Zimmermann | Household electricity survey a study of domestic electrical product usage[END_REF]. However, the residential sector is characterized by a high variability due to the impact of human activity [START_REF] Bahaj | Urban energy generation: The added value of photovoltaics in social housing[END_REF]. Predicting human activities and energy loads of buildings are thus of crucial important to predict energy consumption.

Today, two kinds of models exist to simulate such household consumption. The first model are based on stochastic models [START_REF] Widén | A high-resolution stochastic model of domestic activity patterns and electricity demand[END_REF]. One limitation is that the simulated behaviors do not correspond to real life situations and lack variability. The second approach relies on multi-agent simulations (MAS) [START_REF] Ferreri | Prediction of electrical consumptions using a bio-inspired behavioral model[END_REF]. Such models allow a fine-grained simulation of the human activity. The SMACH platform, developed in collaboration between EDF and several academic partners, is one of them.

Main Purpose

SMACH simulates household activity and electrical consumption. It uses statistical data based on time-use surveys [START_REF] Reynaud | Using Time-Use Surveys in Multi Agent Based Simulations of Human Activity[END_REF] to produce varied and realistic lists of daily tasks for each inhabitant of the household. Based on this information, a multi-agent system simulates the human activity in households. At every time step, the agents of the SMACH platform select the activity to perform, using control parameters such as the current activity of other inhabitants, the price of the energy, their previous activities and the parameters of the tasks. Each task can be associated with the use of electrical appliances that consume electricity. A multi-zone thermal model of the household simulates indoor temperature and the energy consumption for room heating [START_REF] Plessis | BuildSysPro: a Modelica library for modelling buildings and energy systems[END_REF].

The SMACH engine is thus able to generate load curves coupled with activity diagrams. It is used at EDF for research purposes, to understand the electrical energy consumption in existing households, to study the impact of new households configuration or public policies and to anticipate future situations like collective self-consumption at the scale of a neighborhood or electrical vehicles.

Demonstration

Our demonstration will illustrate the possibilities of the SMACH multi-agent simulation through three different user interfaces. Figure 1 illustrates the connection between these interfaces and the platform.

Interface for load curves generation by energy experts

While it is possible to manually configure all the details of the household (number of inhabitants, list of tasks with their duration parameters, list of electrical appliances, etc), the SMACH platform can generate these parameters automatically from statistical data. With this expert interface (Figure 2), the household generation is configured by selecting several parameters including the number of households, their geographical area, the characteristics of the building and appliances, and the inhabitants policies related to energy use. The system then generate as many households as asked (often thousands for large scale studies), which are then individually simulated by SMACH, producing one load curve and one activity diagram for each household. In the demonstration we will generate a city population and produce the activity diagrams and the load curves. The user interface is used by energy experts to study a large variety of configurations. The dedicated interface (Figure 3) allows modellers to demonstrate to people the simulation of their own household in real time. The participants can interact with the simulation and change the behavior of each member of the family during the simulation. In the demonstration , we will show how people can interact with the platform to modify the behavior of the agents. This interface has been used to validate the SMACH model and the realism of the produced simulation.

Educational Interface

EDF developed an Educational Interface for SMACH, with the purpose of increasing awareness of general audience about the impact of occupant activities on the buildings energy consumption.

Thanks to this interface, the user can easily configure a household and set up consumption habits and general policies such as the setpoint temperature for room heating. It can then see how minimal changes on such parameters impact the energy consumption. The demonstration will present the creation of a household and show the difference between a base case scenario and a modified configuration (Figure 4).

Conclusion

The present demonstration showed various interfaces developed with the SMACH multiagent platform and the use cases they answered to. We discuss their operation and results for professional use and for general audience.

Fig. 1 .

 1 Fig. 1. SMACH general architecture

Fig. 2 .

 2 Fig. 2. Load curves generation interface

Fig. 3 .

 3 Fig. 3. Participatory simulation interface


Jérémy Albouys-Perrois

Nicolas Sabouret

Yvon Haradji

Mathieu Schumann

Christian Inard

A Co Simulation Of Photovoltaic Power Generation And Human Activity For Smart Building Energy Management And Energy Sharing

We present a framework and a model for the simulation of collective energy self-consumption strongly coupled to occupant activity in households. The model combines multi-agent simulation of human activity, a dynamic model of building energy including Domestic Hot Water (DHW) and all electrical appliances, and local generation of photovoltaic energy. A cooperative energy exchange policy between households was defined in order to maximise the use of locally generated PV electricity at the neighbourhood scale. In this first implementation, three households A, B and C were simulated, one being the PV energy producer. The DHW model was modified to benefit from PV electricity. Thanks to the energy exchange policy, a total of 83% of the energy generated by household A is used locally in the neighbourhood (compared to 38% when there are no energy exchanges with household B and C). The next step of this study is to add a model of energy storage in several self-consumption configurations.

