Material Conductivity

Overview

Material conductivity for liquid water transport quantifies the ability of porous building materials to conduct moisture in the liquid phase under capillary suction and moisture gradients. This property, distinct from vapor diffusion, governs liquid water movement through interconnected pore networks and determines redistribution rates, drying potential, and moisture accumulation patterns in building envelopes.

The liquid transport coefficient represents a fundamental hygrothermal material property required for accurate moisture analysis in wall assemblies, roof systems, and foundation structures where capillary action drives moisture movement.

Physical Mechanisms

Capillary Transport Physics

Liquid water movement in porous materials occurs through multiple interconnected mechanisms:

Primary driving forces:

Capillary suction gradients (dominant in unsaturated conditions)
Moisture content gradients
Temperature-induced flow
Gravity effects (vertical assemblies)

Pore-scale phenomena:

Capillary meniscus formation and movement
Film flow along pore walls
Corner flow in angular pores
Hygroscopic moisture redistribution

The liquid flux density follows a diffusion-like relationship:

q_l = -D_w × ∂w/∂x

Where:

q_l = liquid moisture flux density (kg/m²·s)
D_w = liquid transport coefficient (m²/s)
w = volumetric moisture content (kg/m³)
x = spatial coordinate (m)

Moisture-Dependent Conductivity

Liquid transport coefficients exhibit strong dependence on moisture content, typically spanning several orders of magnitude across the moisture range:

D_w(w) = D_ws × f(w)

Where:

D_ws = liquid transport coefficient at saturation
f(w) = dimensionless moisture function

The moisture function commonly follows exponential or power-law relationships:

f(w) = [(w - w_h)/(w_cap - w_h)]^n

Where:

w_h = hygroscopic moisture content (kg/m³)
w_cap = capillary saturation moisture content (kg/m³)
n = material-specific exponent (typically 5-15)

Transport Coefficient Relationships

Suction-Based Formulation

The capillary conductivity relates directly to the moisture retention curve through the Darcy-Buckingham relationship:

K(ψ) = k_rel(ψ) × K_sat

Where:

K(ψ) = capillary conductivity as function of suction (kg/m·s·Pa)
k_rel(ψ) = relative conductivity (dimensionless)
K_sat = saturated conductivity (kg/m·s·Pa)
ψ = capillary suction pressure (Pa)

Diffusivity-Conductivity Relationship

The liquid diffusivity relates to capillary conductivity:

D_w = K(ψ) × (dψ/dw)

Where:

dψ/dw = slope of moisture retention curve (Pa·m³/kg)

This relationship links the transport coefficient to fundamental pore structure characteristics through the retention curve.

Material-Specific Properties

Clay Brick and Masonry

Clay brick exhibits relatively high liquid transport coefficients due to connected capillary pore networks:

Moisture Content (w/w_cap)	D_w (m²/s)	Relative Conductivity
0.95 - 1.0 (near saturation)	1×10⁻⁷ to 5×10⁻⁷	1.0
0.80 - 0.95	5×10⁻⁸ to 1×10⁻⁷	0.2 - 0.5
0.60 - 0.80	1×10⁻⁸ to 5×10⁻⁸	0.05 - 0.2
0.40 - 0.60	1×10⁻⁹ to 1×10⁻⁸	0.005 - 0.05
0.20 - 0.40	1×10⁻¹⁰ to 1×10⁻⁹	0.0005 - 0.005
< 0.20 (hygroscopic range)	< 1×10⁻¹⁰	< 0.0005

Typical parameters for red clay brick:

D_ws (saturated): 2×10⁻⁷ m²/s
Exponent n: 8-12
Capillary saturation: 150-200 kg/m³
Hygroscopic moisture: 2-5 kg/m³

Concrete Materials

Concrete liquid transport varies significantly with mix design, water/cement ratio, and age:

Normal concrete (w/c = 0.50):

Saturated conductivity: 5×10⁻⁸ to 2×10⁻⁷ m²/s
Moisture exponent: 10-15
Strong aging effects (decreasing conductivity)

