Metallurgical and Materials Transactions B

, Volume 39, Issue 1, pp 108–115

Kinetics of Pressureless Infiltration of Al-Mg Melts into Porous Alumina Preforms


    • Department of Materials EngineeringIndian Institute of Science
    • Material Mechanics LabJohn F. Welch Technology Center, General Electric
  • Vikram Jayaram
    • Department of Materials EngineeringIndian Institute of Science

DOI: 10.1007/s11663-007-9111-9

Cite this article as:
Patro, D. & Jayaram, V. Metall and Materi Trans B (2008) 39: 108. doi:10.1007/s11663-007-9111-9


Effective “hydrodynamic” radii governing infiltration kinetics of reactive Al-Mg melts into alumina preforms were found to be three orders of magnitude smaller than the average pore size of the packed bed and also smaller compared with the kinetics for a nonreactive system. A sinusoidal capillary model was developed to predict flow kinetics within the packed bed. For the reactive system, two factors were ascribed for additional melt retardation: (1) different intrinsic wettabilities of the two liquids on alumina, thereby leading to significantly different “effective” local contact angles; and (2) local solute depletion from the meniscus, which was incorporated as a time-dependent contact angle.


Melt infiltration is a versatile technique for processing of both metal and ceramic-matrix composites[1] and multiphase materials in powder metallurgy.[2] The pressureless infiltration technique[3] has been employed for making near net-shaped composites by infiltrating Al-Mg melts into SiC, Al2O3, and Si3N4 in a nitrogen atmosphere. The presence of both Mg in the system and a minimum partial pressure of N2 were shown to be crucial for this process.[3] It has been shown[4] that Mg has a twofold role in the process: initiation and continuation of infiltration. Termination of infiltration was associated with the local depletion of Mg from the melt front leading to formation of passivating products, either Al2O3 or MgAl2O4 under open conditions (where the infiltration front is exposed to the atmosphere). Using a different self-sealing configuration, Al could be infiltrated into Al2O3 preforms in air with Mg present externally at the billet-preform interface.[5] With this configuration, infiltration was shown to continue for longer periods of time, consequently producing greater thickness of composite. Composite formation rates for the Al/Al2O3 system are found to be extremely slow in the range mm/h to cm/h, which is also found in other systems[68] processed through the melt infiltration technique. Such rates are found to be two to three orders of magnitude slower than that predicted by fluid flow using a uniform capillary bundle model based on the average of the pore size distribution (∼mm/s).[5,8]

From a physical standpoint of flow through porous media, more realistic models of nonuniform capillaries have been proposed[9,10] to explain the slow rise of liquids. Recently, a sinusoidal capillary model has been developed for infiltration of nonreactive liquids in porous ceramics.[11] Flow under such conditions was shown to be governed by an “effective hydrodynamic” radius, one to two orders of magnitude smaller than the average pore radius. The origin of this “unphysical” radius was rationalized based on a consideration of the driving forces on the meniscus while moving through the larger, rate-limiting segment. Capillary pressure is dictated by rmax, while viscous drag is determined by rmin (rmax and rmin being the diameter of the pore and throat, respectively), thereby leading to slow flow rates.

However, high-temperature melt-infiltrated system are reactive associated with dissolution of the ceramic in the melt, depletion of reactive species from the melt,[12] and formation of interfacial reaction products during infiltration,[13] which either lead to a reduction in permeability of the porous compact[13] or change the melt chemistry and energetics of different interfaces in the system. Such chemical reactions additionally influence (in many cases retard)[13,14] the infiltration kinetics over and above that dictated by the physical flow of fluid through the compact. In such a process, reaction kinetics and solute transport are interactively coupled with the dynamics of fluid flow in a complex fashion due to the moving boundary nature of the process, with the slower of the two mechanisms controlling the infiltration rate. The activation energy determined from the temperature dependence of infiltration kinetics sheds insight into the rate-controlling mechanisms. Reported activation energies for many systems[15,16] are in the range of 100 to 400 kJ/mol indicating a chemical reaction-controlled kinetics.