Introduction

Energy self-consumption consists in generating energy using a local source (photovoltaic panels, windmill, etc.) and consuming part or all of this locally generated energy [START_REF] Luthander | Photovoltaic self-consumption in buildings: A review[END_REF][START_REF] Matallanas | Analysis of the Self-consumption Possibilities in Small Gridconnected Photovoltaic Systems in Spain[END_REF]. However, in usual situations, only a small part of this energy can actually be consumed by the producer itself, namely 25 to 40% according to [START_REF] Luthander | Photovoltaic self-consumption in buildings: A review[END_REF]. Several reasons can explain these low figures of selfconsumption. The building energy needs represent the main part of the electrical energy consumption in the world. According to [START_REF] Chwieduk | Towards sustainable-energy buildings[END_REF][START_REF] Zimmermann | Household Electricity Survey A study of domestic electrical product usage[END_REF]), 57% of the final energy consumption of the households in Europe is used for space heating. But the periods of energy consumption do not necessarily coincide with the periods of local energy generation. For instance, the need for space heating often occurs while PV panels energy generation is null. In addition, [START_REF] Bahaj | Urban energy generation: The added value of photovoltaics in social housing[END_REF] showed that a precise evaluation of electrical energy consumption needs to take human activities into account. But like the heating loads, these energyconsuming activities rarely coincide with the periods of local energy generation.

In this context, one solution to optimise the use of local energy generation is to support energy exchanges between various self-consumer buildings [START_REF] Tushar | Transforming energy networks via peer-to-peer energy trading: The potential of game-theoretic approaches[END_REF][START_REF] Wu | Optimal management of local energy trading in future smart microgrid via pricing[END_REF]. This can help households to compensate an excess of energy production by using this energy in another household. Predicting human activities and energy loads of buildings are thus of crucial importance to design practical solutions for efficient energy management in the context of energy sharing. In the present study, both the energy demand of the building and the inhabitant activities are considered.

We used multi-agent systems for simulating human activities coupled with building energy models in order to study energy self-consumption and energy exchanges between households. A multi-agent system can be defined as a set of processes i.e. the agents which exist together, share common resources, and communicate with each other [START_REF] Ferber | Multi-agent systems : an introduction to distributed artificial intelligence[END_REF]. Coupling activity and energy simulation allows to study different exchange configurations and technical solutions which can improve energy self-consumption, such as energy trading [START_REF] Tushar | Transforming energy networks via peer-to-peer energy trading: The potential of game-theoretic approaches[END_REF], energy storage [START_REF] Braun | Photovoltaic self-consumption in Germany using Lithium-Ion Storage to increase self-consumed photovoltaic energy[END_REF] or load management [START_REF] Widén | Improved photovoltaic selfconsumption with appliance scheduling in 200 singlefamily buildings[END_REF]. The overall goal of our work is to assess the efficiency of several technical and policy solutions for energy exchange, by quantifying the rate of self-consumption at the household and district scale. This paper focuses on the first implementation of a specific energy exchange policy, and is organised as follows: In the second section, previous works about energy self-consumption, energy exchange and simulation of human activities are presented and discussed. The third section is devoted to presenting the SMACH simulator (Multi-Agent Simulation of Human Behaviour), used for the dynamical simulation of human activities and energy consumption in buildings. Section 4 describes the model of collective energy selfconsumption. Section 5 presents the case study and the results. We then present the conclusions and future work.

Related works

Multi-Agent Simulation of activity and electrical consumption

Simulation of human behaviour linked to electrical energy consumption prediction in buildings has been a growing centre of interest in the recent years (Ferreri et al. 2017;[START_REF] Kashif | Simulating the dynamics of occupant behaviour for power management in residential buildings[END_REF][START_REF] Amouroux | Simulating human activities to investigate household energy consumption[END_REF]. Thus, many studies, based on multi-agent systems (MAS), proposed models to simulate human activity and electrical energy consumption. These models allow a precise simulation of human activity, which is a key factor for electrical energy consumption prediction. For instance, (Ferreri et al. 2017) used a method based on a psychological model which represents the habits of the inhabitants. This method allows the authors to produce load curves based on the use of electrical appliances. However, the building thermal behaviour is not simulated. On the contrary [START_REF] Kashif | Simulating the dynamics of occupant behaviour for power management in residential buildings[END_REF]) proposed a cosimulation where the building and the human activity were simulated. Human behaviour is simulated thanks to Brahms platform [START_REF] Sierhuis | Brahms: a multi-agent modelling environment for simulating work processes and practices[END_REF]) which supports a fine-grain description of the appliances electrical behaviour. However, this model does not include energy self-consumption and the possibility to simulate exchange between different households. The approach proposed by the SMACH project [START_REF] Amouroux | Simulating human activities to investigate household energy consumption[END_REF]) is based on two main components. First, SMACH simulates the human activity by combining fine-grain automated reasoning with statistical behaviour studies [START_REF] Reynaud | Using Time-Use Surveys in Multi Agent Based Simulations of Human Activity[END_REF]. The second component is the multi-zone thermal model of the building, which simulates indoor temperatures and energy consumption. The building is modelled using the BuildSysPro Modelica library, and the SMACH platform and the building energy model are co-simulated using the FMI standard [START_REF] Plessis | Coupling occupant behaviour with a building energy model -A FMI application[END_REF]. But energy self-consumption and energy exchanges between buildings had not been implemented in these models yet.