High-performance concrete (w/c = 0.35):

Saturated conductivity: 1×10⁻⁹ to 1×10⁻⁸ m²/s
Moisture exponent: 12-18
Very low conductivity in partially saturated state

Concrete Type	D_ws (m²/s)	w_cap (kg/m³)	Exponent n
Normal (w/c 0.55)	2×10⁻⁷	120-140	10-12
Medium (w/c 0.45)	5×10⁻⁸	100-120	12-15
High-perf (w/c 0.35)	5×10⁻⁹	80-100	15-18
Lightweight	5×10⁻⁷ to 2×10⁻⁶	200-400	6-10

Wood and Wood-Based Materials

Wood exhibits anisotropic liquid transport with distinct longitudinal, radial, and tangential coefficients:

Softwood (pine, spruce):

Direction	D_ws (m²/s)	Relative Magnitude
Longitudinal	1×10⁻⁶ to 5×10⁻⁶	100-500×
Radial	5×10⁻⁹ to 2×10⁻⁸	5-20×
Tangential	1×10⁻⁹ to 5×10⁻⁹	1× (reference)

Hardwood (oak, maple):

Generally lower transport coefficients
More pronounced anisotropy
Vessel structure creates preferential paths

Engineered wood products:

Material	D_ws (m²/s)	w_cap (kg/m³)	Notes
Plywood	2×10⁻⁸ to 1×10⁻⁷	400-500	Glue layer effects
OSB	5×10⁻⁸ to 3×10⁻⁷	500-600	High variability
Particleboard	1×10⁻⁷ to 5×10⁻⁷	600-800	Rapid capillary uptake
MDF	3×10⁻⁸ to 2×10⁻⁷	700-900	Density dependent

Insulation Materials

Most fibrous and foam insulations exhibit very low liquid transport coefficients:

Mineral wool:

D_ws: 1×10⁻⁸ to 1×10⁻⁷ m²/s
Primarily gravity drainage, limited capillary action
Moisture retention: 1-5 kg/m³ at typical RH

Cellular glass:

Effectively zero liquid conductivity (closed cells)
Transport only through cracks or damaged cells

Wood fiber insulation:

D_ws: 5×10⁻⁸ to 3×10⁻⁷ m²/s
Hygroscopic buffering capacity
Moderate capillary redistribution

Temperature Dependence

Liquid transport coefficients increase with temperature due to reduced viscosity and increased molecular mobility:

D_w(T) = D_w(T_ref) × exp[β(T - T_ref)]

Where:

T = temperature (°C)
T_ref = reference temperature, typically 23°C
β = temperature coefficient (1/°C), typically 0.02-0.04

Viscosity correction approach:

D_w(T) = D_w(T_ref) × [η(T_ref)/η(T)]

Where:

η(T) = dynamic viscosity of water at temperature T

For water between 0-50°C:

At 0°C: η = 1.79 mPa·s (relative factor: 1.77)
At 10°C: η = 1.31 mPa·s (relative factor: 1.30)
At 20°C: η = 1.00 mPa·s (relative factor: 1.00, reference)
At 30°C: η = 0.80 mPa·s (relative factor: 0.80)
At 40°C: η = 0.65 mPa·s (relative factor: 0.65)

This produces approximately 10-15% change in liquid conductivity per 10°C temperature change.

Measurement Methods

Cup Test Methods

Modified cup tests determine liquid transport coefficients through controlled moisture gradients:

Experimental setup:

Material sample with defined thickness
Known moisture content gradient
Steady-state flux measurement
Temperature control

Calculation:

D_w = (q_l × Δx)/(Δw)

Where:

Δx = sample thickness (m)
Δw = moisture content difference (kg/m³)

Absorption-Desorption Methods

Capillary absorption test:

Measures water uptake rate versus time
Determines A-value (kg/m²·s^0.5)
Relates to liquid conductivity through:

A² = D_w × w_cap × ρ_dry

Where:

ρ_dry = dry density (kg/m³)

Pressure plate extraction:

