Marouane Alaoui-Selsouli

A Mohafid

N M Najib

Najib M Najid
email: najib.najid@univ-nantes.fr

Lagrangian Relaxation based Heuristic for an Integrated Production and Maintenance planning Problem

Keywords: Production, Maintenance, Integer Programming, Time Windows, Shortage, Heuristics

Lagrangian relaxation based heuristic for an integrated production and maintenance planning problem

Marouane Alaoui-Selsouli, Abdelmoula Mohafid, Najib M Najid

1.

Introduction

Maintenance is a task closely related to production scheduling in industrial settings. It is the function that allows maintaining or restoring equipment to a specific state and guaranteeing a given service. Production and maintenance activities conflict since maintenance is generally considered as a secondary process in companies that have production as their core business. Indeed, preventive maintenance activities are often carried out in hours or days out of service.

Therefore, the number of breakdowns increases and the availability of production equipment is reduced. We can notice then that production planning and maintenance are addressed separately in the literature and also in the industry. As a remedy to this problem, the maintenance planning should be an integral part of the overall business strategy and should be coordinated and scheduled with manufacturing activities. So, maintenance should be considered as integral parts of the production plan rather than as interruptions to that plan and any violation of the maintenance schedule will induce a violation of the production plan integrity.

In this paper, a new integrated production and maintenance planning problem is studied considering a single production line at the tactical level. For production planning, the single stage multi item capacitated lot sizing problem with demand shortages is proposed. The objective is to determine the schedules and lot sizes of multiple items that share capacity constraint resources. The problems deals with tight capacities and when the capacity is insufficient to produce the total demand, it is spread among the items by minimizing the total amount of demand shortages. The maintenance planning problem is to determine the dates of preventive maintenance in time windows according to reliability of production equipment and demand. When preventive maintenance actions are carried out the production line is restored to as good as new (AGAN) state, i.e. the system has the same lifetime distribution and failure rate function as a brand new one, and when a production line fails, a minimal repair is performed to restore the system to the failure rate it had when it failed (as bad as old (ABAO) state). The resulting problem is modeled as a linear mixed-integer program to minimize production, inventory, setup, demand shortage, preventive and corrective maintenance costs.

To our knowledge, there are only few works dealing with this issue. An integrated aggregate production planning and maintenance problem was tackled initially by Weinstein and Chung (Weinstein and Chung, 1999). The authors presented a three part-model to solve the conflicting objectives of system reliability and profit maximization. An aggregate production plan is first generated, and then a master production schedule is developed to minimize the weighted deviations from the specified aggregate production goals. Finally, work-center loading requirements, determined through rough cut capacity planning, are used to simulate equipment failures during the aggregate planning horizon. Unlike Weinstein and Chung, Aghezzaf et al [START_REF] Aghezzaf | An integrated production and preventive maintenance planning model[END_REF]) proposed an integrated aggregate production planning and maintenance model for a system that is periodically renewed and minimally repaired at failure. They assumed that any maintenance action carried out on the system in a given period reduces the system's available production capacity during that period. The objective was to find an integrated lot-sizing and preventive maintenance strategy of the system that satisfies the demand for all items over the entire horizon without backlogging, and which minimizes the expected sum of production and maintenance costs. An extension of the above work is treated by [START_REF] Aghezzaf | Integrated production and preventive maintenance in production systems subject to random failures[END_REF] by considering parallel production lines. Recently, we treated the problem of integrating production and maintenance for small instances in [START_REF] Najid | An Integrated Production and Maintenance Planning Model with time windows and shortage cost[END_REF]). The integrated model and the separate model (where production and maintenance are planned separately) were solved and a comparison between integrated and separate models was studied and showed the effectiveness of the integrated one. [START_REF] Nourelfath | A genetic algorithm for integrated production and preventive maintenance planning in multi state systems[END_REF]) integrated preventive maintenance with tactical production planning in multi-state systems. The objective is to determine an integrated lot-sizing and preventive maintenance strategy of the system that will minimize the sum of maintenance, setup, holding, backorder, and production costs, while satisfying the demand for all products over the entire horizon. While all above mentioned papers consider that preventive maintenance activities should be planned at a fixed date, the present work provides more flexibility to preventive maintenance tasks with time windows to better optimize the overall cost of production and maintenance.

The remainder of the paper is organized as follows. In the second section, the description and mathematical formulation of the problem are presented. The heuristics to solve the integrated problem are developed in the third section and some computational results are showed in the fourth section. Finally, we end up with conclusion and prospects in the last section.

Mathematical model

Preventive Maintenance Policy

Our preventive maintenance (PM) policy is planned in time windows and based on the periodic PM policy, see e.g. [START_REF] Barlow | Optimum preventive maintenance policies[END_REF], Nakagawa (Nakagawa 1981a, b), [START_REF] Wang | Some maintenance models and availability with imperfect[END_REF]. In the classical periodic PM policy, the equipment is maintained at fixed time intervals (k=1, 2…) where ( is the optimal number of PM period and is the length of each period t H) is the optimal length of PM period. Therefore, PM tasks will be performed periodically in the beginning of period's t =1, +1, 2 +1, 3 +1, +1 etc. In our study, The PM actions are planned in time windows where and is the number of preventive maintenance activities during the horizon, and is defined as:

Thus, a preventive maintenance task will be carried out at the earliest in the beginning of the period or at the latest in the beginning of the period and will complete within the period in which it started. The parameter k which determines the width of the time windows is chosen to avoid their overlapping:

Moreover, we assume that each preventive or corrective maintenance action carried out on the production line consumes capacity units and at the beginning of the planning horizon the production line is considered as new. When a preventive maintenance is planned, the production line is restored to AGAN state and when a production line fails, a minimal repair is performed to restore it to "as bad as old" (ABAO) state. The production line is considered here as a complex system and the failure rate is an overall rate of the whole line. It is also assumed that the failure distribution of the production line is known. Let and denote its corresponding probability density and cumulative distribution functions, respectively. Let denotes the failure rate function of the production line at time .

Finally, we assume that expected failures increase with elapsed time since the last preventive maintenance.

The objective of the maintenance problem is to decide when performing preventive maintenance activities in predetermined time windows and reducing the number of failures.

The expected maintenance cost during the horizon is defined as the sum of preventive and corrective maintenance costs.

Planning Time windows

To determine time windows, we need to estimate, for each period t of the horizon, the expected number of failures, denoted essential to compute the expected maintenance cost per unit time.

The optimal length of preventive maintenance period corresponds to the period t which minimizes the expected maintenance cost per unit time, denoted CM(t), and given by :

Where and are respectively preventive and corrective maintenance costs, and is the expected maintenance cost during [0, t] and given by:

Example:

If we consider an horizon with 9 periods and an optimal length of preventive maintenance period ( ), the maintenance planning, without considering production constraints, is shown in figure 1. By using equation ( 2), k is equal to 1 and then time windows in the whole of horizon are defined as shown in figure 2 [Figures 1,2]

Integrated production and maintenance planning model

The studied problem is an integrated production and maintenance planning model where preventive maintenance activities are carried out in time windows. The production planning considers a planning horizon H of length covering N periods of fixed length , and a set of items to be produced on a single capacitated production line. During each period , a demand of the item should be satisfied (figure 3). Items are produced on a production line with known capacities given in unit time, and processing time is expressed in unit time per item. Furthermore, the demand shortage is allowed to be unfulfilled due to insufficient capacity and using a high unit cost for each item lost.

[Figure 3] Notations Index:

i: Items. t: Periods.

Parameters:

: Demand of item i to satisfy during period t.

K (t) : Available capacity in period t.

: Set-up cost of producing one unit of item i in period t.

: Fixed cost of producing one unit of item i period t.

: Variable cost of holding one unit of item i by the end of period t.

: Unit cost for demand shortage of item i in period t.

: Expected maintenance cost when preventive maintenance task is carried out in period t.

: Processing time for each item i.

) : Expected capacity consumed by each preventive maintenance action in period t.

(t) : Expected capacity consumed by each corrective maintenance action in period t.

: Expected capacity consumed by maintenance when preventive maintenance task is carried out in period t.

: Vector of N elements contains the expected number of failures in each period t, when no preventive maintenance task is performed.