Simulation of energy self-consumption

The various research conducted so far about energy selfconsumption (SC) has focused on improving SC rate of households. The SC rate is usually defined as the ratio of the locally generated energy and energy consumed by the producer during a certain amount of time. [START_REF] Luthander | Photovoltaic self-consumption in buildings: A review[END_REF] reviewed photovoltaic simulations for households and studied various methods used to improve the energy SC rate. They proposed two solutions based on Demand Side Management and storage technologies. [START_REF] Braun | Photovoltaic self-consumption in Germany using Lithium-Ion Storage to increase self-consumed photovoltaic energy[END_REF]) studied the impact of using a local battery on the energy self-consumption rate and showed that the amount of local energy consumption can reach 82% for an individual household. The authors also simulated the energy generation of an empirical PV panels model (based on real data sets) during one-year. However, the authors did not use simulation in order to get consumption data, they used statistical energy consumption profiles for three types of household. Likewise [START_REF] Munkhammar | Quantifying self-consumption of on-site photovoltaic power generation in households with electric vehicle home charging[END_REF]) used yearly simulation results to demonstrate that the use of electric vehicles as batteries can improve SC rate by 37%. The method used by the authors for the calculation of energy SC was a stochastic model based on a Markov-chain and a simple PV model based on solar irradiance data.

However, energy storage systems and Demand Side Management are not the only way to improve the energy SC rate. With a self-generated energy, it becomes possible for the household to exchange energy with the neighbourhood. The smart grid (SG) technology which can be defined as a network with a bidirectional flow of electricity and information [START_REF] Farhangi | The Path of the Smart Grid[END_REF]) allows this kind of exchange process. The current research about energy trading focuses on studying algorithms to exchange energy. [START_REF] Tushar | Transforming energy networks via peer-to-peer energy trading: The potential of game-theoretic approaches[END_REF] worked on the ability of algorithms based on a game theory approach to regulate energy exchanges. In addition [START_REF] Yaagoubi | Energy trading in the smart grid: A distributed game-theoretic approach[END_REF]) used a non-cooperative game algorithm to exchange energy between households. They proposed a fair algorithm to trade energy, which means that two households buying local electricity with the same parameters will pay the same price to the producers. However, the various models previously described do not simulate the link between energy SC and human activity. Most of the time, the human activity models do not include the capacity to simulate the energy SC or energy trading; and the simulation of energy self-consumption is mostly based on a static energy consumption data without any human activity model. Concerning energy trading configurations related to energy self-consumption, the study of the literature associated to our first surveys led to a first set of categories of exchange policies between households:  Distribution policy: each household is allowed a fixed rate of energy from each means of production;  Cooperative policy: the energy produced in the neighbourhood is shared between the households within contractualised rules;  Competitive policy: the energy will be bought and sold on an energy market where buyers and sellers will interact to exchange energy. Within this general framework for energy selfconsumption, in which we develop our models and analyses, this paper focuses on one of the identified cooperative policies, as a first implementation for the interaction of self-consumption and human activities in households. In this case study, the use of energy storage systems is not yet considered, but will be added in the following studies, as literature and demonstrators already suggest it has an important impact on self-consumption rate and exchange policies.

Simulation of human activity

In our work, the simulation of human activity linked to energy consumption is carried out by using the SMACH platform.

In this platform, software agents represent the individuals of the households. Each agent's runtime consists in selecting daily tasks to do. The sequence of tasks, chosen by the agent each minute, produces an activity diagram. Moreover, the various activities of the inhabitants are linked to electrical appliances, which consume electricity. As a consequence, the simulator is able to generate load curves associated to the activity diagram (Figure 1 and Figure 3).

The activity model

The initial challenge of the SMACH platform was to produce activity diagrams, on a daily basis, which are realistic representations of human activities throughout the day, and consistent with the different household. SMACH needed also to be able to generate variability in the occupant activities from day to day [START_REF] Feldman | Reconceptualizing Organizational Routines as a Source of Flexibility and Change[END_REF], in order to simulate a realistic year.

