Probabilistic Neural Network prediction of liquid- liquid two phase flows in a circular microchannel

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1 Journal of Scientific & Industrial Research Vol. 73, August 2014, pp Probabilistic Neural Network prediction of liquid- liquid two phase flows in a circular microchannel R Antony, M S G Nandagopal, S Rangabhashiyam and N Selvaraju* Department of Chemical Engineering, National Institute of Technology Calicut, Kozhikode , Kerala, India Received 4 January 2014; revised 26 April 2014; accepted 10 June 2014 The present work proposes towards flow pattern prediction in a liquid- liquid microchannel flow through a circular channel. Mass transfer in a microchannel mainly depends on the flow regime inside the channel. The liquid-liquid two phase flow regime in a microchannel depends on the flow velocity and the junction characteristics. Hence, the prediction of patterns has a superior role for the characterisation of mass transfer rates. This paper experimentally investigates the flow pattern in an 800 micro meter diameter microchannel with T junction. The slug length variation corresponding to varying inlet flow rate for the aqueous (water) organic (kerosene) liquids is visualised and measured. A model for the prediction of liquid- liquid flow patterns in a circular T-shaped microchannel is designed using Probabilistic Neural Network (PNN). The designed PNN algorithm is explicitly validated by comparing the predicted patterns with the experimentally observed data. Keywords: microfluidics, microchannel, probabilistic neural network, flow pattern prediction Introduction In microfluidics, microchannels with a hydraulic diameter less than 1 mm is used to process (Reaction, Extraction, Testing, etc.) the fluids in micro volumes. They are fabricated by advanced micromachining or lithography techniques 1. A microreactor holds many advantages over conventional type reactors like batch and plug flow reactors. Developments of new miniaturized micro reactors are possible by integrating microfluidics concepts in chemical reactors. Small diameter of the channel implies high surface to volume ratio, favours enhanced heat and mass transfer. Micro channel structures and their nature hold a great impact on the current industrial scenario 2. Micro level chemical reactions or mixing provide easy handling of hazardous reactions and also imply a high safety and efficiency over other conventional type reactors by enabling a good control over the reactions 3. The formation of liquid- liquid flow patterns highly depends on the fluid hydrodynamics, junction properties and the inlet flow rate. Two phase flows are generated when the partially miscible or immiscible solutions are brought into contact in *Author for Correspondence selvaraju@nitc.ac.in micro channels. Gas-liquid and liquid-liquid flows are the most common two phase flows observed in micro reactor systems, generated with the help of T or Y shaped junctions 4. Study of mass transfer, mixing, extraction and reactions with microchannel is not possible without thorough knowledge in the flow patterns and it owes a predominant role in the design of control scheme for the microchannel two phase reaction systems. The quantitative prediction of liquid- liquid flow patterns is available in literature, but it is observed to be comparatively complex than the artificial neural network based prediction algorithm 5. The present work intents to develop a single flow pattern predictor, which is capable of indicating all possible immiscible liquid- liquid flow patterns in a circular microchannel system with their diameter ranging from 530 µm to 900 µm using probabilistic neural network. The motivation of the present work is originated from the existing research on gas- liquid pattern predictions 6,7. Comparatively, our proposed prediction model predominates the existing one in two aspects like dearth of prediction algorithm for immiscible liquid-liquid flow in microchannel, existing models predicts the flow patterns for microchannel of particular diameter, while the proposed model predicts over any microchannel diameter compass.