= [NB(1), NB(2), NB(3)… NB(T)]

Decision variables:

: Binary set-up variable of item i in period t.

: Quantity of item i produced in period t.

: Inventory of item i at the end of period t.

: Demand shortage for item i in period t.

: Binary preventive maintenance variable (1 if preventive maintenance is carried out in the beginning of period t, 0 otherwise).

: Binary variable (1 if in period t the last preventive maintenance ended in period j, 0 otherwise).

The mathematical formulation of the integrated problem is given below :

Subject to:

The objective function (7) minimizes the sum of the set-up, holding, production, demand shortage, and maintenance (preventive and corrective) costs over the whole N-periods horizon. Constraint ( 8) is the inventory balance equation. Constraints (9.1) and (9.2) are the capacity constraints that consider preventive and corrective maintenance. Indeed, if a preventive or corrective maintenance activity is carried out, a part of the available capacity is consumed. Constraint (10) relates the continuous production variables to the binary setup variables. Constraint (11) expresses that quantity lost of item i in period t must be less than or equal to demand of item in period t. Constraint (12) ensures that one maintenance must be carried out in the interval . Constraint (13) ensures that two preventive maintenance actions cannot be carried out in successive time periods. Constraints ( 14)-( 16) force variable to 1 if, in period t, the last preventive maintenance ended in period j, 0 otherwise. Those constraints are equivalent to .

Constraints ( 17)-( 20) express non-negativity and integrality constraints.

Evaluation of and

When preventive maintenance activities are performed in period t, the expected cost generated and the capacity consumed by maintenance, are, respectively, and . The maintenance cost in this period t is the sum of preventive and corrective maintenance costs.

The corrective maintenance cost in period t is the product of the expected number of failures and the corrective maintenance action cost in the same period. Thus, the expected maintenance cost in each preventive maintenance period t is:

The same reasoning can be applied for the capacity consumed by maintenance task in a preventive maintenance period t.

Notice that if no preventive maintenance action is performed, the expected maintenance cost and the capacity consumed in period t are, respectively, the expected cost generated and the capacity consumed by corrective maintenance:

With j is the period where the last preventive maintenance activity was performed.

Heuristic for ULSP-TW-SC

In our decomposition method, the integrated production and maintenance problem is divided into a set of sub-problems. Each sub-problem is a single item uncapacitated lot sizing problem with time windows and shortage cost called ULSP-TW-SC. This sub-problem is a combination of the single item capacitated lot sizing problem with shortage cost (ULSP-SC) treated by Aksen et al [START_REF] Aksen | The single-item lot-sizing problem with immediate lost sales[END_REF] solved in and a maintenance problem where preventive maintenance tasks are planned in time windows.

Subject to:

(8) -( 24) excepting capacity constraints (9.1) and (9.2).

The solution of the problem (ULSP-TW-SC) was carried out by using the optimization solver "XpressMP" and the results showed that the computation time increases exponentially when the number of periods becomes important.

The numerical tests were performed on a computer with an Intel Core Duo 2.13 GHz and 4 GB of memory. For each planning horizon length such that 0 ≤ N ≤ 150, we generated 10 problems randomly. The demand shortage costs are selected between 30 and 100 and the demand in each period of the horizon is chosen in the interval [20.100]. The average computation time needed to solve these problems is given in Table 1. These results are also shown graphically in Figure 4. Note the exponential growth of computing time from N = 70.

[Table 1] and [Figure 4]

To solve the problem (ULSP-TW-SC), a heuristic based on a dynamic programming algorithm proposed by Aksen et al. [START_REF] Aksen | The single-item lot-sizing problem with immediate lost sales[END_REF]) is developed. The expected gap between the optimal solution (or a lower bound) obtained by the solver and the one provided by the heuristic is equal to 0.113%. The main steps of this heuristic are described below:

Step 1: Solve the single item Uncapacitated Lot Sizing Problem with Shortage Cost (ULSP-SC) to optimality using the dynamic algorithm addressed by Aksen et al [START_REF] Aksen | The single-item lot-sizing problem with immediate lost sales[END_REF] and based on the structural characteristics stated in lemmas 1 to 3.

Lemma 1:

Under assumption that , the first lemma suggests that there is an optimal solution such that demand in a given period will be fully satisfied if procurement is made in that period.

Lemma 2:

The second lemma suggests that there is an optimal solution such that we will procure in a given period only if the inventory level at the end of the preceding period drops to zero. This principle is also known as the zero-inventory ordering policy of the Wagner-Whitin solution (Wagner et Whitin, 1958), according to which beginning inventory in a period of procurement activity is always zero. In our lost demand model, it is slightly altered such that we might have both and if the demand is not met.

Lemma 3:

The third lemma suggests that there is an optimal solution such that if we lose any demand in a given period, then we should lose the entire demand in that period. In other words, it prohibits partial loss of demand. If , then must equal .

The proofs of the lemmas 1 to 3 can be found in [START_REF] Aksen | The single-item lot-sizing problem with immediate lost sales[END_REF].

Step 2: Select the first time window, plan a preventive maintenance task in the period when the total cost of production and Maintenance is minimal.

Step 3: Update the total cost of production and maintenance, select the next time window and plan a preventive maintenance task in the period when the total cost is minimal.

Heuristic based on Lagrangian relaxation (LH)

Our heuristic is based on the Lagrangian relaxation approach. The general idea is to decompose our integrated production planning and maintenance problem to N sub-problems easy to solve by relaxing the resource capacity constraints (10) and by using a set of Lagrange From Lagrangian relaxation theory (Fisher, 1981), is a lower bound of the optimal solution of MCLSP-TW-SC. The greatest lower bound attainable with the Lagrangian relaxation is provided by multipliers obtained by solving the following Lagrangian dual problem (LD) which can be solved efficiently by a sub-gradient optimization procedure (Fisher, 1981).

Subject to:

The main advantage of using a Lagrangian relaxation is that it usually preserves most of the original problem structure. This makes it easier to use the relaxed problem solution to generate a feasible solution for the original problem. Therefore, a very efficient heuristic method to solve MCLSP-TW-SC could be obtained by applying the sub-gradient optimization procedure and by checking, at each iteration, if the solution provided by the primal sub problem is a feasible solution of MCLSP-TW-SC, i.e. if

, then this solution is optimal. Otherwise, this solution can be modified by using a perturbation procedure (smoothing procedure) to generate a feasible solution for MCLSP-TW-SC. A detailed heuristic based on this idea is presented in the following subsection.

Lagrangian heuristic algorithm

Our overall solution method to solve MCLSP-TW-SC is a modified sub-gradient optimization procedure. At a given iteration, if the Lagrangian solution is not feasible for MCLSP-SC-TW, this solution is modified using the heuristic described in following sub-section 4.2 to find a new feasible solution for MCLSP-TW-SC, if its value is better than the current upper bound, it becomes the new one. The Lagrangian multipliers are initially set to zero and updated on each iteration to maximize the objective function of dual relaxed problem (LD) according to the formula:

:= max (0, + ),
Where is the sub-gradient of given by: . is the norm of the sub-gradient vector and is the sub-gradient step size:

, we start with and divide by 2 if any improvement of is seen after some iterations. Finally, the stopping criterion is based on maximum number of iterations or when the Gap between upper and lower bounds is smaller than a value . A detailed description of the Lagrangian heuristic is found below: -Maximum number of iterations is reached.

-Or when Gap is less than a value ( > 0).

Smoothing Procedure

In order to find a feasible solution at each step of the Lagrangian relaxation, we propose a procedure to provide an upper bound, denoted NAM. It is based on the Lagrangian solution obtained at each step of the Lagrangian heuristic algorithm. Since the capacity constraints (9.1) and ( 9.2) are relaxed, the Lagrangian solution violates them. The NAM heuristic is mainly based on a smoothing procedure to lower shortages by reusing missing resource capacities. The heuristic is based on the work of Trigeiro et al. [START_REF] Trigeiro | Capacitated lot sizing with setup time[END_REF] who proposed an efficient Lagrangian relaxation heuristic for the classical multi-item capacitated lot sizing problem with setup times. Recently, Brahimi et al [START_REF] Brahimi | Capacitated multi-item lot-sizing problems with time windows[END_REF]) proposed a generalization of Trigeiro et al [START_REF] Trigeiro | Capacitated lot sizing with setup time[END_REF]) smoothing heuristic to solve the multiitem capacitated lot sizing problem with time windows. Notice that the NAM procedure uses the Propositions 5 and 6 and the formula below, that computes the overtimes in each period, to find a feasible solution and to improve it.

