Page 25 - ICJ Jan 2026

TECHNICAL PAPER

like enclosed pores, the specific surface for sphere of radius surface area of evaporating surface of pendular water at a
9
15 nm, 3 / 15 × 10 /m, and corresponding values of k v are shown given degree of saturation is related to (dp – t) . For example,
2

2
in the Table 17 for two temperatures. Value reported of k v by for sphere surface area is s pW = 4p (r – t) and for cylinder s pW

[38]
Pratt for moist sand is 0.014 W/m.K at 23.8 °C . Values may be involves a square of dimension term involving length and radius.
much higher depending upon s pW . Usually fraction of enclosed pore is high, thus; for the purpose
of explanation consider only the spherical pore analogy. Hence,
The evaporation-condensation mechanism thus contributes simply one can write s pW = dp (1 –cθ) . Therefore, k v (θ) = f(−θ),
2
2
significantly to heat transfer within partially saturated porous i.e., decreasing function of θ. As degree of saturation, increases
material as illustrated through above example. As pendular heat transfer due to evaporation-condensation would reduce
water is adhered to the solid surface on one side and exposed and possibility of a quadratic relationship appears to exist
to air on the other, the layers of water and air form a series as indicted by Jakob’s factors. To explain, as the degree of
combination across the heat conduction path within pore, both saturation increases beyond pendular water, a funicular state
in case of enclosed as well as enclosing pores. The evaporation- allowing bridge formation by liquid water across the solid
condensation heat transfer is parallel to above series path as establishing continuous water path isolating air bubbles attains
illustrated in Figure 26. As air offers high resistance to heat flow, in the pores. This is shown in Figure 27. In this situation, three
in this state at lower degree of saturation, equivalent conduction parallel paths co-exist within pores for heat transfer; first, a path
through the pore is mostly due to evaporation-condensation. having water and air layer in series as stated earlier; second, a
Simple algebraic explanations are as follows,
new path having only water to transport heat across the pore;
; k a is small and θ is also small, hence, and the third, parallel path due to evaporation condensation
k ep (θ) ≈ k v (θ). as shown in Figure 28. In this stage, the conductivity across

Consider n 1 numbers of spherical pores of average radius r 1 and
n 2 numbers of cylindrical pores of radius r 2 in one m area of the
2
material constituting total porosity, then degree of saturation
is as given below. The spherical pores represent enclosed pore
and cylindrical pore represent enclosing pores. The degree of
saturation θ 1 for spherical pores and that θ 2 for cylindrical pores
is as follows,

where, t is the thickness of pendular water layer with appropriate
subscript 1 and 2 for spherical and cylindrical pores respectively.
The l 2 is length up to which the pendular water has penetrated
the cylindrical pore. In general, the thickness of pendular layer
t is related to degree of saturation (θ) through the characteristic Figure 27: Water bridge across solid in porous material at higher degree
dimension dp of the pore and a constant (c) as t = cdpθ. The of saturation

Water Air Air
conduction conduction Water conduction
conduction

Conduction through Water Bridge

Evaporation condensation Evaporation condensation

Figure 26: Schematic representation of heat flow path within pore with Figure 28: Schematic representation of heat flow path within pore with
pendular moisture state funicular moisture state

30 THE INDIAN CONCRETE JOURNAL | JANUARY 2026