Design of Experiments for Coatings E-Book

Albert Rössler

• Herausgeber: Vincentz Network
• Kategorie: Wissenschaft und neue Technologien
• Serie: European Coatings LIBRARY
• Sprache: Englisch

Seitenzahl: 262

Veröffentlichungsjahr: 2014

Beschreibung

In order to efficiently develop and improve coatings formulations, it is essential to analyse the several factors affecting their properties. For this purpose, Albert Rössler has compiled a comprehensive overview of the statistical approach of design of experiments (DoE), pointing out its effects and benefits for coatings development. Based on real-world applications in coatings formulation, he shows that statistics don' t have to be that dry and difficult mathematics. Essential for everyone who wants to dive into the topic quickly and start using DoE straight away.

Leseprobe

Albert Rössler

Design of Experiments for Coatings

Cover: Adler-Werk Lackfabrik GmbH & Co. KG

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Albert Rössler

Design of Experiment for Coatings

Hanover: Vincentz Network, 2014

EUROPEAN COATINGS LIBRARY

ISBN 3-86630-885-X

ISBN 978-3-86630-885-5

© 2014 Vincentz Network GmbH & Co. KG, Hanover

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EUROPEAN COATINGS LIBRARY

Albert Rössler

Design of Experiment for Coatings

Preface

For sure you have experience with such problems: the complex production process or the demanded coating properties are affected by several factors (grinding time, binder content, amount of additives, drying time, etc.). You would like to improve the system and do not know which are the most dominant factors. No wonder, as long as your formulation is assembled by 10 components. The experimental setup get out of hand, results are unintelligible and the documentation is fragmentary at the end. In this situation you might got already the advice to try the statistical approach by design of experiment (abbreviated DoE). Nice, but what is that? Beside, statistics sounds like mathematics and at the moment you are too busy for such things?

Well, time and some distance from the daily business will be necessary, if you read this book. However, the aim is a short and generally understandable overview regarding the effects und benefits of DoE by examples in step with actual practice. The examples are based on real-world applications in coatings formulation. This adds the important strong application flavour to this book, makes it useful as a reference tool and show that statistics doesn’t have to be that dry and difficult mathematics. In addition, requirements for the approach are illustrated, which are quite often general principles in experimental design and project management. It is not possible to describe the topic without any statistics or mathematics, but formulas and derivations are at the least possible amount in this book. So, the prerequisites are relatively modest. In addition, there is no claim to be complete, because the topic and connected mathematic methods as well as tools for data analysis are too extensive. Due to this, the textbook familiarize first-time user and already practicing laboratory assistants, engineers and chemists with possible applications and high potential of the method. It is important to succeed the entrance and to get a feeling of success by try and error. It’s no problem, if not everything is clear in the first run. Experience about useful applications and limits will be generated in the course of time. After that, this technique will attend you for sure as valuable providing tool for a long time. The skills acquired in dealing with this method can also be employed in other applications, such as adhesives and sealants as well as all other engineering and scientific issues.

Chapter 1 introduces the method and shows especially the difference to the classical approach. With an example directly out of the “coating-formulation kitchen” it will be helpfully shown, how the systematic method DoE can reduce the daily mania in the research laboratory. Derived from today’s criteria of success in R&D, also general principles of project management and design of experiments are illuminated.

Chapter 2 reflects the design methods and introduce into the important preliminary step of drawing up a strategy of experimentation. State of the art experimental designs are presented together with their properties. This should help for precise selections later on in practice. Planning as preliminary step is the basic for all further details and the potential savings are naturally enormous. Therefore, planning is of much higher importance as the subsequent data analysis. A lot helps a lot in this context!

Chapter 3 is devoted to the data analysis and interpretation. During this period the basic principle „nothing ventured, nothing gained“, can be applied. Only data from perfectly planned and designed experiments ends up in reasonable interpretations. On the other hand, the best set of data is useless, when no interpretation and good compression is performed. Where is the limit? How valid and precise are the conclusions? These are some questions, which will be answered in Chapter 3.

Chapter 4 introduces the standard optimization processes and describes how to convert modelling results into concrete action. The determination of cause and effect correlations during the identification of the most dominant factors is only one part of the story. It is also of high importance to find those operating conditions, which lead to a maximum, minimum or a certain value (or range) of the target response. In addition, just optimizing a problem will end up very often in results, which are sensitive against small variations in the factor settings due to disturbances. To look on the issue in its entirety, also strategies for robustness studies are described, leading to processes and products that perform better in the field due to variability reduction. In a manner of speaking: finding a needle in the haystack.