Proposition 5: From the solution obtained by solving the Lagrangian problem, if in period t and for l = {1 ... j-1}, then a set-up of production has been performed in period t and the next setup was planned in period t + j, therefore:

and for and for

Proof

At each iteration of the algorithm 2, the relaxed problem of (MCLSP-TW-SC) is solved. If we notice that and for then there was unavoidably the setup of one or several items in the period t.

According to lemma 2, we never produce in a period when the inventory level of a previous period is non-zero, i.e.

In our case, an amount of one or several references was produced in the period t ( ) as the overtimes are greater than zero ( ). Moreover, since for we can deduce that one or several items have not been produced between period's t+1 and t+j-1 and that their demands were met by the inventory built in the period t, so .

and for and for

Our NAM procedure is described as follows:

Step1: After solving the relaxed problem, several cases arise. According to Proposition 5, the surplus amounts produced are shifted from period t to period t+1 using Proposition 2 (see section 4.1.2).

Step2: in some periods, if and the quantity of one or several items is lost, then the demand shortage should be shifted to a quantity produced in the current period according to Proposition 3 (see section 4.1.2).

Step 3: From the solution obtained by steps 1 and 2, if, at a given period, and

, a quantity of one or several items produced in period t+1 is shifted to the previous period, since the available capacity is exceeded in period t+1 and isn't fully used in period t.

Step4: After the step 3, we must verify that, in each period, the available capacity is not exceeded. Otherwise, if at a given period, and such , a quantity of one or several items is selected to be lost in the same period according to Proposition 4 (section 4.1.2). Else if and such , the quantity lost of one or several items in period t+1 will be a quantity produced in period t according to Proposition 4.

Computational results

In this section, we present different tests resulting from the application of the Lagrangian heuristic, denoted (LH). Our algorithms were implemented in the Java programming language. The computations were tested on an Intel Core 2 CPU 2.2GHz PC with 4GB RAM.

Computational tests are performed on a series of extended instances from the lot-sizing library LOTSIZELIB, initially described in [START_REF] Trigeiro | Capacitated lot sizing with setup time[END_REF]). These instances are denoted by trn-N, where n = 6, 12, 24 is the number of items and N = 15, 30 is the number of periods.

These instances are characterized by variable resource consumption equal to one, and enough capacity to satisfy all demands over the planning horizon. They are also characterized by important setup costs, small setup times. Since these instances have enough capacity to satisfy all demands over the planning horizon, some modifications were made to induce shortages.

A planning horizon composed of N production periods of fixed length is considered to produce a set of items on the production line with an available capacity. The production, setup, and holding costs are, respectively, 10, 30, and 5. Four parameters are considered for the analysis:

Problem dimension:

The problem dimensions represented by the number of items n and the number of periods N = 15 and 30.

Production capacity:

The capacity required, in each period, is initially computed as lot-forlot solutions were implemented. Then, the capacity is obtained by dividing the later result by the target average utilization of capacity . The factor is set to 0.95 and 1.1 corresponding respectively to situations with tight and too tight capacity constraints.

Demand pattern:

The demand for each item in each period is generated randomly on the interval [20,100].

Shortage cost: the shortage cost is considered as penalty cost and its value for each item is All problem tests are generated with Weibull distribution of production line. The shape and scale parameters are respectively , and . The cost of preventive maintenance action is set to , and the cost of minimal repair action is given by . The capacity lost when a preventive maintenance task and minimal repair action are carried out, is respectively and . Table 2 shows the expected number of failures in each period NB(t) as a function of system's age.

We assume that the system lifetime is distributed according to weibull distribution with failure probability density function f(t) and failure rate function r(t).

[Table 2]

To have a meaningful comparison, we compare the results of the lagrangian heuristic to those obtained by XpressMP solver. The computational results of the heuristic (LH) and the solver are shown in Tables 3 and4. The gaps between the best lower bounds or optimal solution obtained and the upper bounds provided by the heuristics and by the solver are computed respectively by the given formula suggested by [START_REF] Millar | Lagrangean heuristics for the capacitated multi-item lotsizing problem with backordering[END_REF]: The different gaps are expressed using equations ( 28) and ( 29).

The stopping criterion of the XpressMP computation is a time limit equal to 3600 seconds or when the gap reaches a minimal value ( ). For the Lagrangian heuristic, it is when a number of sub-gradient iteration reaches a maximum of iteration and also if the gap is small than .

[Table 3]

Tables 3 and4 summarize the computational behavior of the Lagrangian heuristic and the computational results given by the solver. The gaps and CPU time are computed for each instance with the following parameters: the number of items (n), the number of periods (N), shortage cost for each item and capacity tightness.

The results obtained with solver are very interesting. Indeed, most of instances are solved to optimality or are very close to optimal solution, but also require a significant amount of CPU time. Therefore, we developed heuristic to reduce computation time and to obtain a high quality solution. Then, a heuristic based on lagrangian relaxation (LH) is implemented. The results provided by (LH) are shown in Table 3 when capacity is too tight and in Table 4 when capacity is larger (tight capacity).

[Table 4]

We notice from Tables 3 and4 that the heuristic LH can solve some instances to optimality.

Others instances, which are not solved to optimality, have very small gaps and the upper bounds of the Lagrangian heuristic are very close to the upper bounds obtained by the solver and the deviation from the solver doesn't exceed 0.97%. Also, we can observe that the CPU time of the Lagrangian heuristic enhance partially when we increase the number of items and considerably when we increase the number of periods. Finally, the computation time of the heuristic is much smaller than that of the solver for the same or a close result.

Conclusion and perspectives

We have formulated a mixed-integer linear programming model to plan jointly production and maintenance activities. The model takes into account the reliability (expected number of failures) production and maintenance costs, and demand shortage. Preventive maintenance is carried out in pre-determined time windows, and corrective maintenance is performed to restore the system to an operating state without changing the failure rate function.

Computation results show that the Lagrangian heuristic (LH) seems a good trade-off between the solution quality and time execution. Therefore, for a decision maker who is interested in a good solution quality and a short execution time, our Lagrangian heuristic can be an appropriate approach to solve the problem.

A Sensitivity Analysis would be a good perspective of this work to study how a change in the model data changes the optimal solution.

An extension of our model to the concept of imperfect maintenance can be very useful to model a more realistic and accurate maintenance operations, which are in reality neither perfect nor minimal.

Finally, other heuristics can be developed and compared to solve our integrated problem in a reasonable time.

maintenance in production systems. Annals of Operations Research, 91, 305-318. Weinstein, L., and Chung, C., (1999). Integrating maintenance and production decisions in a hierarchical production planning environment. Computers & operations research, 26, 1059-1074.

  multipliers in the objective function of the MCLSP-TW-SC model. Let the Lagrangian function, the mathematical formulation of relaxed problem (MULSP-SC-TW) is stated below: -(24) excepting capacity constraints (9.1) and (9.2). The Lagrangian relaxation of the capacity constraints of the MCLSP-TW-SC decomposes the model into n single-item uncapacitated lot-sizing problems with shortage cost and time windows, denoted ULSP-TW-SC and solved in section 3.

  Perturbation procedure: a heuristic is used to find a feasible solution using a smoothing procedure as described in the following sub-section 4

  generated from the follows intervals [I1], [I2] and [I3].  [I1]: [0.5*(Production cost+ setup cost), 1.5*(Production cost+ setup cost) ]  [I2]: [0.5*(Production cost+ setup cost), 2.5*(Production cost+ setup cost) ]  [I3]: [0.5*(Production cost+ setup cost), 3.5*(Production cost+ setup cost) ] Six classes of instances are created:  Class A, Class B and Class C: Too tight capacity and shortage cost for each item is generated from [I1], [I2] and [I3], respectively.  Class D, Class E and Class F: Tight capacity and shortage cost for each item is generated from [I1], [I2] and [I3], respectively.