To achieve this goal, SMACH uses a data-oriented approach based on the results of Time Use Surveys (TUS) (see [START_REF] Reynaud | Using Time-Use Surveys in Multi Agent Based Simulations of Human Activity[END_REF]. These surveys consist in 27000 notebooks, on which the 18500 participants wrote their current activity every 10 minutes over a complete week and weekend day. A typology of activities turns these notebooks into a database of human profiles (age, employment, social class, etc) related to the described activities.

The SMACH simulator first generates realistic synthetic households, based on national statistical databases of the population. Each household is composed of one or several agents characterized by their profile (age, socioeconomic class); the building they live in is characterized by its date of construction's thermal regulation, and its appliances. SMACH also computes the following statistical information from the TUS, for each individual profile and for each possible task the individual can choose to perform:  The task rhythm, i.e. the average number of repetition of the activity by day or by week.

 The task preferential periods i.e. indicate the periods of the day (or the week) which are favoured to perform the activity.

 The task duration: minimum duration and maximum duration of the activity. For example, SMACH can extract from the TUS that an upper middle class individual, active, between 20 and 40 years old, living in a household in a specific city would do his shopping once per week, usually around 8:00PM, with a standard deviation of 1 hour and with a duration of 30 minutes with a standard deviation of 15 minutes. This set of possible tasks is a part of description of the household. This provides a static description of the household's everyday life.

The agent model

The second part of the SMACH simulator consists in transforming this static description into a dynamic simulation. At each time step of the simulation, the agents select a task to perform. This selection is made by a mechanism based on dynamic priority levels. The priority levels are modified by parameters which influence the choice of the activity. For example, the current time and the number of previous realisations of the activity, depending on the rhythm and the preferential periods, impact the task selection. The selection mechanism also avoids oscillations between similar tasks, and considers the tasks performed by the others members of the household to satisfy dependency constraints between tasks, and to be able to perform collective activities. The current price of electricity can also lead agents to select less energy consuming tasks during peak-time periods, depending on the household's internal energy policy. A task dynamically selected from the static tasks pool becomes an action, and is performed by the agent. By realising this action, one agent will also exchange information with the others inhabitant of the household

Evaluation

The validity of the resulting simulations has been verified by comparing the activity diagrams and the consumption of simulated families with real families [START_REF] Huraux | Simulations multi-agents de l'activité humaine : application dans le contexte résidentiel français[END_REF]. The authors used a participatory simulations approach in which participants control the different agents in the household by selecting their activity manually. The participants validate the agent model by comparing the simulated activity diagram with the real activity diagrams obtained through participatory evaluations. The load curves generated by SMACH were also successfully compared to the real measured load curves. [START_REF] Reynaud | Using Time-Use Surveys in Multi Agent Based Simulations of Human Activity[END_REF]) also validated the activity model and the agent at larger scale. They generated a large amount of activity diagram with SMACH and compared the result with the notebook obtained though the Time Use Surveys. The authors showed that the activity diagrams simulated by SMACH, are similar to the actual activities from a statistical point of view, with some variability at the individual level. Aggregated load curves produced by SMACH were also compared to aggregated open data load curves from the electric distribution grid, showing a statistical accordance of the platform's results.

Model for collective energy self-consumption

Our contribution is to integrate energy self-consumption and energy exchange into the SMACH models. Figure 2 illustrates the general workflow of the SMACH simulator (blue boxes of Figure 2). Starting from the static description of the household, the agent model select a task to perform an action. This action will use electrical appliances. The simulation will compute their consumption and energy cost depending on the current tariff. The inclusion of the collective energy self-consumption is achieved by adding three new components (orange boxes of the Figure 2). First, we implemented a PV panels simulator. Second, we defined energy self-consumption rules for the appliances. Finally, we defined an energy exchange policy and an energy exchange model for the households.

Adding PV panels to simulate self-consumption

The building thermal model coupled with SMACH platform was initially developed with the Modelica language and the BuildSysPro library [START_REF] Plessis | Coupling occupant behaviour with a building energy model -A FMI application[END_REF]). This model is a detailed multi-zone thermal model. For the implementation of the PV panel model, we decided to use the same model library for its simplicity when defining electrical-thermal interfaces. The model simulates a crystalline silicon PV panels. Its inputs are the weather file, and it computes the generated electrical power (in kW) according to the following parameters:

 Surface  Tilt  Azimuth  Cleanliness of the panel
The model of the PV panels is used as a different Fonctional Mock-up Unit (FMU) than the building itself, yet can be interconnected with the building energy model. This allows us to modify the PV panels model and the building thermal model independently, and to pre-process PV generation if needed.