The evolution of capillary forces at the moving front has been ignored in earlier studies. In many high-temperature systems, wetting kinetics are important and a large initial contact angle decays exponentially with time, in agreement with the following empirical relation:[17]
$$ \theta {\text{(}}t{\text{)}} = \theta _{{eq}} + \theta _{{eq}} {\text{ exp (}}A - Bt{\text{)}} $$
where θ(t) is the instantaneous contact angle, θeq is the equilibrium contact angle, and A and B are constants. Spreading times are found to be three to four orders of magnitude larger for reactive systems compared to inert liquids due to effects related to ridge controlled spreading, adsorption, and kinetics of compound formation.[18] Such nonequilibrium effects, specifically those associated with compound formation, manifest in time-dependent (kinetic) contact angles and become significant when the infiltration time becomes comparable to the characteristic wetting time in these systems. A time-dependent contact angle (Eq. [1]) was incorporated in the Washburn equation to determine infiltration kinetics during nonequilibrium wetting.[17] Flow was found to be retarded compared to the case of static wetting (i.e., using θeq).

The objective of this article is to understand infiltration kinetics in the reactive Al-Mg/Al2O3 system by investigating different aspects of the problem, viz. (1) the kinetics of infiltration from a fluid flow perspective and (2) coupling between chemical effects and fluid flow. To fulfill this, investigation and measurement of the kinetics were conducted in both a nonreactive as well as a reactive system. A phenomenological model and numerical analysis of infiltration process has been developed from a purely physical aspect of fluid flow and chemical effects are incorporated in the model.

Experimental Procedure

Preparation of Porous Preforms and Alloys

Infiltration experiments were conducted with two different liquids (a) polyethylene glycol (PEG 600, M/s Merck, India) at room temperature and (b) Al-Mg melts at temperatures of 800 °C to 975 °C into porous packed alumina beds. Powder preparation and bed preparation were carried out meticulously for ensuring reproducibility of results as described previously.[11] The particle sizes of fused alumina used in the study were 25 to 37, 63 to 75, and 90 to 125 μm. The Al-Mg alloys were prepared by standard casting technique. Billets of 8 mm diameter and a height of 10 to 20 mm were machined from the cast rods for use in infiltration experiments. The inductively coupled plasma–atomic emission spectroscopy (ICP-AES) analysis indicated the alloy composition to lie within 10 pct of the target value.

Configuration and Conditions

A controlled and reproducible infiltration length (i.e., partial infiltration) is vital to obtain a measure of infiltration kinetics. Based on the understanding of the different stages of pressureless infiltration in the Al-Mg/Al2O3 system,[4] the conditions for the experiments were selected as follows:
  1. (a)

    self-sealing conditions (to prevent ingress of air after melting of billet),

  2. (b)

    Mg disc equivalent to 3 wt pct Mg in the melt (as external initiator to reduce incubation period), and

  3. (c)

    upquenched experiments (to prevent excessive loss of Mg).

It was expected that the preceding conditions might promote infiltration for longer lengths without being masked by termination of infiltration due to passivation.[4]
The schematic of the billet/porous compact assembly used for infiltration under sealed conditions is shown (Figure 1) and subsequently referred to as downward, double-sealed configuration (DDS). The alumina packed bed was sandwiched between two Al billets with Mg foil at the interface between the top billet and preform. A graphite foil was placed between the bottom billet and packed bed to prevent infiltration. Experiments were performed in both upward and downward directions. However, the infiltrated lengths were not found to be vastly different, indicating the insignificance of the gravitational potential. The assembly was inserted at the set temperature inside a preheated furnace and 5 minutes allowed for equilibration, followed by specified holding periods. Infiltration kinetics was studied as a function of particle size and temperature.
Fig. 1

Schematic of the billet/preform assembly used for infiltration under sealed conditions (DDS). Infiltration direction is shown with arrow


The pore size distribution of the porous compacts was measured using Hg porosimetry (Poremaster PM 60GT, Quantachrome Instruments, Florida, USA) and further corroborated with image analysis on polished sections of the composite. Furthermore, a relevant pore size distribution of 1.4 to 10.8 μm for the 25 to 37 μm bed, which accounts for the measured flow rates of polyethylene glycol (PEG 600), was extracted as described elsewhere.[11] This was done by truncating the volumetric pore size distribution obtained from Hg porosimetry, to 95 pct, i.e., removing 2.5 pct by volume of the smallest pores and the largest pores since the remaining volume still controls the majority of the flow.