Chapter 5 describes some DoE software solutions on the market. It is not necessary to reinvent the wheel once more and to create all experimental designs by hand. Modern and good designed programs assist the practitioner in the number-crunching.

Short text elements including basic principles are included in all book chapters. They summarize general and essential messages regarding design of experiments and performing experiments. These elements do not replace the rest of the book as a kind of summary, because basic principles are not covering methodical details. Basic principles only intensify relevant messages regarding the philosophy of the DoE-concept. Therefore, they are not used inflationary.

Research and development in coating industry is highly affected by experience. If somebody is working long enough in this branch, a comprehensive treasure of raw material and formulation knowledge will be acquired. This experience is very important and is beside the application knowledge the working basis. However, research and development underlie today tough necessities, because innovative ideas, higher rates of success, shorter time to market as well as lower R&D-costs should be realized in parallel. Therefore, both, a deep understanding of the increasing international customer demands and economic mentality becomes more and more important in research laboratories. In addition, knowledge about the correlations – independent if the recipes, the production or the application process are in focus – is essential for creating innovative, stable, robust, cost-optimized and high-quality products very rapid today. Thus, methods which support purposefully and efficiently working are crucial to be successful.

Design of experiments is one possibility, to reply the challenges of today and to manage the important free space for creativity due to higher efficiency. This book can assist you in this challenging task and shows how coating formulators can benefit from DoE.