  Figure 2: Time windows of preventive maintenance in integrated case

Table 2 :

 2 Expected number of failures Over flow of the solver without obtaining an optimal solution

* :

Table . 1

 . -The average computation time to solve the problem (ULSP-TW-SC)

	12	30	2804.70	0.00	0.05	60
	24	30	2170.73	0.03	0.01	70
	36	30	2009.33	0.03	0.13	96
	48	30	1512.41	0.04	0.08	130
	Class B
	6	15	2677.87	0.02	0.18	10
	12	15	2644.63	0.02	0.05	11
	24	15	2657.81	0.00	0.00	17
	36	15	2629.07	0.00	0.00	22
	48	15	2629.07	0.01	0.10	28
	6	30	191.123	0.00	0.10	27
	12	30	84.194	0.00	0.06	43
	24	30	2666.68	0.00	0.04	69
	36	30	2678.21	0.02	0.25	92
	48	30	2562.49	0.03	0.03	119
	Class C
	6	15	0.718	0.00	0.00	8
	12	15	2632.24	0.05	0.34	13
	24	15	2652.22	0.03	0.39	19
	36	15	2650.65	0.01	0.09	24
	48	15	2667.17	0.01	0.03	33
	6	30	2657.43	0.01	0.03	31
	12	30	2660.38	0.01	0.98	41
	24	30	2672.74	0.03	0.09	68
	36	30	2685.30	0.02	0.14	88
	48	30	2640.75	0.03	0.06	123
			Solver	LH
	Items	Periods	Time (s)	Gap1(%)	Gap2(%)	Time (s)
	Class D
	6	15	2666.58	0.01	0.16	11
	12	15	2642.53	0.01	0.02	13
	24	15	2679.54	0.00	0.00	18
	36	15	2658.76	0.00	0.09	27
	48	15	2677.53	0.01	0.10	36
	6	30	1662.35	0.00	0.10	27

Table 3 :

 3 Computation results: HR vs XpressMP when capacity is too tight

	12	30	7.036	0.00	0.09	46
	24	30	2676.89	0.01	0.06	69
	36	30	1663.35	0.02	0.06	102
	48	30	2532.2	0.03	0.08	150
	Class E
	6	15	2656.7	0.05	0.28	8
	12	15	2651.08	0.02	0.03	13
	24	15	2649.21	0.00	0.00	17
	36	15	2641.19	0.01	0.00	23
	48	15	2687.65	0.00	0.04	35
	6	30	16.708	0.00	0.36	36
	12	30	2635.11	0.01	0.03	43
	24	30	2703.74	0.00	0.00	63
	36	30	2661.22	0.01	0.10	99
	48	30	2677.51	0.01	0.16	141
	Class F
	6	15	1.263	0.00	0.16	12
	12	15	2624.67	0.00	0.01	13
	24	15	4.134	0.00	0.01	19
	36	15	2653.64	0.00	0.02	25
	48	15	2682.07	0.00	0.00	35
	6	30	2771.33	0.00	0.07	27
	12	30	2670.3	0.00	0.03	41
	24	30	2657.09	0.00	0.02	68
	36	30	2659.6	0.00	0.03	91
	48	30	2680.87	0.01	0.33	120

Table 4 :

 4 Computation results: HR vs XpressMP when capacity is tight


Dr Carol Goalard
email: goalard@enstimac.fr

Prof Arezai M Samimi

Prof. J Laurence A Galet

John A Dodds

Mojtaba Ghadiri

Dodds

Ghadiri

Characterization of the dispersion behavior of powders in liquids

Keywords: dispersion, electro-spraying, freeze-drying, granules, high shear, wetting

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Characterization of the Dispersion Behavior of Powders in Liquids

Carol Goalard*, Arezai Samimi**, Laurence Galet*, John A. Dodds*, Mojtaba Ghadiri**

Introduction

It is often necessary to disperse powders in liquids, for example in everyday life we disperse food products or medicines. Dispersion is also used in many stages of industrial processes, whether to give a final form to a product (e.g., a suspension) or as an intermediate production step. When the final product is a powder dispersed in a solvent (e.g., paint) the quality of dispersion defines the quality of the product. A sound understanding of the factors that can influence and limit the formation of dispersions is necessary in order to maximize the efficiency of a production process and the product quality.

The literature on dispersion is not extensive. Schubert [1] investigated modifications to powdered food products to promote rapid dispersion called "instantizing". He studied the kinetics of dispersion of instant powdered milk in relation to the wetting characteristics such as the fat content of the milk and the state of agglomeration of the powder. Here we consider the effect of the structure of talc granules on their dispersion in aqueous media. Talc is chosen because it is widely used in many industrial sectors such as paper, paints, ceramics, cosmetics, and pharmaceutics. It is a hydrophobic and lamellar powder that is hard to disperse in water and hard to granulate. A comparison is made of the dispersion characteristics of two types of talc granules: (a) Fragile highly porous talc granules made by a novel method combining electro-spray and freeze-drying. (b) Strong dense talc granules made with a conventional high-shear granulator. The wetting characteristics of both types of granule have been determined by contact-angle measurements, Washburn capillary-rise experiments, and vapor-sorption isotherms measured by DVS. These results will be reported elsewhere but are not considered further here as they do not differ significantly except in their PEG content.

Electro-spray Freeze-dry Agglomeration

A novel agglomeration process has been used to prepare fragile highly porous spherical granules (Samimi et al.

[2]). In this method an electric field is applied between a nozzle and an annular counter electrode to control the size of liquid droplets which are rapidly frozen when dripped into a bath of liquid nitrogen. When a liquid emerges from a nozzle in air at a sufficiently small flow rate, drops are released individually from the tip of the nozzle. In this dripping mode, the application of an adequate electric potential to the nozzle increases the dripping frequency with a consequent reduction of the droplet diameter (Speranza et al. [3]). Figure 1 shows a schematic drawing of the apparatus used to make the granules. The essential feature is a stainless steel nozzle (I.D. 1 mm, O.D. 1.48 mm) positioned vertically above an annular stainless steel disk. A high-voltage DC power supply is connected to the nozzle, while the stainless steel disk (internal hole 30 mm, external diameter 100 mm) is earthed. The liquid is pumped to the nozzle using a syringe pump SP 200 IZ series, which allows to feed the liquid with a wide range of flow rates. The internal diameter of the Monojet syringe is 38.4 mm and its volume is 140 ml. The optimum liquid flow rate feed in this work is 2 ml/min for which the mode of flow from the nozzle was dripping. The experiments were conducted at room temperature. The electric field was supplied by a high-voltage source Hartley Measurements model 421. The applied DC voltage had a positive polarity and was varied from 0 to 10 kV. Figure 2 shows the change in drop characteristics caused by applying an electric field to the nozzle. The drops are pulled down and the main droplet diameter is reduced while the dripping frequency is increased. The main drop is accompanied by one or more satellites due to the rupture of the liquid filament between the main drop and the liquid meniscus left attached to the nozzle. The diameter and the size distribution of the main droplets depend on the voltage applied, the liquid flow rate, the liquid surface tension, the conductivity, and the viscosity of the liquid. The droplets produced in the dripping mode are collected in liquid nitrogen where they are rapidly frozen. The collected droplets are then freeze-dried in a SB4 laboratory freeze drier thus conserving the spherical shape of the granules. Seven different suspensions of talc particles (d = 6 lm, h = 2.38) in polyethylene glycol and water have been used giving granules between 1 and 1.2 mm. The density of the granules was measured using a Micrometrics AccuPyc 1330 helium pycnometer. The BET specific area was determined using a Micromeritics Asap 2010 with argon. The porosity was measured with a mercury porosimeter Micromeretics AutoPore III. The granule characteristics are given in Table 1.

Figure 3 shows different ESEM views of electro-spray granules: A) a whole granule (10 % PEG, 30 % Talc); B) the external surface (10 % PEG, 20 %Talc); C) a fractured granule (10 % PEG, 30 % Talc); D) a granule with a scratched surface (5 % PEG, 30 % Talc); E) a detail of a broken granule (10 % PEG, 10 % Talc); F) detail obtained using a back-scattering electron (BSE) detector (5 %PEG, 15 % Talc). These photos show that the apparent smooth surface does have some detail and that the inside of the granule seems to have a lamellar structure below a surface skin. Finally, 3-F shows that the talc particles are uniformly and randomly distributed in the granule which is not the case for the PEG binder.