After infiltration experiments, the composites were sectioned longitudinally with a diamond blade using a high speed saw (Isomet 2000, Buehler, Illinois, USA), polished using standard metallographic polishing procedures and finished with 6 μm diamond paste. The infiltration front was found to be irregular (Figure 2) and hence an effective length was measured as discussed later. X-ray analysis was done (JEOL JDX-8040) with Cu Kα radiation and Ni filter with a scan speed of 2 deg/min and 0.02 deg step size for both the composite as well as uninfiltrated powder. Microscopic analysis was carried out using a field emission scanning electron microscope (Sirion, FEI, Inc.) fitted with a super-ultrathin window energy dispersive X-ray detector (EDAX, Inc.) capable of detecting elements up to boron. In a few cases composites were etched with Keller’s reagent to help in the identification of other phases inside the matrix.
Fig. 2

Irregular infiltration fronts for 25 to 37, 63 to 75, and 90 to 125 μm composites processed in air showing dimensions with a ruler (major markings in centimeters)


The average pore size of the different particle size alumina beds, for which the mode of the pore size distribution was measured from image analysis, is presented in Table I, column 2. For the 25 to 37 μm particle size, a pore size distribution of 1.4 to 10.8 μm measured using Hg porosimetry was considered as representative for describing the flow kinetics through the loose particle bed.[11] No pore size distributions could be obtained from the larger 63 to 75 and 90 to 125 μm particle beds by Hg porosimetry due to the difficulty in preparing slip-cast and sintered counterparts.
Table I

Effective Hydrodynamic Radii for Both Low-Temperature and High-Temperature Infiltration into Alumina Packed Beds in Microns

Particle Size

Average Pore Radius

Washburn Radius (PEG 600)

Washburn Radius (Al-3Mg)

25 to 37


0.06 ± 0.02

0.004 ± 0.001

63 to 75


0.25 ± 0.01

0.026 ± 0.005

90 to 125


0.27 ± 0.01

0.028 ± 0.005

The overall infiltration kinetics (hvst plots) for the room temperature infiltration of PEG 600 into packed Al2O3 beds could be well fitted with a parabolic Washburn equation (Figure 3, inset), implying a laminar, steady-state flow on a macroscopic scale inside the porous bed. It further establishes the equivalence between flow kinetics through the porous media and a bundle of uniform capillaries with radii given by reff as per Eq. [2].
$$ h^{2} = \frac{{r_{{{\text{eff}}}} \gamma {\kern 1pt} \,\cos \,\theta }} {{2\eta }}t{\text{ }} $$
$$ v = \frac{{r_{{{\text{eff}}}} \gamma \cos \,\theta }} {{4\eta h}} $$
where γ = liquid surface tension, θ = contact angle, η = liquid viscosity, and v = meniscus velocity. The effective or hydrodynamic radius, reff, is an indicator of the infiltration kinetics with the meniscus velocity being proportional to reff. The hydrodynamic radii or Washburn radii for capillary flow of PEG 600 into different packed beds are summarized (Table I, column 3) and serve as a benchmark for the nonreactive capillary flow kinetics.
Fig. 3

Infiltration kinetics of Al-3Mg into various powder beds at 800 °C. Inset shows parabolic (h2t) kinetics for PEG 600 into 25 to 37 μm packed bed

For the high-temperature infiltration experiments with Al-3 wt pct Mg melts, the sectioned composites were found to have an irregular front (Figure 2). The effective infiltration length as a function of particle size is shown in Figure 3. The need to define such a parameter is based on visual observation of the sectioned composites. Infiltration was found to proceed preferentially along one side and sometimes leave behind large uninfiltrated portions in the wake of the infiltration front (highlighted in Figure 2). This indicates that the melt starts off nonuniformly from one side of the billet/preform interface. In such cases, the effective infiltration length was calculated by visually estimating the total volume of composite formed and averaging it over the cross section of the crucible to give the effective infiltration length (Figure 3) as
$$ {\text{effective infiltration length }} = \frac{{{\text{total volume infiltrated}}}} {{{\text{cross sectional area of crucible}}}}{\text{ }} $$
There was difficulty in accurately measuring the volume fraction of preform infiltrated that led to errors of ±15 pct in the values of effective infiltration length.