Innsbruck, Austria, Mai 2014

Albert Rössler

Contents

1 Design of experiments – systematic mania?

1.1 Design of experiments as part of the challenges and criteria of success in modern R&D

1.2 A typical experiment in coatings formulation

1.3 Factors, Levels, etc. – some vocabulary at the beginning

1.4 Classical design of experiments and the limitations

1.4.1 Conventional methods – more diversity is not possible

1.4.2 Limits in case of the classical approach

1.4.2.1 Number of experiments in case of many factors

1.4.2.2 Non-linear effects and domain dependence

1.4.2.3 Universality of the statements

1.4.2.4 You desire, we play – multiple responses

1.4.2.5 The gain of knowledge and new information is too slow

1.5 Design of experiments – what’s that?

1.5.1 Design, factors and effects

1.5.2 Interactions

1.6 Where is the statistics?

1.7 Models – pictures of reality

1.8 Overview, possibilities, benefits and limits

1.9 A brief history of statistical design of experiments

1.10 References

2 Planning is essential – a lot helps a lot

2.1 General principles for setting up a DoE investigation

2.1.1 Strategy of experimentation and guidelines for pre-experimental planning

2.1.2 Overcome experimental errors – identical replication

2.1.3 How to overcome trends – randomization and arrangement in blocks

2.1.4 Normalization, centring, orthogonal design

2.1.5 Not realizable, irregular combinations – the experimental region

2.2 Factorial designs – the heart of DoE

2.2.1 Two levels, two factors – 22-design

2.2.2 Two levels, three factors – 23-design

2.2.3 The general design with two levels – 2k-design

2.2.4 Factorial designs with centre-points

2.2.5 Blocking with factorial designs

2.3 Fractional factorial designs – to separate the wheat from the chaff

2.3.1 Basic principle of the reduction – confounding

2.3.2 Blocking – perfect suited for the 24-1-design

2.3.3 Types of fractional factorial designs

2.3.4 Plackett-Burmann designs

2.3.5 DoE in colour measurement of a red-metallic base coat – 26-1-fractional factorial design

2.4 Non-linear effect designs

2.4.1 Central composite designs

2.4.2 Three- and higher level designs

2.4.3 Mixed designs

2.4.4 Box-Behnken designs

2.4.5 D-optimal designs – egg-laying wool-milk-sow

2.5 Mixture design – a huge area

2.6 Qualitative classification

2.7 References

3 Number-crunching – nothing ventured, nothing gained in data analysis

3.1 Evaluation of raw data

3.1.1 Transformation

3.1.2 Outliers

3.2 Confidence intervals – where are the limits?

3.3 Regression – the best model

3.3.1 Basic principles

3.3.2 Confidence intervals for the model parameters

3.3.3 Basic principles and standard assumptions for regression analysis

3.4 Residual diagnostic – what does the deviations mean?

3.5 Analysis of variance – how certain we can feel?

3.5.1 Introduction

3.5.2 Example: Colour measurement of a base coat – ANOVA

3.6 References

4 Parametric optimization and sensitivity analysis – finding a needle in the haystack

4.1 Strategies for optimization – how we can do it better

4.1.1 Method of the steepest ascent/descent

4.1.2 Box-Wilson’s method

4.1.3 EVOP-Method (evolutionary operations)

4.1.4 Simplex-method

4.1.5 Further optimization methods

4.2 Multiple responses

Example: Multiple optimization of blocking and film formation in a clear coat

Example: Optimization of an indoor paint

4.3.1 Qualitative analysis of the response surface

Example: Disturbance in levelling of a pigmented base coat

4.3.2 Quantitative analysis of the regression model

4.3.3 Taguchi-method

Example: Micro foam in a thick-coat glaze finish

4.4 References

5 DoE-Software – do not develop the wheel once more

Autonomous commercial software-packages for DoE:

Statistic packages

EXCEL-based Software

Appendix 1 – Precision, trueness and accuracy

Appendix 2 – Location and spread parameters

Example: pH-value of a lime paint

Example: pH-value of lime paints

Appendix 3 – Normal distribution

Example: pH-value of a lime paint

References

Appendix 4 – Confidence intervals

Example: pH-value of lime paints – continuation

Appendix 5 – Hypothesis, tests and conclusions – statistical tests

Example: Picking mushrooms

Example: Comparison of two standard deviations

Example: ANOVA – comparison of two square sums

References

Appendix 6 – Three-component diagrams

Appendix 7 – Linear regression

Example: Estimation of the glass transition temperature via DSC

References

Appendix 8 – Failure mode and effect analysis, FMEA

References

Appendix 9 – General references

Acknowledgements

Author

Index

1 Design of experiments – systematic mania?

1.1 Design of experiments as part of the challenges and criteria of success in modern R&D

A rapid change engraves the world of business in the 21th century. Due to the progressive globalization and the connected increasing competition, market conditions become tougher. Companies are constrained to establish a restrictive culture of continuous product- and process-improvement. Otherwise quality problems and low efficiency end up in a dramatic financial loss. Only fast, flexible and powerful operating will survive in the future. Cost aspects, quality of the products and short cycles of development (time to market) [1, 34, 36] are the essential directions of impact for enterprises today (see Figure 1.1).

Figure 1.1: Criteria of market success [1]

Derived from these aspects, research and development (R&D) underlie today tough necessities, because innovative products, higher rates of success, shorter time to market as well as lower R&D-costs should be realized in parallel [2]. Thus, the following most essential criteria of success in modern R&D can be mentioned [1, 34, 36]:

• A deep understanding of the (increasing international) customer demands (success factor customer value orientation).

• Goal-oriented and efficient advance during product and process development considering the principles of economics – maximum amount of relevant information with a minimal effort for experiments (success factor efficiency).

• Knowledge about the correlations within the process chain – independent if the recipes, the production or the application process are in focus (success factor system knowledge).

• Generation of additional synergy and velocity due to a platform strategy or a robust building block system already in the period of development [27, 35]. Due to that, it is not necessary to develop a completely new product for each customer demand (and to produce it later on) (success factor efficient diversity, managing the product complexity).

• Integrated thinking as mentality already during research and development, to avoid a so called local limited island optimization without looking on the up- and downstream demands (e.g. fast and efficient production) (success factor integrated mentality and efficiency).

• Stability and quality of the products and processes (success factor quality).

Figure 1.2: Steps during a R&D-project inclusive a feedback loop for the information

These criteria are only completely successful, if in addition

• the R&D department is based on a high performance organisation, raising the synergies between different R&D groups, technologies and issues as well as supporting dynamics in contact with the customer or during dealing with comprehensive issues due to a strong project organization in parallel to the structural organization (success factor structure)[31], an optimized project management inclusive a project culture is existing [32].

• the organisation and the company culture are the homeland of creativity and continuous improvement (success factor innovation culture, discussion culture and failure management).

• enough resources are present to ensure the essential free space for creativity and short reaction times also at high capacity utilization (success factor capacity planning),

• process cost calculation is in focus and manufacturing costs are always under consideration in their entirety (success factor process thinking).

• R&D team consist of flexible, highly qualified, team-minded and motivated employees, who live this philosophy, share knowledge with each other, are open for new aspects – leading the company daily to success (success factor employees).