Evolution of the energy consumption model

We changed the way the various electrical appliances of the household consume the energy produced by the PV panels. Figure 2 shows that the generation of local energy does not affect the agent model as well as the activity diagram. At the stage of the study, only the impact of collective energy self-consumption on the Electric Water Heater (EWH) is studied. This choice was motivated by the fact that this appliance is automatically turned on or off according to the price of the electricity and the temperature of the water. Moreover, excluding electric heating, the EWH is one of the main sources of electrical consumption in the house (Pérez-Lombard et al. 2007). In our extended model, the EWH will be turned on as soon as the PV panels produce a sufficient amount of energy. If the energy generation is above a threshold, the EWH will use the available energy to heat the water. As an example, an EWH with a nominal power of 2000W would use the PV electricity if the PV panel's power exceeds 1000W. The EWH is given propriety over the other appliances for the consumption of PV electricity. With this operating mode, we guarantee that the EWH will have the necessary energy to operate. For the other electrical appliances, first, the energy need of all the appliances is evaluated. Then, we deduce the The EWH can still operate during low-cost energy time period or whenever the water temperature is critically low. In these cases, it will use the electricity from the distribution grid.

Modelling exchanges between buildings

To implement collective energy self-consumption, the definition of prosumer as defined by [START_REF] Tushar | Transforming energy networks via peer-to-peer energy trading: The potential of game-theoretic approaches[END_REF]) is used. Each building in the current simulation can exchange information about the household energy consumption and generation for energy sharing. Five different states in the process of energy selfconsumption are defined: 1. The prosumer consumes his own production; 2. The prosumer consumes the excess of energy of his neighbours; 3. The prosumer sends the excess of energy from his own production to his neighbours; 4. The prosumer consumes energy from the network; 5. The prosumer sells energy to the network.

The decision of sharing energy depends on the exchange policy agreed by each household. As mentioned in the Related Works, three types of policies namely distribution, cooperative and competitive were identified. The policy affects the amount and price of the energy exchange. In this first implementation, we focus on the interactions between households with one producer and several consumers, considering states 1, 3 and 4 in the prosumer model. We used an additional model to coordinate the energy exchanges, without simulating the behaviour of an energy trading place in detail. From the generic framework described above, a cooperative policy in which the producer gives all his excess of energy to his neighbours was adopted, as a first case study. In this model, the consumers will consume all the energy excess they can absorb. The model consists in two steps. First, the simulation of a time step with only the producer is carried out. He will generate energy with his PV panels and consumes energy according to his activities. Then, he sends a message to all the consumers with the remaining amount of energy. Second, the same time step for all the consumers is simulated. The consumers use the information about the remaining available energy to support their own energy consumption decisions. They notify to the producer the amount of the energy produced by the PV panels they used during this time step. All households use the same priority model of energy consumption for the shared PV energy: EWH first, then the other appliances.

Case study and results

Context of simulation

The SMACH simulator has the capacity to generate large scale synthetic households and building energy models. The implementation of collective self-consumption at a large scale is part of our current work. However as a first step, we considered three individual households A, B and C of the same neighbourhood in the city of Nice, France. The three houses are presented in Table 1 and the three families in Table 2.

Two active families (households A and C) and one family of retired inhabitants (household B) are simulated. The households are generated based on the Time Use Survey. The possible activity diagrams of each household are all different, however households A and C present similarities, like the fact that the members of the household go to work during the day (Figure 3). Household A is an energy producer thanks to its PV panels. Households B and C are consumers. For the producer, the PV panels characteristics are the following:  Area : 20 m²  Tilt : 30°  Azimuth : South The power of the PV panels is 2.5 kWp (kilo Watt-peak). Houses A, B and C have no electrical heating.

Table 1: Description of the three houses

Using these models, we assessed the impact of this collective energy self-consumption strategy on the energy consumption of the different families. We modelled the PV so that the energy generation of household A is sufficient to support a part of the energy consumption of household B. These families are different in terms of activities. The family of the household A is mainly outdoor during the day when the main part of the local energy is produced whereas for household B the family is indoor during the day The EWH consumes less energy from the network. The total energy consumption of the appliances in this second simulation is 180 kWh for one month of simulation. Even if the Household is the same, the two activity diagrams of the two simulation which lead to Figure 4 and to Figure 5 are different. This is inherent to the multi-agent simulation which introduces variability from week to week. That is why the total consumption is not the same.

During one month, household A consumes only 40% of its available PV energy. The energy excess is returned to the network. However, this energy excess could be used as part of exchanges with other households.

Impact of collective energy self-consumption

Figure 6 shows the consumption of household B while household A exchanges its excess of energy. The energy consumption of household B occurs mainly between 10AM and 5PM. The EWH energy consumption is the highest during this period. During the night, the EWH is turned on in order to maintain the water set point temperature. The energy consumption in the evening is The exchange allows covering 38% of the energy consumption of the household B. In addition, it provides 62% of the household A energy to the other houses. So the energy production of one household is sufficient to cover a large part of the energy consumption of the other households thanks to the exchange.