2 526 J SCI IND RES VOL 73 AUGUST 2014 Liquid-Liquid flow Patterns in a Microchannel Two phase flows have a good importance in continuous type chemical reactors. The term two phase flow indicates either liquid liquid flows or gas-liquid flows. For the prediction of flow patterns in a microchannel, four types of flow patterns are considered namely: bubbly/ droplet flows, slug/ bullet flows, annular flow, churn/ mixed flows 2,4,5. Bubble/ Droplet Flow: When the flow rate of the non wetting phase is much lower than the one of the wetting phase, droplets/ bubbles will form with the diameter less than the internal diameter of the channel 2 resembling a bullet flowing through the channel. Segmented Flow: Segmented flows looks like bullet shaped or curved rectangle shaped flows in the channel. Segmented flows are formed when the ratio of flow rates for the wetting to the non wetting phases is close to unity. 2 Annular Flow: When the ratio of flow rates for the wetting phase to non wetting phase is very small, the wetting phase is confined to the wall, flowing as an annular film. 2 Mixed Flow: This flow pattern shows a mixed property of all flow patterns. In some region it resembles like bubbles, in some other portion, as slugs, and sometimes undefined pattern. 2 Experimental Setup T junction used for study has cross sectional area of 800µm, which is made by micro drilling in a acrylic block acrylic (1). The micro drilled T junction is connected to a 60 cm long Teflon tube (2) with the same diameter (Atopelec Pvt Ltd, Beijing, China). The T junction has a length of 3 cm in its outlet (which is connected to the Teflon tube (2)) and 2 cm for each inlet and is connected to the micro syringe infusion pumps (Plenumtech Pvt. Ltd., India) (3). The micro syringe infusion pumps are having an injection rate of 0.1 ml/hr to 1200 ml/ hr (accuracy up to +/- 1%). The flow patterns are measured by a digital camera with inverted lens (Nikon 1 V 1 with 1200 fps and screen resolution 921k dots) (4). The flow patterns are visualised by connecting the camera to a laboratory computer with a USB. The microchannels are illuminated by arranging LED light strips (6) for getting better visualisation. During the experimental runs, the mixture from the outlet of the capillary channel was collected in a glass beaker (7). Flow patterns inside the channel are analysed by passing two inlet fluids with different flow rates. The inlet liquids used are distilled water and kerosene. The whole experiments were conducted in room temperature. The obtained flow patterns were analysed graphically. Methods for the prediction of flow patterns Neural network algorithm is the core prediction method adopted here for the flow pattern prediction of immiscible liquid-liquid in a microchannel. Artificial Neural Network is a computational simulation of a biological neural network in performing the functions collectively. Generally, an artificial neural network contains three types of parameters: inter connection between nodes, updating the weights in the inter connection, activation function that converts neuron s weighted input to the output function. Computational neural network models are generally referred as artificial neural networks and are essentially simple mathematical models with a function f: X Y or a distribution over X or both X and Y, but sometimes models are also associated with a particular learning algorithm. In neural based prediction of flow patterns, the function, f is trained with a set of inputs and outputs. Neural network model for pattern classification in the proposed work is based on feed forward type networks. Feed forward (in which no loops are formed by network), and feedback (in which one or more loops are formed) type neural networks are the common categories in an artificial neural network. Neural Network for pattern prediction Pattern prediction is an important application of the neural network, and has a great efficiency compared to other prediction methods. The basic application of pattern prediction in microfluidics is for the design of immiscible liquid liquid reaction in micro reactors. Most of the micro reactors are designed focussing on slug flow based reaction as its modelling is also easy compared to other patterns. The effective slug flow pattern prediction is possible with the help of good pattern predictors such as neural network based algorithm. To achieve better efficiency in the prediction and least error rate, forward type networks are preferred 6. Probabilistic Neural Network (PNN) Probabilistic neural network is using an exponential function as activation function and is used to compute nonlinear decision boundaries which

3 SELVARAJU et al.: PROBABILISTIC NEURAL NETWORK PREDICTION 527 approach the Bayes optimal. The probability density functions of PNN are evaluated using the Parzen s nonparametric estimator and PNN utilizes one probability density function for each category 6. The generalized form of PNN is shown in figure 1 and represented with the equation, Y T 1 ( x xij ) ( x xij ) x) = exp[ ]... (1) d / 2 d (2π ) σ 2σ ij ( 2 Where d denotes the dimension of the pattern x, σ is the smoothing parameter and x ij is the neuron vector and T indicates transpose of the matrix 6. The figure 1 shows that a PNN is composed of four layers namely input layer (containing input nodes), hidden layer (containing hidden nodes), pattern layer (containing class nodes) and decision layer (with a decision node). The input nodes in the PNN does not perform any computational operation and thus simply pass out the