Central element of each development in natural science and engineering is the experiment, including measurements or simulations on the computer (see Figure 1.2). It is an elementary unit of each research project. Unfortunately, in technical oriented branches it’s still an illusion to develop a new product just on the writing desk. The interactions in systems (e.g. surfactants, thickener, binder, solvent) are too complex and simulation tools are very often imprecise (e.g. regarding the long term behaviour). The high degree of interactions in coating formulations (e.g. a white wall paint) is shown in Figure 1.3a). Already the fact, that 13 or even more different components are present in the system, which might be from 10 different suppliers, describes the high complexity of chemical as well as physical interactions. Interactions are also obvious due to the fact, that single components have a different active potential in different formulations. It is not enough to look only on single interactions and to test raw materials in standard formulations. An example based on the gloss and spread rate of white pigmented wall paints is shown in Figure 1.3b). Wetting agent A can achieve quite good results in binder 1, but not such a high level in binder 2. However, the behaviour of wetting agent B is the opposite way around. Thus, the quite common 1:1 exchange of raw materials has only limited explanatory power about the potential of single raw materials. Integral formulation optimization is the essential part of the game, to raise the whole potential. This ends up, at least in case of high-end products, inevitably in an intensive and open cooperation between coating manufacturer and the raw material supplier (success factor network, cooperation, open innovation). Otherwise robust products cannot be realized in an acceptable time frame.

In addition, in practice mainly formulations with a long history are present and the path of formation development cannot be reconstructed. Very often components are added to a formulation due to some problems, but nobody will remove them afterwards – independent if the trigger for the problem is still present or not. Last but not least the extensive unknown chemical and physical design of the raw materials makes the situation even worse. Altogether, geniality and innovation consists still today – as already Thomas A.Edison said – of 1 % inspiration and 99 % transpiration, or in other words, no pain, no gain.

Figure 1.3a: Integral formulation optimization: Complexity and interactions in a coatings formulation [40]

Partly, the experiments are also connected with an extreme high effort, a lot of time and high costs. Thus, methods which support the above mentioned aspects by

• a systematic, structured approach during (research) projects, experiments, etc.,

• a reproducible and objective analysis of cause-and-effect-correlations in case of experiments, products and processes and

• an adaption of the experimental effort according to the requirement during (research) projects

are crucial for the success of the companies.

Figure 1.3b: Integral formulation optimization: Gloss and spread rate for a white wall paint as a function of the binder and the wetting agent [33]

Every approach which supports or even enables this method of operation is, because productive and value added, welcome. Only by this way [22, 23]

• unnecessary loops for variations during the development of products and processes can be reduced or even avoided,

• precise statements can be performed and subsequent steps can be initiated,

• the relevant influencing factors of a system can be identified (success factor system knowledge),

• certain lacks in products or processes can be identified already preventive by a systematic analysis of influence and undefined or hardly controllable influence factors already in the development stage. This ensures a sustainable success with robust products and processes that can be used in a large application window.

• exact prediction of the experimental effort can be performed,

• all relevant experimental data are available in a reproducible manner after the experiments,

• not necessary experiments can be avoided,

• technicians will be faster in their daily business,

• the odds of success for realizing real technology jumps in an acceptable time frame with defensible costs are finally increasing.

The importance of increasing the system knowledge should not be underestimated (success factor system knowledge). Of course each development is generating a comprehensive treasure of empirical values about the realized product, the raw materials, the applied aggregates, etc. However, thereby hardly any quantitative statements are generated. Outsider will have the feeling, that these empirical values are more than less only qualitative feelings of single persons with a low reproducibility. As a consequence, precise predictions about system behaviour cannot be realized. Unfortunately modern high performance products permit no tolerance concerning this matter. Designed as boosters for the company, a perfect balanced relation between cost structure and property profile is crucial. Simultaneously all functionalities of the products must be realized and continuously improved with a decreasingly number of raw materials suppliers. In addition, the performance characteristics should be robust against disturbances. Only an extensive and for everybody in the company available, documented factual knowledge about the relevant parameters of the system enables – by combining with the empirical values and intuition – efficiently procedures for the development of new products or for the fast elimination of troubles. In parallel, these skills allow a significant improve in the performance of the coating systems, because the whole complex and interacting system is optimized. System knowledge is also essential for the successful application of the already emphasized standardized technological platforms (success factor efficient diversity, managing the product complexity), because the building blocks will be used in many systems [27]. Utilizing rigorous standardization will reduce variation and create flexibility and predictable outcomes. Thus, it is important to have a good knowledge about these modules.

