Modelling Mixed Powder Properties: 
Beyond Classical Mixing Rules​

Background

In pharmaceutical formulation development, many key decisions are guided by powder-level properties such as particle size distribution, density, and flowability. These properties are inherently process-independent, yet they strongly influence downstream manufacturability across multiple unit operations, including blending, granulation, and direct compression.

While these properties are routinely measured for individual raw materials, the behavior of powder mixtures is significantly more complex. The properties of a blend rarely follow simple linear trends as a function of composition, particularly when powders of different nature—such as cohesive APIs and free-flowing excipients—are combined.

Accurately predicting mixed powder properties therefore represents an important, yet challenging, step in rational formulation design.

Limitations of Classical Mixing Rules

Traditionally, mixed powder properties are estimated using simple mixing rules, such as:

  • Linear or weighted averaging based on mass or volume fraction
  • Empirical correction factors
  • Rule-of-mixtures approaches derived from idealized assumptions

In some cases, these approaches deliver acceptable performance, particularly when the components have similar physical characteristics or when one component dominates the formulation.

However, their limitations become apparent when:

  • Powders differ strongly in particle size, morphology, or cohesion
  • Highly cohesive APIs are blended with free-flowing fillers
  • Property evolution exhibits nonlinearity or abrupt transitions

Under such conditions, simple mixing rules fail to capture phenomena such as component interactions, dominance effects, and threshold behavior, leading to inaccurate or misleading predictions.

Complexity in Powder Mixtures

The properties of powder blends emerge from multiple interacting factors, including:

  • Relative proportions of the components
  • Particle size and size distribution mismatches
  • Surface properties and cohesion
  • Morphological differences
  • Inter-particle and inter-component interactions

In many systems, the contribution of a component is not proportional to its fraction in the blend. Instead, percolation-type behavior can occur, where a component begins to dominate a given property only after exceeding a critical concentration. Below this threshold, its influence may be limited; above it, the property can change rapidly.

Such behavior is commonly observed, for example, when a small amount of a highly cohesive API begins to control blend flowability, or when a plastically deforming excipient starts to dominate mechanical response beyond a certain loading.

Capturing these nonlinear and interaction-driven effects requires modelling approaches that go beyond predefined functional forms.

Neural Network Approach to Mixed Powder Properties

To address this complexity, Elegent employs neural network-based models for the prediction of mixed powder properties. These models are designed to:

  • Learn nonlinear relationships between component properties and blend behavior
  • Capture interaction effects between powders of different nature
  • Account for the influence of component dosage across the full composition range

Material-level descriptors—such as particle size metrics, density, morphology-related proxies, and flow-relevant characteristics—are provided as inputs for each component. The neural network learns how these descriptors combine and interact in a mixture, without imposing restrictive assumptions about linearity or dominance.

This approach allows the model to implicitly represent phenomena such as:

  • Percolation thresholds
  • Component dominance and masking effects
  • Synergistic or antagonistic interactions

Importantly, these effects are captured simultaneously, rather than being introduced through separate correction factors or empirical rules.

In-House Models for Process-Independent Powder Properties

Using this framework, Elegent has developed in-house models for predicting a range of process-independent mixed powder properties, including:

  • Particle size distribution descriptors
  • Bulk and tapped density
  • Powder flowability metrics

These predictions are generated directly from the properties and proportions of the individual components, without reference to a specific downstream process.

Because these properties are foundational to many unit operations, the models can support decision-making across a wide range of manufacturing routes. For example:

  • Early screening of excipient combinations
  • Evaluation of formulation robustness prior to process selection
  • Identification of potential risks related to flow or segregation

Role in Formulation Decision-Making

By providing reliable predictions of mixed powder properties, these models form an important input layer for higher-level CQA and process models. They enable formulation scientists to explore composition space systematically and to understand how changes in formulation propagate through material properties toward process performance.

In this way, modelling mixed powder properties serves as a critical link between raw material characterization and process- and product-level outcomes, supporting informed, data-driven decisions early in development.

If you’d like, I can next:

  • Add a worked example illustrating percolation behavior in a blend, or
  • Align this page more closely with the CQA modelling pages by explicitly linking mixed powder properties to downstream CQA predictions.