inputs of random variables x to each neuron in hidden layer. The hidden layer consists of neurons equal to the total number of training variables. The hidden layer on receiving the input from input layer calculates the Euclidean distance between each random variable and the training set of data that constitute the hidden layer which is then pass through an activation function, ϕ i. T ( x xij ) ( x xij ) ϕi ( x) = exp[ ]... (2) 2 2σ The class layer then computes the summation and gives out the arithmetic mean of the output of the hidden layer for each class, C k using, Y ij (x). Assuming the prior probability for each class and the cost associated for each misclassification to be equal, the output layer classifies any random variable x by comparing the output of class layer for each class and then following the Bayes classification theorem 8 as, Ck ( x) = avg[max( g k ( x))]... (3) where, g k =avg(g k,i )... (4) Fig. 1 Architecture of a PNN Network and is a nonlinear function of the smoothing parameter. Usually, the weights which are connected to the output layer from hidden layer are one or zero on PNN; for each hidden unit, a weight of 1 is used for the connection going to the output that the pattern belongs to, while all other connections are given weights of 0. The output unit performs classification according to the well-known Bayes s theory. For the design of the predictor, it requires a set of inputs and outputs for the training of the network. When the number of input-output sets increases, the accuracy of the network for prediction also will increase. Probabilistic neural network Algorithm Step 1: Pre-processing of data i. Collect the data for the PNN based prediction algorithm. ii. Define the set of values for the training and testing purposes. Here from the literature, the data is collected. And then transform it to the format of PNN. Step 2: Training of PNN i. Train the network, with the help of PNN training algorithm, input and output matrices. ii. Identify the suitable value of spread constant s. The value of s cannot be selected arbitrarily. A too small s value can result in a solution that does not generalize from the input/ target vectors used in the design. In contrast, if the spread constant is large enough, the radial basis neurons will output large values for all the inputs used to design a network. Step 3: Testing of PNN i. Define the matrix for the testing of the PNN network. ii. Verify the predicted and actual values for the efficiency check of the network. Collection of Data The experimental data for training of the network is collected from three literatures. This paper considered circular microchannel for the collection of data shown in figure 2 (a). The source of data is as follows: 1. Flow pattern map of water- kerosene in a 900 µ m channel 9 2. Flow pattern maps of mineral oil (Marcol 82) - deionized water flow in a 793 and 667 µ m channel 10

4 528 J SCI IND RES VOL 73 AUGUST Flow pattern map of water- kerosene in a 530 µ m channel 11 Results and Discussion Flow regime analysis Water and kerosene was pumped to investigate the flow patterns in the T-shaped microchannel with a diameter of 800 µm. In the study, three flow patterns namely, droplet flow, slug flow, and mixed flow, were observed successively. For the higher flow rate of kerosene (8-45 cm/s) and at lower flow rate of water ( cm/s), the droplet flows were observed. The slug flow patterns were observed over a wide range of water to kerosene flow rate ratio. It is observed that slug flow is formed over a flow rate range of 0-50 cm/s for kerosene and cm/s for water. The observed patterns are shown in the figure 2 (b). Effect of inlet flow rates on Slug Length The slug length variations based on the inlet flow rates were also measured. The dependence of the slug length on slug velocity at identical flow rates of both phases (aqueous and non aqueous) were observed. Fig. 2 (a) Flow pattern map collected from literature (b) Flow pattern map Liquid- Liquid Flow in an 800 micro meter Circular Teflon tube followed with a T Junction The slugs length tend to decrease slightly while increasing the velocities of the inlet flow rates due to the rapid penetration of dispersed phase into the continuous phase. This segregates the continuous stream into number of alternative water kerosene segments. Here the slug length increases linearly when the ratio between the flow rates decreases. The study has been investigated using the 800 µm dia. Microchannel. Prediction of the patterns (0.53mm< D h < 0.9mm) The collected data set is used for the training for the neural network. Probabilistic neural network design is carried out through Matlab R2008a. The trained network is then taken for testing with the experimental set of data to check its accuracy for prediction. Flow pattern data are collected from literature for a circular microchannels over a range of 530 µm to 900 µm are used for training neural network. So, this paper considered the flow map for the circular micro channels with a cross sectional diameter over a range of 530 µm to 900 µm. The data collected from three existing flow pattern studies are combined for training the proposed network and a set of values are choose for testing. Values 1, 2, 3, and 4 are assigned for the different patterns in the collected data (Table 1). Selection of PNN Network A probabilistic neural network (PNN) is a kind of radial basis network suitable for classification problems and returns a new probabilistic neural network. If spread is near zero, the network acts as a nearest neighbour