Overall, these methods lead to a cost reduction, optimized time schedules and dramatic reduction in time to market (money) for new products – finally representing a modern, powerful R&D-strategy. Especially useful auxiliaries join in the phase of planning, which represents the basic for each project and each experiment (see Figure 1.2) [1](success factor project management and front-loading). In this period the strategy for further experiments is defined. Errors from this period influence the whole project and can compromise the aim of the project. In addition, the costs per each change in the product design or production process are increasing drastic during the project time (see Figure 1.4) [3]. A rule of thumb tells, that the cost for bug fixing decuple from each project step to the next [19]. To describe this also with an example, think about planning a house. In the very beginning, it has to be decided if wood or bricks are used for construction. Later on, maybe if the house is already under construction, any chance from wood to bricks will be very expensive. In the worst case, the house has to be pulled down. A good planning increases the odds of success!

Basic principle: Planning represents the basic step for each project. A rule of thumb tells, that the cost for bug fixing decuple from each project step to the next, because errors from the very beginning influence the whole project and can compromise the aim of the project. Therefore, front loading in the development process is a basic principle, because there is a maximum design space to explore alternative solutions thoroughly.

Figure 1.4: Influence of decisions on the target achievement and caused costs during the progress of a project [3]

All people are planning, when they would like to do something, which is different from the daily routine. If somebody would like to buy a car, he will think first of all which demands should be fulfilled: A certain label? A diesel engine or an alternative fuel vehicle? Five doors to insert the buggy into the car comfortable or a small and compact car to find a parking place simply in the city? Afterwards a sequence has to be defined to reach the aim (car dealer, newspaper, etc.) [30].

Also during experiments one or more factors are changed depending on the question behind. Thus, experiments are different from observations! Due to this fact, each experimental series need – as buying a car – a strategy of experimentation. The experimental design is aligned with the aim/target at the very beginning and is afterwards executed step by step. However, in the daily practice of a laboratory the conception of experiments is carried out – in contrary to buying a car – very often not highly reproducible and neatly arranged. This is for sure not always necessary, because of dealing with simple questions and a huge treasure of empirical values. However, it is not supposed to derive each experiment of a series by random or by intuition just due to the result of the previous experiment (see also random-method and intuitive method in Chapter 1.4.1). This procedure is not calculable in costs and not reproducible for outsiders. Only planning can prevent generating not necessary experimental data and ensure that all relevant information is present to verify the statements.

Basic principle: Each experimental series has to be based on a strategy. An experimental design is defined at the beginning aligned with the desired goal and is afterwards executed step by step. Each experiment of a series cannot be derived by random or by intuition based on the result of the previous experiment. This procedure would be not calculable in costs and not reproducible for outsiders.

Planning is therefore more than just facing problems in a certain way. First of all, the target has to be defined as precise as possible [30, 32]. What is the problem and what is the desired result are the most important questions in this period. It is crucial, that there is a clear indication by simple, quantitative and easily measureable (by a validated method)definition of the target (see also Chapter 1.6 and 2.1). Target definition is team work. If there is no clear aim, each participant has its own individual target. Stress, conflicts and inefficiency are pre-programmed. Very often, people are subject of false conclusions by thinking that everybody in the team has the same picture in mind. Ask 6 persons to draw a mode of transportation and you will get 6 solutions from airplanes up to cars. The target agreement was not precise enough. Without such a target agreement, projects will end up in a catastrophe.

The worst case will happen, if the target is moving during the project. This should be prevented, but keep in mind that planning is always a hypothesis which has to be adjusted with cumulative knowledge. The thesis can be summed up by a statement of the German field marshal Helmuth von Moltke, that “no plan survives contact with the enemy”. Demands of customers can change abrupt, e.g. when the competitor comes to the market with new attractions or trends. Therefore, projects should be started only, when enough capacity is available. Otherwise the risk of moving targets is increasing due to slow progress and lag of time in the project [28, 29]. Be aware of the fast technical development in some branches!

Basic principle: Defining the purpose of a project is crucial for the ability of the project team to solve the issue. Due to this, the team can focus on the relevant factors and targets [28]. Teams must have a clear indication and understanding of the target, which should be declared in written form, simple, quantitative and easily measureable by a validated method.

Experimental series should generate objective and authoritative information (based on data). It is therefore – as shown in Figure 1.2 – partly necessary to have a feedback loop. This means, that the design is modified due to some new insights from data analysis and further experiments are done. Thus data are never equal to information. Methods, which can also assist during this interaction between design and results of experiments, are of outstanding value. Experiments are usually iterative and especially in case of first efforts or learning experiments the degree of feedback is quite high.