Infiltration kinetics for the powder beds was seen to scale with the particle size. However, the 63 to 75 and 90 to 125 μm powder beds displayed similar infiltration kinetics. The infiltration profile for the different powder beds at 800 °C (Figure 3) was fitted to parabolic kinetics using the Washburn equation (Eq. [2]) to give hydrodynamic radii for capillary flow of Al-3 wt pct Mg melts into packed alumina beds (Table I, column 4). The relevant properties for Al-3 wt pct Mg obtained from literature are η = 1.04 × 10−3 Pa·s,[19] γ = 0.795 N/m,[20] and θavg = 85 deg (varies between 83 to 88 deg).[21] The hydrodynamic radii for infiltration (Table I) were found to be two to three orders of magnitude smaller than the average pore size for all the particle size beds. Furthermore, the kinetics for reactive infiltration (Al-Mg/Al2O3 couple) was found to be an order of magnitude slower than that for nonreactive infiltration (PEG 600/Al2O3 couple) for similar particle sizes.

The XRD of the melt processed composites (Figure 4) shows presence of spinel, MgAl2O4 (JCPDS 75-1796), which is formed at the interface of Al-Mg and Al2O3. In partially infiltrated samples, XRD of the uninfiltrated discolored powder of the loose powder compact shows the presence of spinel phase at the interface, indicating that the spinel forms as a result of vapor phase reaction between Mg vapor and Al2O3 reinforcement as per the reaction
$$ 3{\text{Mg}}({\text{v}}) + 4{\text{Al}}_{2} {\text{O}}_{3} ({\text{s}}) = 3{\text{MgAl}}_{2} {\text{O}}_{4} ({\text{s}}) + 2{\text{Al }}({\text{l}}) $$
Scanning electron micrograph (SEM) of the uninfiltrated particles of the compact (Figure 5) ahead of the front indicates formation of granular features on the surface. Energy dispersive spectroscopy (EDS) (Figure 5, inset) indicates Mg enrichment of the surface.
Fig. 4

Al-Mg/Al2O3 composite showing spinel phase
Fig. 5

Uninfiltrated particles ahead of front showing granular features on surface. Inset shows EDS from the particle surface with significant Mg enrichment due to spinel formation

It is imperative to rationalize the extremely slow flow kinetics for both the nonreactive and reactive situations. A nonuniform capillary model (sinusoidal capillary) based on periodic changes in cross-sectional area of a flow path inside the porous compact has been developed[11] to account for the origin of this unphysical radius governing infiltration kinetics. In addition, we shall highlight the significance of the effective local contact angle of the two liquids with different wettabilities inside the channels of the porous medium in influencing infiltration kinetics. However, this is a physical model that considers only capillary driving forces and viscous retarding forces. This model will be further extended to the case for reactive infiltration, which is associated with concomitant changes in melt chemistry due to interfacial reactions.


Slow capillary flow kinetics through porous media has been modeled using a sinusoidal capillary.[11] The modified pore size distribution of the 25 to 37 μm packed bed (1.4 to 10.8 μm) was used as input parameter for the sinusoidal capillary giving an effective hydrodynamic radius of 0.04 μm, in good agreement with the experimentally-observed value of 0.06 μm for capillary rise of PEG 600 through packed Al2O3 bed. However, this is strictly true under conditions where the effect of the local contact angle was not significant. (Local contact angle refers to the sum of the static contact angle, θ and the angle, φ due to inclination of the capillary wall with the local direction of flow as shown in Figure 6.) The influence of effective local contact angle will be considered with respect to infiltration of Al-3 wt pct Mg melts inside an alumina sinusoidal capillary.
Fig. 6

Geometrical representation of meniscus with effective contact angle varying with position in capillary due to inclination of wall

A sinusoidal capillary representation of the porous media can be expressed as
$$ r = r_{0} + {\text{A}}\sin {\left( {\frac{{2\pi z}} {\lambda }} \right)} $$
where ro = average radius, A = amplitude of variation, z = length along profile, and λ = wavelength of fluctuation.

The wavelength, λ, represents the average length between a pore and pore neck and is typically found to be equal to the average particle size for porous media considered (based on observations of optical and SEM micrographs of polished sections) though statistically long and short wavelength flow paths exist in any random packed bed.