However, 38% of the household A energy is still unused. Within this cooperative redistribution strategy, we add another house in the exchange, namely household C. This household will consume the excess of energy from household B and more precisely 38% of the household A energy production.

Figure 7 shows the energy consumption of household C during one day. The profile of the load curve of this house is similar to the load curve of household A. But by looking more closely, only 24% of the total energy consumption is provided by the energy exchange with household B and 61% of this energy is consumed.

The amount of energy received by household C is low since households A and B consume most of the locally generated electricity. Moreover, there is always energy that remains unused despite the implementation of the exchange. The gain for household C is limited due to the fact that members of the family work outside during daytime, hence the importance of taking precisely inhabitants activities into account. A total of 83% of the energy generated by household A is used locally in the neighbourhood (compared to 38% when there are no energy exchanges with household B and C).

Conclusion

We presented a collective energy self-consumption model coupled with local energy generation by PV panels. A model of energy exchanges between one producer and two consumers was simulated. This model is based on the SMACH platform which simulates realistic human activities and energy consumption of households.

The energy consumption of the EWH calculated for household A remains high even with the PV panels, as 38% of the energy consumption comes from the distribution network. This energy is consumed mainly during the night while there is no PV generation. In this first use case without energy storage, the amount of PV energy household A consumes is independent of the energy exchange process with household B and C, as he is the only producer and distributes the remaining energy.

Collective energy self-consumption must be used in order to improve the use of locally generated electricity at the district scale.

The general framework and the case study results led to the conclusion that collective energy self-consumption could be relevant for optimizing the use of local energy generation. Moreover, for each energy exchange policy identified in our general framework, energy consumption from local generation or exchange could be increased or optimised through various means, that will be studied in the next steps of our work. One solution would be to encourage inhabitants to shift some activities or appliance use during the period of energy generation, through information or incentives. However some activities would be difficult to shift, such as fridge operation or lighting. In existing buildings, energy consumption due to TV, computers, cooking and cleaning only represents 10% of the total energy consumption of the households. In this case, the energy saving brought by the use of PV panels could be low. But the situation could be different for low-energy buildings, for which electrical appliances have a greater importance in the energy balance.

Another solution is the use of an energy storage system in order to store the energy provided by the PV panels. The use of energy storage systems will be include in the study as it will influence energy exchange and consumption. We plan to simulate both collective and individual energy system storage since they impact the energy consumption differently.

We presented a first implementation of our collective selfconsumption framework. The overall goal of this work is to create a model able to study a wide variety of collective energy self-consumption configurations. These configurations will include:  Various energy exchange policies within a neighbourhood, and between neighbourhoods;  Electricity prices and their impact on behaviour and energy consumption (the price of locally generated and exchanged electricity, the price of energy storage, and the market price of energy);  Various equipments related to local energy generation, including those dedicated to energy storage.

The simulation of numerous clusters of households with a collective energy self-consumption policy is also a goal of this work, with several identified strategies, using simplified building models and energy exchange places, where the energy exchange is done at a contractual level.

Figure 1 :

 1 Figure 1: Load curve and activity diagram generated by SMACH

Figure 2 :

 2 Figure 2: SMACH model with the addition of collective self-consumption

Figure 3 :

 3 Figure 3: Example of activity diagram of members of household A, B and C

Table 2 :

 2 Figure 4: Energy consumption of the EWH and the other appliances without PV panels for the household A

Figure 5 :

 5 Figure 5: Energy consumption of household A with PV panels energy generation

Figure 6 :

 6 Figure 6: Energy consumption of household B with exchange

Figure 7 :

 7 Figure 7: Energy consumption of household C with exchange


Student Member, IEEE Spiros Kotopoulis
email: s.kotopoulis@2005.hull.ac.uk

Antje Schommartz

Senior Member, IEEE Michiel Postema

Safety Radius for Algae Eradication at 200 kHz -2.5 MHz

Safety radius for algae eradication at 200 kHz -2.5 MHz

I. INTRODUCTION

A LGAE are known to cause many health hazards to hu- mans including skin rashes, gastrointestinal, respiratory and allergic reactions, [START_REF] Stewart | Cyanobacterial lipopolysaccharides and human health[END_REF] and liver cancer [START_REF] Fleming | Blue green algal (cyanobacterial) toxins, surface drinking water, and liver cancer in florida[END_REF]. In addition, blue-green algae may have implications on aquatic and semiaquatic animals, such as fish [START_REF] Bury | The toxicity of cyanobacteria (blue-green algae) to freshwater fish[END_REF] and platypus.