High Shear Granulation

Talc has been agglomerated in 200 g lots in a conventional 2 kW Diosna high-shear granulator with a 2 liter bowl and using a solution of 5 % polyethylene glycol in water as a binder (Chateau [4]). A preliminary study with a Caleva Mixer Torque Rheometer was carried out and led to the choice of a wetting ratio of 0.2 ml/g and a three-phase program for the speed of rotation. Phase I: 5 mins with a stirrer at 300 rpm and a chopper at 200 rpm. Phase II: 3 mins with a stirrer at 800 rpm and a chopper at 500 rpm, Phase III: 5 min with a stirrer at 500 rpm and a chopper at 200 rpm. The resulting granules were sieved in 5 size classes. Observations by ESEM (see Figure 4) show that the talc granules produced by the Diosna high-shear granulator are roughly spherical and rather compact. The characteristics of the granules did not permit mercury porosimetry to be used and a measure of the porosity of the largest size class was determined by counting and weighing certain number of granules. This gave a value of 40 % porosity and was taken to be characteristic of the other size classes.

Dispersion

Two methods have been used to investigate the dispersion behavior of granules in liquids. The first method is based on a novel optical fiber sensor which allows the increase in concentration of the particles to be followed as the dispersion proceeds. The second method uses an Insitec laser diffraction instrument in a Spraytech bench to follow the changes in particle-size distribution as dispersion proceeds.

Optical Fiber Sensor

This technique has been presented in detail elsewhere [5]. Essentially the particles are poured on the surface of the liquid in a baffled stainless steel vessel stirred by an impeller. Two mechanisms occur: The first is immersion where the granules cross the liquid surface. The second is erosion or break-up where the talc particles become dispersed in the liquid. The signal from the optical fiber sensor gives curves as shown in Figure 5 which are fitted to a two-parameter exponential model.

Xt A1 À expÀkt 1 X(t) is the fraction of dispersed particles at time t. k (s -1 ) is the dispersion rate of the particles which includes the immersion and dispersion. The greater k is, the faster is the dispersion. The constant A corresponds to the final stage of the dispersion and A equals 1 when all the particles are dispersed in the liquid.

Insitec

The second method used for following the dispersion of the granules in liquids is with an Insitec EPCS in-line laser diffraction instrument fitted in a Malvern Spraytec bench holding a rectangular glass vessel (50 mm, 100 mm). This system gives a real-time continuous measurement of the particle-size distribution (d 10 , d 50 and d 90 ) and light obscuration related to the concentration of the dispersed suspension. In these experiments a constant mass of granules contained in a wire mesh holder is introduced into 1 liter of distilled water with minimal magnetic agitation to avoid the sedimentation of the particles. This mode of introduction means that there is no resistance to immersion and the only kinetic effect is that due to granule erosion and break-up.

Figure 6 shows that the particle size in suspension increases for the first 10 s after which there is a slow decrease until they stabilize at the particle size of the primary talc particles when disintegration is completed. The decrease in obscuration has been fitted by:

O t O ∞ expÀk′t′ 2
where O (t) is the obscuration at time t, O ∞ is the minimal obscuration at the end of disintegration. k′ is the dispersion rate that does not include immersion.

Comparison

Tables 2 and3 give the fitting parameters from the dispersion experiments where the k, t and A values are determined with the optical fiber sensor and the k′ and t′ values are determined in the experiments with the Insitec. The t and t′ values are those corresponding to 90 % of the final state of dispersion. Examining the dispersion times t′ and t. For the electro-spray granules, the greater the talc content, the longer is the dispersion time t′, which does not include immersion. It may be that the t′ values are also linked to the high PEG content, but the variability of the results does not allow us to confirm this. For the high-shear granules the dispersion time t (including immersion) passes through a minimum at a granule size of 500-630 lm. It seems that granules smaller than this size do not cross the liquid surface as easily as heavier granules, and that granules larger than this optimum size take longer to break up and disperse.

Similar observations were made previously by Schubert [1]. This observation can not be made for the electrospray granules as they were all the same size. In general the electro-spray granules have higher t values than the high-shear granules but this does not take into account the size effect. Also for the electro-spray granules it can be seen that the higher the talc content, the lower is the k′ value, meaning the longer the dispersion takes. It should be noted that those electro-spray granules which have a higher talc content are heavier, which facilitates immersion and affects the k values. The A values for the electro-spray granules were all equal to 1 suggesting that they all became fully dispersed to primary particles. This is not the case for the high-shear granules where A is much less than 1.

Conclusion

The experiments with various sieve fractions of highshear granules confirm that there is an optimum size of granule for rapid dispersion. The electro-spray granules with a very low bulk density and a high porosity are found to disperse completely into primary particles whilst, in the stirring conditions used here, the highshear granules only reduce to small agglomerates (50 lm). This suggests that to achieve the best immersion and dispersion highly porous granules but also heavy granules are required.

  Fig. 1: Dripping arrangement.

Fig. 2 :

 2 Fig. 2: Formation of drop without and with electrical field.

Fig. 3 :

 3 Fig. 3: Environmental Scanning Electron Microscopy images (ESEM) of the granules obtained by electro-spray and freeze-drying.

Fig. 5 :

 5 Fig. 5: Dispersion kinetics (Talc 30 %, PEG 5 %).

Fig. 6 :

 6 Fig. 6: Particle diameters and obscuration Insitec during the dispersion of granules (Talc 30 %, PEG 5 %).

Table 1 :

 1 Characteristics of electro-spray freeze dried granules.

	PEG (%)	Talc (%)	Density	Porosity	S BET
	5	15	1.94	90	6.5
	5	30	2.31	84	5.5
	10	10	1.83	84	4.1
	10	15	1.82	86	5.1
	10	20	1.98	84	4.8
	10	30	2.17	80	3.6
	20	15	1.64	79	3.9

  Samimi, Y. Ding., M. Ghadiri, D. W. York, Combined process of electro-spraying and freeze-drying for production on nanoparticle assemblies with view of redispersion, (personal communication). [3] A. Speranza, M. Ghadiri, Effect of electrostatic field on dripping of highly conductive and viscous liquids. Powder Technol., 2003, 135, p. 361. [4] M. E. Chateau, Mise au point d'un détergent sous forme solide. PhD Thesis, INPT Toulouse 2003. [5] C. Goalard, L. Galet, J. A. Dodds, Characterisation of the dispersion behaviour of talc. 8 th International Symposium on Agglomeration, Bangkok, 16-18 March 2005.

	5 Nomenclature
	A	-	constant in Eq. (1) corresponding
	k k′	s -1 s -1	to the quality of final dispersion dispersion rate dispersion rate determined by Spraytec
			not including immersion
	O(t) S BET m 2 /g specific surface by the BET method -obscuration at time t
	t	s	time
	t′	s	timeinSpraytecexperiments ,not
			including immersion time
	X(t)	-	fractionofparticlesdispersedattimet
	6 References
	[1] H. Schubert, Instantization of powdered food products,
	Int. Chem. Eng, 1993, 33, p. 28.
	[2] A.

Table 2 :

 2 Dispersion parameters for electro-spray granules.

	PEG (%)	Talc (%)	k (s -1 )	k ′ (s -1 )	t(s)	t′(s)
	10	10	0.096	0.045	23	51
	5	15	0.117	0.054	19	42
	10	15	0.046	0.040	49	57
	20	15	0.098	0.071	23	32
	10	20	0.231	0.035	9	66
	5	30	0.093	0.021	24	107
	10	30	0.081	0.017	28	135

Table 3 :

 3 Dispersion parameters for high shear granules (PEG 5 %).

	Size (lm)	A	k(s -1 )	k ′(s -1 )	t(s)	t′(s)
	250-315	0.58	0.13	0.0022	17.3	1063
	315-500	0.68	0.59	0.0103	3.9	222
	500-630	0.59	0.62	0.0111	3.7	206
	630-800	0.72	0.054	0.0089	42.3	257
	800-1	0.67	0.052	0.0039	44.2	589


A Roman-Gutierrez

J Sabathier

S Guilbert

L Galet

B Cuq
email: cuq@ensam.inra.fr

Characterization of the surface hydration properties of wheat flours and flour components by the measurement of contact angle

Keywords: Wheat flour, Sessile drop, Hydration, Surface properties, Contact angle, Wettability

The surface wettability properties of two wheat flours with different technological properties and of the main wheat flour components (starch, damaged starch, proteins, and soluble and insoluble pentosans) have been studied. The wettability properties were measured on compacts (produced by a classical compaction technique) by using the sessile drop method. The two selected wheat flours were characterized by relatively low values of contact angles (68j) and high rates of water drop adsorption (20j/s). It was not possible to discriminate the two selected wheat flours. The flour components were characterized by highly different values of surface wettability properties. The compacts based on gluten displayed the ''lowest'' wettability properties, with a high initial angle (85j) and a very low rate of water drop absorption (0.09j/s). The compacts based on starch and damaged starch are characterized by ''high'' surface wettability properties. Significant changes in physical properties (density, porosity, and microstructure) of material during compaction were considered to explain the wettability properties.