Due to the inclination of the angular particle surfaces with respect to the flow direction, the meniscus curvature keeps changing during motion of the liquid through the capillary. The effective contact angle, which determines the capillary driving force, now becomes θ + φ (Figure 6). The curvature induced driving pressure can be expressed as
$$ \Delta P = \frac{{2\gamma _{{lv}} }} {{r(h)}}{\left[ {\cos \,\;\theta - \frac{{2\;\sin \;\phi }} {{{\left\{ {1 + \sin \;{\left( {\theta + \phi } \right)}} \right\}}}}} \right]} $$
where \( \tan \phi = \frac{{dr}} {{dh}} = \frac{{2\pi A}} {\lambda }\cos {\left( {\frac{{2\pi h}} {\lambda }} \right)} \) is the instantaneous slope of the sinusoidal profile.
The final expression for velocity of liquid-vapor interface as derived elsewhere[11] is
$$ \frac{{dh}} {{dt}} = {\left[ {\frac{{2\gamma }} {{r(h)}}{\left( {\cos \;\theta - \frac{{2\;\sin \;\theta }} {{\{ 1 + \sin \;(\theta + \varphi )\} }}} \right)}} \right]}\frac{1} {{8\eta r^{2} (h){\int\limits_{h_{{{\text{initial}}}} }^{h_{{{\text{inst}}}} } {\frac{{dz}} {{r^{4} (z)}}} }}} $$
where r(h) is the local radius and \( \frac{{dh}} {{dt}} \) is the local instantaneous velocity of the advancing meniscus. This equation was solved numerically to obtain height-time plots.
We notice that the condition, ΔP = 0 gives the relationship \( \cos \theta = \frac{{2\sin \phi }} {{{\left\{ {1 + \sin {\left( {\theta + \phi } \right)}} \right\}}}} \). This implies that for a given contact angle (θ < 90 deg), the liquid front is arrested at a position (far below the equilibrium height) where the capillary profile expands to make the meniscus flat (i.e., φ = π/2 − θ giving φ = 49 deg for PEG 600 and φ = 5 deg for Al-3Mg melt). For a given sinusoidal capillary with ro and A constant, this implies a critical wavelength, λcritical, below which infiltration cannot occur, where
$$ \lambda _{{{\text{critical}}}} = \frac{{2\pi A}} {{\cot \;\theta }} $$
For the 1.4 to 10.8 μm sinusoidal capillary (A = 2.35 μm), λcritical = 12.8 μm for PEG 600, and λcritical = 169 μm for Al-3Mg melt.

The packing inhomogeneity in the porous bed leads to local regions wherein λ < λcritical and such regions are not directly filled with the advancing meniscus but have to wait for the fluid to come around and fill these regions due to the 3-D interconnectivity. In other regions of the packed bed, there is a positive driving force for capillary flow. Fluid flow prefers the path of least resistance (i.e., preferential flow channels) within the porous medium and such channels control the volumetric flow rate. The macroscopic kinetics (as measured in the experiments with PEG 600) can thus be adequately represented by such nonuniform preferential flow paths, thereby leading to good agreement between observed values and modeled values, i.e., reff = 0.04 μm (for nonreactive flow).[11]

However, for infiltration of Al-3 wt pct Mg melt, a critical wavelength of 169 μm implies that it cannot spontaneously infiltrate the 25 to 37 μm packed bed (wherein the average wavelength is ∼30 μm), which is contrary to observations. In order to simulate pressureless infiltration, the 1.4 to 10.8 μm sinusoidal model was tuned with a λ > λcritical to predict the infiltration kinetics (Figure 7). The hydrodynamic radius is seen to vary from 0.006 μm (λ = 170 μm) to a λ-independent value of 0.04 μm (λ ≥ 340 μm). Thereby long wavelength regions in the porous bed allow for fluid transport and lead to an effective radius which can be as large as 0.04 μm (upper bound) or as small as 0.006 μm.
Fig. 7

Comparison between predicted infiltration kinetics for Al-3Mg into 25 to 37 μm porous Al2O3 with different wavelengths, λ > λcritical

The smaller hydrodynamic radius (and consequently much slower flow kinetics compared to PEG 600) can be explained based on the poor wettability of Al-3Mg on alumina (θ = 83 to 88 deg). The effective local contact angle oscillates between (θ + φ)min and (θ + φ)max with the local contact angle approaching 90 deg in the broader flow-controlling segment of the sinusoidal capillary. Thereby, the meniscus curvature-induced driving force drops to an extremely small value and leads to additional retardation of the melt over and above that due to the converging-diverging geometry of the sinusoidal capillary. The effective hydrodynamic radius of a given sinusoidal capillary (1.4 to 10.8 μm) is dependent on both the geometry (ro and A) as well as the effective local contact angle, particularly when the effective contact angle (θ + φ) is > 80 deg. Thus the reduction in effective capillary size from 0.04 μm for PEG 600 to a value between 0.04 and 0.006 μm for the Al-3Mg melt is a direct consequence of going from a wetting fluid to one whose effective contact angle is close to 90 deg.