Establishes moisture retention curve ψ(w)
Combined with instantaneous profile method
Yields K(ψ) relationship

Nuclear Magnetic Resonance (NMR)

Advanced technique for direct measurement of moisture profiles:

Advantages:

Non-destructive monitoring
High spatial resolution (sub-millimeter)
Distinguishes liquid phases

Application:

Transient absorption experiments
Inverse analysis for D_w(w)
Validation of exponential models

Inverse Modeling

Numerical optimization determines transport coefficients from measured moisture profiles:

Process:

Conduct controlled wetting/drying experiment
Measure moisture profiles at multiple times
Run hygrothermal simulation with variable D_w parameters
Minimize objective function between measured and simulated profiles
Extract optimized D_w(w) relationship

Objective function:

F = Σ[w_measured(x,t) - w_simulated(x,t)]²

Hygrothermal Modeling Applications

Moisture Balance Equation

Liquid transport coefficient appears in the comprehensive moisture balance:

∂w/∂t = ∂/∂x[D_w × ∂w/∂x] + ∂/∂x[δ_p × ∂p_v/∂x]

Where:

First term: liquid transport
Second term: vapor diffusion
δ_p = vapor permeability (kg/m·s·Pa)
p_v = vapor pressure (Pa)

Coupled Heat-Moisture Transport

Energy balance including liquid transport:

ρc × ∂T/∂t = ∂/∂x[λ × ∂T/∂x] + L_v × ∂/∂x[D_w × ∂w/∂x] + L_v × ∂/∂x[δ_p × ∂p_v/∂x]

Where:

ρc = volumetric heat capacity (J/m³·K)
λ = thermal conductivity (W/m·K)
L_v = latent heat of vaporization (J/kg)

The latent heat terms couple liquid and vapor transport to the thermal field.

Numerical Implementation

Finite difference formulation for liquid transport:

w_i^(n+1) = w_i^n + (Δt/Δx²)[D_(i+1/2) × (w_(i+1)^n - w_i^n) - D_(i-1/2) × (w_i^n - w_(i-1)^n)]

Where:

Subscript i denotes spatial node
Superscript n denotes time step
D_(i+1/2) = 0.5 × [D_w(w_i) + D_w(w_(i+1))]

Stability criterion:

Δt ≤ (Δx²)/(2 × D_w,max)

Design Considerations

Material Selection

Low liquid conductivity materials (protective functions):

Exterior water-resistive barriers
Capillary breaks in foundations
Drainage plane materials
Face-sealed cladding systems

High liquid conductivity materials (redistribution functions):

Interior hygroscopic buffers
Moisture-redistributing layers
Capillary-active insulation systems
Drying-optimized assemblies

Assembly Design

Capillary break placement:

Position materials with D_w ratios > 100:1 to interrupt liquid transport:

Foundation-to-wall transition
Below-grade to above-grade
Masonry veneer cavities
Roof-to-wall interfaces

Liquid transport pathways:

Analyze dominant moisture paths:

Identify highest conductivity materials
Check moisture content operating ranges
Verify drying direction alignment
Confirm capillary break effectiveness

Drying Potential

The drying rate from liquid-saturated conditions depends on liquid conductivity:

t_dry ∝ L²/(D_w × Δw)

Where:

L = characteristic dimension (m)
Δw = moisture content driving force (kg/m³)

Example calculation for brick wall (100mm thick):

D_w,avg = 5×10⁻⁸ m²/s
Δw = 100 kg/m³ (from 150 to 50 kg/m³)
t_dry ≈ (0.1)²/(5×10⁻⁸ × 100) = 2×10⁶ s ≈ 23 days

This represents liquid redistribution time; complete drying requires additional vapor diffusion.

Freeze-Thaw Considerations

High liquid conductivity in cold climates presents freeze-thaw risks:

Critical moisture content:

w_crit = 0.9 × w_cap

Above this threshold, freezing can generate damaging expansion stresses.