Introduction

The study of mechanisms involved in dough formation and more particularly in the stage of flour hydration is essential to identify and control the factors that define dough properties and qualities of end products. Hydration properties of wheat flours have been mainly described from studies of water vapor sorption properties [1,2]. Differences in hydration properties of wheat flours are usually explained by differences in biochemical composition, especially with respect to the contents of damaged starch, proteins, and pentosans [START_REF] Berton | Re ´cent[END_REF].

The physical events involved in functional properties of flours (and more particularly in hydration properties) can be described by considering the surface wettability properties. The surface energy of a solid is a good way to characterize the wettability properties [4]. The surface energy of solids determines the potential level of physical interactions that a solid is able to exchange. The knowledge of this parameter is important for the understanding and prediction of many surface and interface phenomena (e.g., adsorption, wettability, adhesion, and friction).

The surface wettability properties of powders can be estimated by the measurement of contact angles [5]. For the characterization of powders, values of contact angles have been determined by the technique of capillary rise (i.e. measurement of water penetration rates in a capillary that is filled with the powder). Contact angles are then calculated using the Washburn equation. Galet et al. [START_REF] Galet | Re ´cent[END_REF] determined the contact angle of durum wheat semolina and water (87jF 2j) using the capillary rise technique. However, water absorption by wheat semolina induced high swelling of particles and greatly limits the capillary rise of water after 1.5 -2 min. The technique of capillary rise has also been used to estimate the water adsorption capacity of wheat flour [START_REF] Berton | Re ´cent[END_REF].

The wettability properties of material can also be evaluated by the measurement of contact angle of a liquid drop deposited on the surface of the solid. For powders, it is necessary to carry out a preliminary stage of compaction. A water drop or water drops can then be deposited onto the upper surface of the compacts. The liquid -solid contact angle can then be measured using a protractor eyepiece on a goniometer or by photographing the drop and measuring the angle on the print. Secondary, a drop of maximum height can be produced and the measured height used to calculate a contact angle on the print [7,8]. However, one of the major problems in measuring the contact angle on compacts is that the process of compaction may alter the outer surface. Plastic deformation may result in a measured contact angle, which is not representative of the original powder [8]. Buckton and Newton [9] demonstrated for a number of barbiturates that an increase in compaction pressure induced an exponential decrease in contact angle until a plasticization of the compact surface occurred.

The objectives of the work were to describe the surface wettability properties of two wheat flours with different technological properties and of the main wheat flour components (starch, damaged starch, proteins, soluble, and insoluble pentosans). Compacts based on flours or flour components were first prepared by a classical compaction technique. The surface wettability properties were measured directly on compacts by using the sessile drop method. Changes in physical properties (density, porosity, and microstructure) of material during compaction were considered to describe the surface wettability properties.

Materials and methods

Raw materials

Commercial soft and hard wheat flours, industrial wheat gluten (Manito from Eurogerm, Dijon, France), industrial wheat starch (Roquette, Lestrem, France), water-insoluble wheat pentosans (INRA, Montpellier, France), and watersoluble wheat pentosans (CH-8033020, Leuven Bioproducts, Belgium) were used in this work. The damaged starch was obtained by grinding the wheat starch with a mortar grinder (RM 100, Fisher Scientific, France) for 30 min. All products were stored at 4 jC in hermetic cans until needed (for maximum of 1 year). The initial contents of water, damaged starch, ash, and lipids were determined according to AACC methods (44-15, 76-31, 08-12, and 76-12) [START_REF]Approved Methods of the AACC[END_REF]. The protein contents were determined according to Dumas method (NA 2000, Fisons Instrument). The contents of water-soluble arabinoxylans and total arabinoxylans were measured by colorimetric and chromatographic methods according to Rouau and Surget [START_REF] Rouau | [END_REF]. Calculations were done to estimate the contents of the water-insoluble arabinoxylans (i.e. the difference between total and watersoluble arabinoxylans) and starch (i.e. difference to the other components). The biochemical composition of the wheat flours and the flour components is presented in Table 1.

Granulometric fractions of hard wheat flour were then prepared (0-50, 50 -100, 100 -125, and 125-160 Am) by hand sieving according to the French method NF XII-507 [START_REF]Association Franc ßaise de Normalisation[END_REF] using four square meshed sieves (160, 125, 100, and 50 Am). The particle size distribution of wheat flours and flour fractions were determined by using laser granulometry with air drying (Granulometer Laser Masterizer 2000, Malvern, England) at room temperature. The particle size distribution is characterized by the mean diameter (D 50 ) and by the dispersion (D 90 À D 10 )/D 50 [START_REF] Allen | Particle size measurement, Powder Technology Series[END_REF]. One measurement was carried out for each product.

Equilibration conditions

Wheat flours and flour components were first dried in a vacuum drier at 45 jC for 12 h. The dried particles were then equilibrated at different relative humidities (at 0% and 60%) over saturated salt solutions for 1-2 weeks.

Compact preparation

Compacts (13 mm diameter) were prepared by pressing 0.4 F 0.0002 g of powder in a manual hydraulic press (Grasserie Specac, London, England, standard P/N 15.011) at a pressure of 700 MPa for 1 min at room temperature. The compacts were immediately analyzed after preparation.

Contact angle

The wettability properties of powders were estimated by direct observation of the contact angle of a water drop (10 Al) deposited on the surface of the compacts (Fig. 1). Freshly tapped ultrapure water was used. Measurements were carried out with a goniometer (Kru ¨ss G10) equipped with a camera (CDD, 25 images per second) and digital video tape recorder (Sony DSR-30p). Data were treated using the Kru ¨ss software 121. The initial contact angle and its change as a function of time were recorded. The apparent absorption rate of the water drop was calculated by linear regressions (in the initial linear part) of contact angles vs. time curves. For each product, average values and standard deviations were calculated from 16 measurements.

Physical properties

The bulk densities of dried powders and compacts (at 0% RH) were determined by helium pycnometry (Accu Pyc 1330, Micrometrics, Norcross, GA) at 20 jC. According to the gas displacement method, the bulk density (g/cm 3 ) is related to the volume of product in which gas cannot penetrate. One measurement was carried out for each product.

The pore size of samples and the size distribution of pores were measured for dried powders and compacts (at 0% RH) using a mercury porosimeter (Poresizer 9310, Micromeritics Instrument). This instrument is capable of measuring very small pores (1-8 nm diameter) using a maximum pressure of 408 MPa (60 000 psi). One measurement was carried out for each product.

The microstructure of initial dried particles and surface of compacts (at 0% RH) were characterized by using scanning electronic microscope (GSM 6300S, Joel, Japan). The powders were mounted into 13-mm diameter aluminum stubs using double-sided adhesive tape and sputter coated with gold. The scanning electron microscope was operated with a beam accelerating potential of 12.0 kV and images were collected in secondary electron mode.

Mechanical properties of compacts

The hardness of compacts (at 0% RH) was analyzed using the Hardness Erweka TBH 300 (Erweka, Milford, CT, USA).

The breaking force (newton) was measured according to the Jaw test. The friability of compacts was measured with the Friability-Abrasion Tester Erweka TAR20 (Erweka). Measurements were conducted at 30 rpm for 15 min at room temperature. Five measurements were carried out for each product.

Statistical analysis

The statistical significance of the results was assessed using single-factor analysis of variance (ANOVA). Multiple comparisons were performed by calculating the least significant difference using the Excel Software. All tests were conducted at 5% significance level and results are presented.