classifier. As spread increases, the designed network takes into account several nearby design vectors. PNN can be used for the classification of pattern problems. When input value is fed to the input layer of PNN, it computes distances from the input vector to the training input vectors and produces a vector whose elements indicate how close the input is to a training input. The second layer of the network sums these contributions for each class of inputs to produce as its net output a vector of probabilities. At last, a complete transfer function on the output of the second layer picks the maximum of these probabilities, and produces a 1 for that class and a 0 for the other classes 6. Flow pattern Table 1 Flow patterns and their numerical values Assigned Numerical Value Droplet Flow 1 Slug Flow 2 Annular Flow 3 Mixed Flow 4

5 SELVARAJU et al.: PROBABILISTIC NEURAL NETWORK PREDICTION 529 Prediction Efficiency Prediction efficiency of the algorithm depends on the correct prediction of flow patterns. In the present work, two sets of data for the PNN testing were considered. One set of data is acquired from the literature and the second set of data is obtained experimentally. The efficiency of PNN is validated in two ways. At First, checking was done with the existing test data collected from literatures. Secondly, it is clarified with the experimentally observed values. Validation using existing literature data: Here the prediction efficiency is validated with the values collected from literature. Validation result showed % efficiency for the proposed model. But, three patterns went mismatched from the existing literature values with the use of spread value 9. Validation using experimental data: The same algorithm is validated using the experimental data. The validation result showed a total prediction efficiency of % efficiency with a spread value of 15. The flow pattern prediction included bubble, slug and mixed flow maps. The values used for validation using experimental data are shown in figure 2(b). It is found that, the algorithm shows a good agreement for all patterns except mixed flow regime. The efficiency of the network can be improved by using the training of the network with more data. Conclusion The present study adopted the artificial neural network to identify the flow patterns of liquid-liquid flow through micro channels. The PNN is based on feed forward type and is based on radial based function. The flow patterns predicted have been compared with existing literature data and found to be in good agreement for all flow patterns in the first efficiency validation. The modelled neural network is validated with the experimental values obtained and compared the accuracy of prediction in second efficiency validation. The experimentally observed data of bubbly, slug, annular flows better fitted with the PNN model prediction. Nevertheless, the prediction on mixed flow has shown a large error rate for the prediction check with experimentally identified data sets due to the less availability of training set on mixed flow or the less number of mixed flow measurements in the experiment. The analysis over the slug flow regime (800 µm) reveals that the slug length increases with the increase in water to kerosene flow rate ratio. The experiments were repeated by varying inlet flow rates of kerosene and water. Thus the PNN algorithm proved to be a good pattern predictor for the micro channels with the diameter of 530 µm to 900 µm. Independent of channel hydrodynamics, the proposed algorithm is able to predict the flow patterns effectively. This PNN prediction algorithm can further be improved by applying genetic algorithm for the selection of spread constant or by cooperating fuzzy logic for the prediction of patterns. Acknowledgement The financial support of National Institute of Technology Calicut, India (Faculty Research Grant Scheme, Grant No: Dean (C&SR) / FRG10-11 / 0102) is gratefully acknowledged. References 1 Marie C, What can microfluidics do for stem-cell research?, J Biol, 9 (2010) Kashid M N, Renken A & Kiwi-Minsker L, Gas liquid and liquid liquid mass transfer in microstructured reactors Chem Eng Sci, 66 (2011) Bujian X, Wangfeng C, Xiaolei L & Xubin Z, Mass transfer behavior of liquid liquid slug flow in circular cross-section microchannel Chem Eng Res Des, 91 (2013) Zhao C X & Middelberg A P J, Two-phase microfluidic flows, Chem Eng Sci, 66 (2011) Kashid M & Minsker L K, Quantitative prediction of flow patterns in liquid liquid flow in micro-capillaries, Chem Eng Process, 50 (2011) Timung S & Mandal T K, Prediction of flow pattern of gas-liquid flow through circular microchannel using probabilistic neural network, Applied Soft Computing, 13 (2013) Mehta H B, Pujara M P & Banerjee J, Prediction of Two Phase Flow Pattern using Artificial Neural Network, In proceedings of International Conference on Chemical and Environmental Engineering (ICCEE'2013), Johannesburg, South Africa, April Richard O D, Peter E H, David G S & Pattern classification (John Wiley & Sons Inc) 2012, Xubin Z, Dan C, Yan W & Wangfeng C, Liquid-Liquid Two-Phase Flow Patterns and Mass Transfer Characteristics in a Circular Microchannel, Adv Mat Res, (2012) Abdelkader S, Mostafa F, Jacques P & Judith S, Oil-water two-phase flow in microchannels: Flow patterns and pressure drop measurements, Can J Chem Eng, 86 (2008) Ozawa M, Ami T, Awata K, Umekawa H & Matsumoto R, Oil-Water Mixture In Horizontal Mini-Channel, in 22nd International Symposium on Transport Phenomena Delft (The Netherlands) 8-11 November, 2011.