Basic principle: Experiments are usually iterative. Thus, the design of experiments is very commonly modified due to new insights from data analysis of previous experiments. This feedback is essential to have an optimized progress in the ongoing project. The degree of feedback is increasing with decreasing system knowledge at the beginning of the experiments.

For the sake of completeness it should be added, that targets based on facts does not lead without fail to product efficiency. Clever developments are for sure the core of R&D (lat. ingenium – cleverness). Unfortunately, it is very often a perfect stimulation for technicians and engineers, to break a technical record. Therefore, it is important to keep always in mind, that product properties just fulfil the customer demands (success factor customer orientation). It is not necessary – or even more precise useless – to create more features, than aligned with the customer (principle of lean development to avoid muda – muda, japanese meaning uselessness; waste; wastefulness) [37, 38]. Benchmarking and value analysis [20, 21] are perfect possibilities to check this issue. In general, the products should be as simple as possible, but not simpler. The question, which functionalities can be omitted is of the same importance as one about the demanded skills [28]. Companies will be only successful in the long term and with sustainability, when the products are as good as necessary, but not as good as possible. Already an old Chinese saying told us, that the worm must taste the fish, not the fisherman.

Systematic approaches in experimental design represent one way to reply the actual mentioned challenges of R&D. Permitted targets, which are focused by experimental data collection and subsequent evaluation, can only be reached in an efficient way by such a systematic method.

Basic principle: Basic idea and purpose in experimental design is to improve the efficiency (quality and quantitative amount) in product and process development by eliminating the intuitive “trial and error” or even “random” methods with a more systematical approach, transparent correlations and a minimal effort for experiments (which is known already before starting). Thus chances at the market can be perceived earlier by a substantial reduction of the development time.

Economic aspects are today an integral content in the mind of natural scientists and engineers. Design of experiment (DoE) can also be understood as philosophy or mindset, which is as package highly cross-linked with supplemental up- and downstream tools like project management, quality management, benchmarking, Quality Function Development (QFD), Failure Mode and Effects Analysis (FMEA – see Appendix 8), combinatorial material research [24], platform strategy [27], etc. This philosophy can revolutionize product and process design in many kinds. Design of experiment is also an integral element of quality planning and quality management in R&D, construction and process planning [22, 23]. Of all the statistical tools used today, design of experiments offers the most power for making breakthroughs for variability reduction in coatings formulation and processing. Finally, this element perfectly suits to the principles of lean-development, which bear on the analysis of structures, processes and tools regarding dissipation and the definition of possible countermeasures [37, 38].

In the last years laboratory automation has become a really hot topic in coating science. High-throughput-sites supply more and more the development of coatings [25, 26]. Is this increasing the efficiency? Such instruments can only be used in a meaningful way, as long as design of experiments is done at the front end and data analysis is adjusted on this method. Then, the potential of a lab robot can be developed to a whole extend. Intuitive experiments, just looking what happens, rough fathom of limits, etc. has to be done before in the classical laboratory. Otherwise, the effort for programming the machine is too high and the overall equipment effectiveness (OEE) too low. With a combined working strategy High-throughput methods can be enhanced to High-output-methods. Finally market chances appreciate earlier and at better conditions.

1.2 A typical experiment in coatings formulation

The roman philosopher Lucius Annaeus Seneca already mentioned, that “the way through education is very long, but short and effective by examples”. Thus, let us consider as introduction a typical experiment in coatings formulation: adjusting the surfactant content on the amount of solids like pigments, fillers, etc. Precise, we focus on the development of a waterborne filler concentrate made of barium sulphate by using a polymer based dispersant agent. Aim is to adjust the viscosity at a certain value (approximately 2000 mPas at a shear rate of 100 s-1, 20 °C) and to realize in parallel the maximal possible transparency. From earlier experiments it is known, that the maximal amount of an inorganic thickener is limited due to its negative influence on other coating properties to a constant value of 0,3 %. A variation of the concentration or using other thickeners (e.g. polyacrylic base or cellulose ethers) is also not possible. What are you doing?

By intuition, the surfactant will be premixed with water and afterwards the filler will be added by dispersing. A starting point regarding the filler and the surfactant content is known from experience or can be found in a reference formulation. However, before starting a lot of questions have to be answered:

Figure 1.5: General description of a technical system

•