There are chemical methods to control certain species of algae, but these have side-effects such as promotion and growth of other species of algae [START_REF] Ferrier | The effects of barley straw (hordeum vulgare) on the growth of freshwater algae[END_REF] whilst also affecting aquatic life in fresh water ponds and lakes. Therefore, ultrasonic algae control has been under investigation [START_REF] Zhang | Ultrasonic damages on cyanobacterial photosynthesis[END_REF]. The frequencies used are as low as 20 kHz and as high as 1.7 MHz. Most commercially available equipment works in the lower ultrasonic range [START_REF] Postema | Onderzoek naar de veilige toepassing van ultrageluid gebruikt om blauwalg te bestrijden[END_REF]. There have been speculations about the physical mechanism behind the algae eradication, specifically about the role of cavitation.

In this study, we investigate the effectiveness of higher and lower ultrasonic insonification on blue-green algae. From the results, an estimate of the safety radius is made based on current regulations.

Algae strands contain nitrogen-producing cells that make them float. If the membranes of these cells are disrupted by means of ultrasound, the gas may be released analogous to [START_REF] Postema | Ultrasoundinduced gas release from contrast agent microbubbles[END_REF], causing the strands to sink. This is a desirable ecological effect. A measure for the safe use of ultrasound is the mechanical index (MI) [START_REF] Postema | Ultrasound-directed drug delivery[END_REF] defined by

MI = p - √ f , (1)
where p -is the maximum value of peak negative pressure anywhere in the ultrasound field, measured in water but reduced by an attenuation factor equal to that which would be produced by a medium having an attenuation coefficient of 0.3 dBcm -1 MHz -1 , normalised by 1 MPa, and f is the centre frequency of the ultrasound normalised by 1 MHz [START_REF]safe use of diagnostic ultrasound equipment[END_REF]. For MI<0.3, the ultrasonic amplitude is considered low. In clinical diagnostics there is a possibility of minor damage to neonatal lung or intestine [START_REF]safe use of diagnostic ultrasound equipment[END_REF] for 0.3>MI>0.7. These are considered moderate acoustic amplitudes. For MI>0.7, there is a risk of cavitation if gas cavitation nuclei are present, and there is a theoretical risk of cavitation without the presence of cavitation nuclei [START_REF]safe use of diagnostic ultrasound equipment[END_REF]. The risk increases with MI values above this threshold [START_REF]safe use of diagnostic ultrasound equipment[END_REF]. These are considered high acoustic amplitudes.

The maximum values to which divers can be exposed to, stated by the NATO Undersea Research Centre for Human Diver and Marine Mammal Risk Mitigation Rules and Procedures [10]. The maximum acoustic pressure to which mammals can be exposed is 708 Pa at frequencies up to 250 kHz. This corresponds to a mechanical index MI< 0.01 0.3.

II. MATERIALS AND METHODS

To investigate the effect of ultrasonic frequency on algae eradication, three ultrasound transducers were used. A 200-kHz transducer containing a PIC155 single undamped Piezo element (PI Ceramics, Lederhose, Germany), a 1-MHz, PA 188 single undamped element transducer spherically focused at 65 mm (Precision Acoustics Ltd, Dorchester, UK) and a 2.2-MHz transducer containing a Pz37 single undamped element transducer (Ferroperm Piezoceramics A/S, Kvistgård, Denmark).The focal distance of the 2.2-MHz transducer was 73 mm. The design of two transducers is shown in Fig. 1.

The algae used were of the anabaena species. The anabaena were cultured in 2 L of Jaworski's medium at room temperature near a South facing window in an Erlenmeyer flask for 11 days.

The culture was split equally into four 250-mL Perspex beakers: one control beaker and one for each transducer. The transducers were inserted separately in each beaker with the acoustic focus within the sample. Each transducer was turned on for 1 hour. The transducers were subjected to 16-Vpp square pulses at a 11.8-kHz pulse repetition rate transmitted by a V1.0 pulser-receiver (Sonemat, Coventry, UK). A digital picture of the solution was taken every five minutes using an EOS 350D digital photo camera (Canon Inc, Tokyo, Japan). The lighting and exposure settings were controlled and maintained throughout the insonification. Full manual settings were used: ISO 100, Exposure Time 1/50 s, F Number 3.50, Focal Length 18mm, No flash, Centre weighted metering mode, Custom white balance B4, 0 Shift. The digital images were converted to 8-bit grey scale. On both control and insonified solution, a square area of 160 x 160 pixles was taken and the average was grey scale depth was calculated using MATLAB (The Mathworks, Natick, MA). The change in shade from the first image taken just before insonification was calculated and graphed for both control sample and insonified samples.