Results and discussion

The biochemical composition of wheat flours and flour components is presented in Table 1. The principal differences between the two selected flours are the higher contents of proteins, damaged starch, and pentosans for the hard wheat flour. It is important to note that the selected fractions of flour components are not pure fractions. For instance, there is 16% starch in the gluten fraction and 52% of starch in the insoluble pentosan fraction. Nevertheless, it was considered that the functional properties of these fractions could be attributed to their major component.

The characterization of the granulometric distribution of products demonstrated that hard wheat flour particles were on average larger than soft wheat flour particles (Table 2). The average diameter (D 50 ) of flour component particles are presented in Table 2. The average diameter of the starch particles (19 Am) is typical for starch granules. The measured particle diameters for gluten and pentosans (82 -274 Am) cannot describe the characteristics of these components inside wheat flours (which are characterized by smaller sizes). Large diameters for gluten and pentosans resulted from an uncontrolled agglomeration during the purification process.

The wettability properties of wheat flours and flour components were determined by direct measurements of contact angles of a water drop deposited on the upper surface of compacts. As a typical example, the changes in contact angle as a function of time for compacts based on hard wheat flour are presented in Fig. 2. An initial contact angle of 68j was observed for compacts equilibrated at 0% RH (Table 3). Immediately after the deposition of the water drop, we observed a rapid absorption of the water inside the compact. After few seconds, the drop was absorbed by the compact. Apparent water absorption rates were calculated from the almost linear decrease in contact angle as a function of time (Table 4). Compacts based on hard wheat flour (at 0% RH) were characterized by a relatively high value of apparent absorption rate (21j/s). An increase in initial RH (from 0 to 60%) induced a slight significant decrease in the initial value of contact angle (from 68j to 58j) for hard wheat flour and also resulted in a large decrease in values of apparent absorption rate (from 21 to 14j/s). As expected, increasing the initial water content of flour particles before compaction favored the initial wettability properties of the compact surface (i.e. lower initial values of contact angle), but reduced the kinetics of water drop absorption (i.e. higher absorption rates). The presence of water molecules within the compacts (before the deposition of water drop) increased the hydrophilic behavior of compact surfaces, but reduced its capability to absorb the water drop.

The experimental values of initial contact angles and apparent rates of water drop absorption for compacts based on soft wheat flour are presented in Fig. 2 and Tables 3 and4. The wettability surface properties of compacts based on soft wheat flour were close to those described for hard wheat flour (Fig. 1), with a high initial value of contact angle (68j) and low apparent absorption rate (19j/s). It was not thus possible to significantly discriminate the hard and soft wheat flours from measurements of contact angles, although these flours were characterized by slight differences in their chemical composition (Table 1).

In order to estimate the dependence of the surface wettability properties of flours on particle diameter, we measured the contact angles of compacts based on four granulometric fractions of hard wheat flour (Table 5). The initial values of contact angle (65 -71j) for compacts based on the larger fractions (D 50 >50 Am) were not significantly different from those reported for the original flour (68j). Only the smallest fraction (D 50 < 50 Am) was characterized by a slightly lower value (60j). On the other hand, the apparent rates of water drop absorption (11 -13j/s) for compacts based on the larger granulometric fractions (D 50 >50 Am) were significantly lower than those reported for the initial flour (21j/s). The apparent absorption rate (23j/s) of the smallest fraction (D 50 < 50 Am) seemed to greatly contribute to the flour properties.

The surface wettability properties of the flour components were presented in Figs. 2 and3. The flour components were characterized by significantly different values of wettability (Tables 3 and4). The compacts based on starch (at 0% RH) were characterized by a low initial value of contact angle (38j). This low value means that compacts based on starch exhibit ''good'' surface wettability properties. The high apparent rate of water drop absorption (87j/s) is associated with a very short time for water drop absorption inside the compact ( < 1 s). The hydrophilic structure of starch molecules [START_REF] Greer | [END_REF] could explain the high surface wettability properties of starch-based compacts. It should be noticed that Liukkonen [15] found a similar value of contact angle for starch by measuring the contact angle of a microdrop of water directly deposited on the surface of one particle using environmental scanning electron microscope. An increase in initial RH conditions (from 0% to 60%) resulted in a slight significant decrease in initial value of contact angle (from 38j to 30j) and in apparent rate of water drop absorption (from 87j/s to 34j/s). As expected, the initial hydration of starch compacts favored the initial wettability properties, but reduced the absorption rate. The initial value of contact angle for damaged starch was not significantly different from that of starch (Table 3). On the other hand, a lower apparent rate of water drop absorption (22j/s) for damaged starch when compared to starch was reported (Table 4).

The surface wettability properties of the other flour components (gluten, insoluble, and soluble pentosans) were also determined (Fig. 3). In comparison with the properties of flours and starches, the time necessary for absorption of the water drop by these compacts is longer (between 25 and 400 s). The compacts based on gluten (at 0% RH) were characterized by ''poor'' surface wettability properties (Tables 3 and4), with a very high initial contact angle (85j) and low apparent rate of water drop absorption (0.09j/s). The water drop did not spread over the surface of the glutenbased compact and seemed to remain ''intact'' for several minutes. These ''poor'' wettability properties of glutenbased compacts could be associated with its partially hydrophobic nature [START_REF] Greer | [END_REF]. An increase in the initial water content of gluten due to an increase in initial RH (from 0% to 60%) resulted in an expected slight reduction in the values of initial contact angle (from 85j to 67j) and in apparent rate of water drop absorption (from 0.09j/s to 0.07j/s).

For the soluble and insoluble pentosans (at 0% RH), the initial values of contact angles (Table 3) were not significantly different (38j and 40j). These values were close to those previously measured for the starch-based compacts (Table 3) and described high surface wettability properties. These properties of pentosans are in agreement with the Values inside parentheses are standard deviations. Analysis of variance (using the Excel software) was conducted to evaluate the significant differences between average values. Comparison of products (i.e. same column) was done with different letters (a, b, c) when significantly different (at p < 0.05). high water absorption properties that are classically observed for these components [16]. It should be noted that compacts based on pentosans are characterized by a very low rate of water drop absorption (0.07-1.3j/s), which could be due to modifications of the compact surface during the powder compaction. These modifications could explain the unexpected effect (i.e. increase in initial value of contact angle) of an increase in initial RH for insoluble pentosans on their wettability properties (Tables 3 and4).

The initial values of contact angle measured for compacts based on wheat flours are located in between those measured for gluten and for other flour components (starch and pentosans) (Table 3). The contribution of each component to the surface wettability behavior of the wheat flours depends on the surface repartition of flour components. We could suppose a given structural organization of components on the surface of flour particles, which involve mainly the repartition of gluten protein. Changes in particle properties during compaction can also affect the surface particles.

The measurement of surface wettability properties of wheat flours and flour components was carried out by an indirect method. Indeed, it was not possible to directly measure the contact angles of water drops on powdered materials. The determination of contact angles on the upper surface of compacts was firstly considered to describe the properties of particles. However, we have to consider possible structural changes of flours and flour components that could occur during the compaction. The physical properties of particles and compacts were thus characterized in order to estimate the possible structural changes induced by the compaction process (Table 2).

The density of particles and compacts was measured by helium pycnometry (Table 2). The particles of hard and soft wheat flours were characterized by similar values of density (1.47 g/cm 3 ). These values of density are in the classical range (1.3 -1.5 g/cm 3 ) for cereal flours [START_REF] Melcion | Les industries de premie `re transformation des ce ´re ´ales[END_REF]. The density of flour components was found between 1.31 g/cm 3 (for gluten) and 1.54 g/cm 3 (for pentosans). Considering the content and density of components, the theoretical density of flours was calculated (1.48 g/cm 3 ) and was close to the measured values (1.47 g/cm 3 ). Therefore, the densities of flour particles thus depend on the contribution of each component. The densities of compacts were significantly higher than those measured for particles (Table 2). The densities of materials in compacts ranged between 1.7 and 2.9 g/cm 3 . As expected, the compaction of particles induced thus a significant increase in density. The Cam Clay model describes the relationship between the changes in density of powdered material during compaction and the pressure of compaction [START_REF] Baco-Carles | Re ´cent[END_REF]. During compaction under low pressures, deformations of particles are elastic and reversible. During compaction under high pressures, deformations of particles are plastic and irreversible. It is known that starch presents a plastic deformation during compres- sion [19]. Serris et al. [START_REF] Serris | Re ´cent[END_REF] evaluated for starch the critical compaction pressure at 300 MPa before viscoplastic deformations. This value is lower than the pressure applied during our experiments (700 MPa) for the compaction of wheat flours and flour components. The compaction process is thus responsible of the observed increase in material density.