Contact angle variations can additionally result from variations in the interfacial energetics for the reactive Al-Mg/Al2O3 system due to nonequilibrium effects arising from Mg solute variation, which will be examined next.

Reactive Effects

The major chemical reactions occurring during the infiltration process that can possibly influence melt flow kinetics are as follows: (a) evaporative loss of Mg from the melt leading to reduced wettability and (b) reaction of Al-Mg melt with reinforcement to form spinel, thereby altering wettability.

The XRD and SEM (Figure 5) indicate formation of MgAl2O4 on the surface of the particles ahead of the infiltration front. Thus, the Al-3 wt pct Mg melt wets and infiltrates a spinel surface.

The chemistry of the different interfaces in the presence of reactive solute (Mg) and their influence on the contact angle (θ) evolution during the infiltration/spreading process was considered.

Wettability and interfacial energetics

Solid-vapor and solid-liquid

The Mg reacts with the reinforcement to form MgAl2O4 ahead of the melt front. In all interrupted experiments, the bed ahead of the front was found to be discolored. The XRD of the composite (Figure 4) shows the presence of MgAl2O4 phase and SEM revealed formation of granular features on the particle surface (Figure 5).

Wetting angles of Al-3 wt pct Mg melt on Al2O3 and MgAl2O4 at 800 °C have been reported to be the same (83 ± 5 deg),[21] implying that the quantity SVγSL) for the Al-Mg/Al2O3 and Al-Mg/MgAl2O4 systems, are similar. Hence, wettability is not affected (even though the chemistry of the interfaces is changed).


Surface tension of the melt is strongly dependent on the local Mg level.[20] The Mg continues to be depleted from the system due to evaporation ahead of the melt front. A decreasing Mg level increases the surface tension of the melt and the contact angle, θ, that leads to a reduction in the driving force and decelerates the melt front.

The local Mg level at the front at a given temperature was expressed as[4]
$$ {\text{Mg level at front}} = {\text{evaporation rate of Mg }}({\text{I}}) - {\text{net flux of Mg from reservoir }}({\text{II}}) $$
where (I) evaporation rate = function (Mg composition at front); (II) net flux = diffusive flux from bulk (III) – Mg flux used in forming MgAl2O4 (IV); and (III) diffusive flux = function (initial Mg level in alloy, diffusion length across infiltrated portion). Under a quasi-steady-state assumption, it was deduced[4] that both Mg evaporation as well as spinel formation was capable of reducing the local Mg level at the front.
The EDS of the metal channels on different regions at the start and end of the composite did not indicate dramatic differences in the Mg level, even on quenching the setup from the infiltration temperature, all of them averaging out to within 2 to 2.5 wt pct. However, the significance of local Mg concentration at the instantaneous melt front on kinetics can be judged from the observations of infiltration length based on the distribution of Mg in the system. In an experiment with pure Al billet, Mg at the interface and Mg turnings mixed with the powder bed (leading to a starting composition of 6 wt pct Mg in the melt), the complete length of preform was infiltrated with an effective length of 30 mm in 15 minutes at 800 °C (Figure 8(a) and Table II, 2). However, with an Al-5 wt pct Mg billet and Mg at the interface (leading to a larger initial Mg content in the melt ∼8 wt pct), a smaller infiltration length of 22 mm was observed in 15 minutes at 900 °C (Figure 8(b) and Table II, 3), which is unexpected considering that fluid properties (low η and large γ cos θ term) dictate that the melt velocity be faster at 900 °C compared to 800 °C.
Fig. 8

(a) Mg turnings mixed with powder bed with Al billet and 3 wt pct Mg at the interface (800 °C, 15 min) and (b) Al-5 wt pct Mg billet with 3 wt pct Mg at interface (900 °C, 15 min, infiltration downward)

Table II

Infiltrated Lengths inside the 25 to 37 μm Alumina Bed for Different Melt Compositions and Different Location/Distribution of Mg

Experiment Number

Alloy/Infiltration Conditions



Length (mm)

Time (min)

Length (mm)

Time (min)


Al - (3Mg at interface) (800 °C)



20 to 50



Al - (3Mg at interface) + 3Mg mixed with alumina bed (800 °C)