Mitigation strategies:

Specify low-conductivity outer layers
Provide adequate drainage
Include capillary breaks
Design for rapid spring drying

ASHRAE and Code References

ASHRAE Standards

ASHRAE Standard 160 - Criteria for Moisture-Control Design Analysis:

References liquid transport coefficients for hygrothermal modeling
Specifies material property requirements for simulation
Defines acceptable moisture performance criteria

ASHRAE Research Project RP-1325:

Compiled liquid transport data for common materials
Established measurement protocols
Created material property database

ISO Standards

ISO 15148 - Hygrothermal Performance of Building Materials and Products:

Standard test method for water absorption coefficient
Relates A-value to liquid transport coefficient
Specifies specimen preparation and conditioning

ISO 12572 - Water Vapor Permeability:

Complementary to liquid transport measurement
Combined analysis for full moisture transport characterization

Modeling Tools

Software packages requiring liquid transport coefficients:

WUFI (Wärme Und Feuchte Instationär):

Comprehensive hygrothermal simulation
Built-in material database with D_w(w) functions
Validated against field measurements

DELPHIN:

Advanced coupled heat-moisture-salt transport
User-defined transport functions
Research-oriented platform

COMSOL Multiphysics:

Custom PDE implementation
Moisture-dependent property functions
Couples to structural, thermal, and other physics

Quality Control and Validation

Material Variability

Liquid transport coefficients exhibit significant batch-to-batch variation:

Typical coefficient of variation (COV):

Clay brick: 30-50%
Concrete: 40-70%
Wood products: 50-100%
Engineered materials: 20-40%

Sampling requirements:

Minimum 5 specimens per batch
Test multiple moisture content levels
Document manufacturing source
Record environmental conditioning history

Measurement Uncertainty

Sources of uncertainty:

Moisture content determination: ±5-10%
Flux measurement: ±10-15%
Specimen geometry: ±2-5%
Temperature control: ±3-8%

Combined uncertainty:

Typical range: ±25-40% for D_w determination
Improved to ±15-25% with advanced techniques

Validation Approaches

Component-level validation:

Conduct controlled wetting experiments
Measure moisture profiles at multiple times
Compare to simulated profiles using measured D_w
Adjust parameters within uncertainty bounds

Assembly-level validation:

Field monitoring of wall sections
Embedded moisture sensors
Multi-year data collection
Inverse calibration of transport properties

Advanced Topics

Hysteresis Effects

Liquid transport coefficients differ between wetting and drying:

D_w,wetting > D_w,drying (at same moisture content)

Hysteresis ratio:

HR = D_w,wetting / D_w,drying

Typical values: 1.5-3.0 for most porous materials

Modeling approaches:

Separate wetting/drying functions
History-dependent conductivity
Main curve with scanning curves

Multi-Phase Transport

In saturated or near-saturated conditions, air phase affects liquid transport:

Effective liquid conductivity:

D_w,eff = D_w × (1 - S_a)

Where:

S_a = air saturation (fraction of pore space occupied by air)

Trapped air reduces effective conductivity by 20-50% in field conditions.

Salt Effects

Dissolved salts alter liquid transport through:

Viscosity changes
Surface tension modification
Pore structure degradation

Salt-laden materials:

10-30% increase in D_w at moderate salt concentrations
Crystallization damage creates new transport pathways
Long-term conductivity increases in masonry

Summary

Material conductivity for liquid water transport represents a critical hygrothermal property governing moisture redistribution, drying rates, and moisture accumulation in building assemblies. The strong moisture dependence, spanning orders of magnitude, necessitates careful characterization across the full moisture range. Proper application of liquid transport coefficients in hygrothermal modeling enables accurate prediction of envelope moisture performance and informs material selection and assembly design decisions.

Key engineering parameters:

Saturated conductivity D_ws: 10⁻⁹ to 10⁻⁶ m²/s (material dependent)
Moisture exponent n: 5-18 (controls shape of D_w(w) function)
Temperature coefficient: 2-4%/°C
Measurement uncertainty: ±25-40% typical

Design applications:

Drying time estimation
Capillary break placement
Material compatibility analysis
Freeze-thaw risk assessment
Hygrothermal simulation input data