For the determination of wettability properties of powders by the measurements of contact angle on compacts, we also have to consider the porosity of the material. The measured values of porosity for initial particles (Table 2) are typical of nonporous particles (porosity < 0.8%), except for pentosans (porosity = 46-49%). Wheat flour, gluten, and starch particles did not present any intra-particular porosity. The high values of porosity measured for the pentosan particles can be explained by a specific structural organization (i.e. a porous fibrous structure) of pentosan molecules (Fig. 6). Porosity at mercury was also measured for the compacts based on wheat flour or flour components (Table 2). A real inter-particular porosity was observed for the compacts, with values ranging from 30% to 35%. Compaction of flour particles did not permit to obtain homogenous compact without a high inter-particular porosity. Even if the compaction pressure was very high (700 MPa) and induced a densification of particles, the compaction conditions did not permit to ensure a perfect agglomeration of particles (i.e. without inter-granular porosity). The presence of intergranular porosity in compacts significantly affects the kinetic parameters (i.e. apparent rates of water drop absorption) [START_REF] Baco-Carles | Re ´cent[END_REF]21]. In order to get a better description of the compact structure, the compact surface was observed by scanning electronic microscopy and compared to the initial structure of particles (Figs. 456). Compacts based on wheat flour were characterized by a relatively ''poor'' adhesion between particles (which were still observable) and by the presence of a large number of holes and crackings (Fig. 4). The low adhesion of flour particles inside compacts permits the formation of inter-granular porosity (Table 2) and can also be considered responsible in the ''poor'' mechanical properties of these compacts (Table 2). Wheat flour-based compacts were characterized by high friability and are fragile.

For the compacts based on wheat gluten, we observed a relatively fine adhesion of the initial particles (Fig. 4), with an apparent ''melting'' of some particles. Starch-based compacts were characterized by an apparent fine adhesion between the initial particles (Fig. 5). Holes and crackings are still observable on the surface of compacts based on starch or gluten. Low values of hardness (14 -72 N) and very low values of friability (0-5%) characterized the fine adhesion between particles that formed these compacts (Table 2). For the compacts based on pentosans, we observed a very organized structure with strong interactions between the initial particles (Fig. 6). It was then not possible to discriminate the initial structure on the surface of compacts. This structure was responsible in high mechanical properties of compacts (Table 2). It should be noticed that some holes and crackings are still observable (Fig. 6).

The microstructure description of the compact surfaces thus confirmed the presence of inter-particular porosity inside compacts, due to a ''poor'' adhesion between particles or to the presence of holes and crackings (except for pentosan compacts). The kinetic parameters of the wettability properties depend on two phenomena: (1) water diffusion inside particles and (2) water absorption in the intergranular porosity. It was thus not possible to discriminate the contribution of each phenomenon.

Conclusion

The results obtained in this paper demonstrated that the measurements of contact angle of water drop deposited on the surface of compact give relevant values of wettability properties for cereal-based powders. Initial values of contact angles were considered to evaluate the contribution of wheat components to the surface properties of wheat flours. The determination of physical properties of compacts (i.e. density, porosity, and microstructure) demonstrated that physical changes occurred during the preparation of compacts (i.e. increase in density and porosity), and partly affected the values of apparent rate of water drop adsorption. A complementary approach to describe the dynamic changes in surface wettability properties of cereal-based powders would be considered by using a microanalysis technique based on measurements with an environmental SEM of contact angles of a water microdrop, directly deposited on one particle [15].

Fig. 1 .

 1 Fig. 1. Typical example for the measurements of contact angle by the method sessile drop of compact (based on hard wheat flour). The initial contact angle (A) and after 3 min (B).

Fig. 2 .

 2 Fig. 2. Changes in contact angle of a water drop deposited on compacts based on hard wheat flour (E), soft wheat flour (4), damaged starch (+), or starch (o) (pre-equilibrated at 0% RH) as a function of time after the drop deposition.

Fig. 3 .

 3 Fig. 3. Changes in contact angle of a water drop deposited on compacts based on wheat gluten (E), insoluble pentosans (+), or soluble pentosans (.) (pre-equilibrated at 0% RH) as a function of time after the drop deposition.

Fig. 4 .

 4 Fig. 4. Microstructural characterization by scanning electron microscopy of powders and compacts based on hard wheat flour and soft wheat flour (equilibrated at 0% RH).

Fig. 5 .

 5 Fig. 5. Microstructural characterization by scanning electron microscopy of powders and compacts based on the wheat starch, damaged starch, or gluten (equilibrated at 0% RH).

Fig. 6 .

 6 Fig. 6. Microstructural characterization by scanning electron microscopy of powders and compacts based on insoluble pentosans and soluble pentosans (equilibrated at 0% RH).

Table 1

 1

	Chemical composition of the wheat flours and flour components
	Product	Water content	Chemical composition (% db)
		(% db)	Protein	Starch	Damaged	Total	Soluble	Ash	Lipids
					starch	arabinoxylans	arabinoxylans
	Soft wheat flour	14.8	10.5	86.5	3.65	1.51	0.49	0.44	1.25
	Hard wheat flour	15.3	12.9	84.0	6.57	1.76	0.45	0.47	1.28
	Gluten	14.8	79.8	15.6	3.28	0.65	0.20	0.47	0.29
	Starch	14	0.22	98.9	1.73	0	0	0.12	0.03
	Damaged starch	13.7	0.21	98.9	22.0	0	0	0.13	0.03
	Insoluble pentosans	15	5.23	51.7 a	2.85	37.8	0	3.78	-
	Soluble pentosans	10.6	-	1.0	0.21	-	99.0	-	-
	db is defined as dry basis.

a Content of glucan molecules and resistant starches produced during preparation of samples for measurement of insoluble pentosanes.

Table 2

 2 Physical characterization of wheat flours and flour components

	Product	Initial powders				Compacts
		Particle size distribution	Density	Porosity	Density	Porosity	Hardness	Friability
		D 50 (Am)	Dispersion (Am)	(g/cm 3 )	at Hg (%)	(g/cm 3 )	at Hg (%)	(N)	(%)
	Soft wheat flour	68	2	1.47	0.60	1.72	33	fragile	50
	Hard wheat flour	90	2	1.47	0.58	1.72	34	fragile	42
	Gluten	82	2	1.31	0.45	1.71	30	14	5
	Starch	19	1	1.50	0.65	1.92	35	31	3
	Damaged starch	18	1	1.54	0.80	2.0	34	72	0.2
	Insoluble pentosans	124	3	1.53	49	2.83	35	483	0.1
	Soluble pentosans	274	2	1.50	46	2.88	32	191	0.1

Table 4

 4 Apparent rates of water drop adsorption by compacts based on wheat flours and flour components (equilibrated at different relative humidities) Values inside parentheses are standard deviations. Analysis of variance (using the Excel software) was conducted to evaluate the significant differences between average values. Comparison of products (i.e. same column) was done with different letters (a, b, c, d, e) when significantly different (at p < 0.05). Comparison of equilibration conditions (i.e. same lines) was done with different Greek letters (a, h) when significantly different ( p < 0.05).

	Products	Rate of water drop absorption (j/s)
		Equilibrated at 0% RH	Equilibrated at 60% RH
	Hard wheat flour	21 (2) b/a	14 (2) b/h
	Soft wheat flour	19 (2) b/a	15 (1) b/h
	Gluten	0.09 (0.01) d/a	0.07 (0.01) d/h
	Starch	87 (16) a/a	34 (5) a/h
	Damaged starch	22 (2) b/ À	-
	Insoluble pentosans	1.3 (0.1) c/a	1.4 (0.2) c/a
	Soluble pentosans	0.07 (0.01) e/ À	-

Acknowledgements

The authors acknowledge financial support from CON-ACyT (Consejo Nacional de Ciencia y Tecnologia) of Mexico (Doctorate bourse 72743).