Every 10 minutes a 20-µL sample was taken from the insonified solution. These were looked at under a CHA microscope (Olympus Corporation, Tokyo, Japan) and photographed. From these photographs, cell deterioration and chlorophyll damage was determined. To investigate the effect of ultrasound on chlorophyll, fluorescent light was used. When fluorescent light is projected onto chlorophyll it is absorbed and re-emitted as a red glow. The red glow denotes that the chlorophyll is still active and can photosynthesize, thus the algae strands are still alive.

After one hour insonification, twenty four 1-mL samples were removed from each insonified solution and put into a culture dish to see the effect of ultrasound on growth. Twentyfour control samples were taken. The culture dish was left in sunlight for 30 days.

III. RESULTS AND DISCUSSION

Fig. 4 shows the microscopic effect off ultrasound on the floating bodies in the algae solution. From 0 minutes to 60 minutes of insonification, no change was seen in the physical structure of the algae for the whole frequency range. Illuminating the algae with fluorescent light showed that the ultrasound had no effect on the chlorophyll activity for the whole frequency range. The active chlorophyll shows that the algae strands are still alive and able to photosynthesize.

Examples of increased clarity after insonification and increase in amount of sunken bodies can be seen in Fig. 2 and Fig. 3 respectively. Fig. 2 shows a faster and constant increase in brightness over time compared to the control experiment. The insonified sample maintained a greater brightness throughout the whole insonification period. At 55 minutes the insonified sample is 54% clearer than the control sample. Similar results were obtained for the whole frequency range. Fig. 3 shows shows a decrease in brightness over time compared to the control experiment. The insonified sample has gathered algae at the bottom of the beaker at a greater rate than that of the control experiment. More algae had sunk to the bottom of the beaker as compared to the control experiment throughout the whole duration of the insonification. At 55 minutes the insonified sample was 280% darker than the control sample showing greater amount of algae had sunk than that in the control sample. Similar results were seen throughout the whole frequency range. Clearly, the algae that were floating in the beaker dropped to the bottom at a faster rate than the control sample. This is attributed to the disruption of the floating bodies by the ultrasound.

The grey scale measurements for the culture dish can be summarised as follows. At 200 kHz, 1.0 MHz and 2.2 MHz, the samples were 15%, 41% and 34% brighter respectively, as compared to the control sample. These results support the hypothesis that the algae that have sunk are less capable of multiplying. Hence, insonification may prevent algae bloom.

In the acoustic focus, the highest sound pressure was calculated to be 219 kPa at 2.2 MHz, i.e., mechanical index of MI<0.15. Clearly, these values are much lower than the cavitation threshold. Comparing the acoustic outputs of the transducers to the NATO Undersea Research Center Human Diver and Marine Mammal Risk mitigation Rules and Procedures, i.e., 708 Pa between 31.5 kHz and 250 kHz, at very close distances the threshold for safe diving is surpassed. From insitu measurements of commercial equipment, it is estimated that the safe radius for swimmers is 15 m [START_REF] Postema | Onderzoek naar de veilige toepassing van ultrageluid gebruikt om blauwalg te bestrijden[END_REF]. Although the worst-case mechanical index close to the transducers is MI<0.3, some acoustic pressures determined are higher than those allowable by the NATO Undersea Research Center Human Diver and Marine Mammal Risk mitigation Rules and Procedures.

IV. CONCLUSION

It is possible to eradicate blue-green algae in the clinical diagnostic range. Taking into account the geometry,the low attenuation in water, and the NATO Undersea Research Centre for Human Diver and Marine Mammal Risk Mitigation Rules and Procedures, even at these low voltages, the safe swimming distance is at least several meters away from the sound source.

Fig. 1 .

 1 Fig. 1. (a) Undamped 2.2-MHz ultrasound transducer with d = 1" diameter and ra = 35 mm acoustic lens. (b) Undamped 200-kHz ultrasound transducer with h PG = 10 mm.

Fig. 2 .

 2 Fig. 2. Water clarity as a function of ultrasonic exposure time for a 1.0 MHz frequency. Higher values show greater clarity.

Fig. 3 .

 3 Fig. 3. Water clarity at the base of the beaker as a function of ultrasonic exposure time for a 1.0 MHz frequency. Lower values show more sunken algae.

Fig. 4 .

 4 Fig. 4. Microscopic image sequence showing the effect of 200 kHz -2.5 MHz ultrasound on algae. Each frame corresponds to 565 × 565 µm 2 . Under fluorescent light the red shows active chlorophyll.

V. ACKNOWLEDGMENTS

This work has been supported by EPSRC grant EP/F037025/1, RAE grant L7-1062, the HERI Research Pump Priming Fund, and the Ruth und Gert Massenberg-Stiftung. We would like to thank John Adams, The University of Hull, for support with the experimental setup.