15 to 35



Al-5Mg + (3Mg at interface) (900 °C)



45 to 110**


*Upper limit to kinetics with no influence of Mg loss using Washburn equation and reff = 0.006 to 0.04 μm (from Fig. 7)

**Upper limit assuming θ = 0 deg, η ∼ 1 × 10−3 Pa·s, and γAl-8Mg = 0.73 mJ/m2 (from Ref. 20 and using /dT = −0.25 mJ/m2/K)

This difference in infiltration kinetics can be explained from considerations concerning the local Mg depletion at the melt front. Magnesium was replenished at the moving melt front more efficiently and frequently when Mg is mixed in the powder bed compared to the long-range diffusion from the bulk reservoir that is needed when Mg was placed either at the interface or alloyed with the billet. The diffusive velocity of Mg in the Al-Mg melt (based on reported values of D0 and Q)[22] varies between 1.5 to 5 μm/s in the temperature range 800 °C to 975 °C, which is smaller than the observed melt velocity of 7 to 20 μm/s in the same temperature range. This suggests that Mg diffusion from the bulk reservoir to the instantaneous melt front is rate limiting. Similar effects have been observed in the Al-Si-Mg/SiC system as well.[12]

The upper limit for infiltration kinetics for the Al-Mg melt is considered next, under a scenario where there is no Mg loss from the system (i.e., a hydrodynamic radius reff between 0.006 and 0.04 μm, Figure 7). For experiment 8(a), the kinetics for Al-3 wt pct Mg melt (not 6 wt pct, Mg since all of the Mg mixed with the powder bed is not available but dissolves progressively into the melt during infiltration) predicts an infiltration length of 15 to 35 mm in 15 minutes (Table II, 2). The actual infiltration length is 30 mm, which is within the predicted range. This implies that the infiltration kinetics lies close to the upper bound given by the scenario of nonreactive fluid flow through the packed bed when solute depletion is absent.

Progressive depletion of Mg from the melt meniscus leads to an increasing contact angle and this was incorporated as a time-dependent contact angle in the sinusoidal capillary model. Infiltration in uniform capillaries has been modeled using a time-dependent contact angle. Following the procedure previously described,[17] the constants A and B (Eq. [1]) for the Al-3Mg/sapphire system were derived from reported wetting kinetics[21] and are A = 0.148 and B = 0.0004. For the present case of infiltration of Al-Mg melts into alumina preforms, a similar kinetics of contact angle increase (from 85 to 89 deg) was assumed, as a result of depletion of Mg locally from the instantaneous front.

The infiltration kinetics inside the 25 to 37 μm loose powder bed is plotted (Figure 9) for both static and kinetic wetting conditions using the sinusoidal capillary model with wavelengths of 170 and 340 μm, respectively. Retardation was observed in all cases independent of wavelength and was more significant for the smaller wavelength compared to the larger one. This implies that the combined effect of both a time-dependent contact angle and the wall curvature leads to the maximum flow retardation, which is the reason for slower infiltration kinetics in the reactive system compared to the nonreactive system in the present study. However, it should be emphasized that even if the wall curvature were not important (i.e., good wettability), flow could still be retarded in the Al-Mg system due to reactive effects related to local depletion of Mg from the melt surface.
Fig. 9

Comparison between predicted infiltration kinetics for Al-3Mg into 25 to 37 μm porous Al2O3 with and without a time-dependent contact angle for different wavelengths. Dynamic θ refers to θ increasing from 85 to 89 deg


For infiltration in the reactive Al-Mg/Al2O3 system, the measured effective hydrodynamic radius was found to be three orders of magnitude smaller than the average capillary size and an order of magnitude smaller compared to the infiltration kinetics for a purely nonreactive system. This was attributed to two factors: (1) retardation effects due to a wall curvature, which results in a larger effective contact angle as a result of poor wettability of Al-Mg melt on alumina; and (2) Mg loss from the system resulting in a time-dependent contact angle θ leading to additional retardation due to an ever-decreasing driving force. Incorporation of such effects in the sinusoidal capillary model was able to rationalize the observed slow infiltration kinetics for the reactive Al-Mg/Al2O3 system.


We are thankful to Saswata Bhattacharyya (Department of Materials Engineering, IISc) for development of the numerical model and analysis. Financial support for this work was provided by the Volkswagen Foundation through a grant for a collaborative project with TU-Darmstadt, Germany.

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