Why the same temperature fluctuation damages two ice creams differently

Two ice creams leave the same freezer at −18 °C.

Both warm to −12 °C during distribution. Both later return to −18 °C.

Temperature excursion is identical. Yet one product may mobilize more water, expose more crystal surface to melting, and experience greater textural damage.

Why?

Heat shock is not defined by temperature span alone. It depends on where both temperatures fall on each product’s freezing profile, how much water changes phase, how long product remains warm, how quickly its centre follows surrounding air, and how many times cycle repeats.

This chapter begins with one measurable quantity: amount of water that melts during warming and can refreeze during cooling. Tharp and Young call this Texture Stability Index, also described as Heat Shock Index. It then asks what index can and cannot tell us.

Heat shock is a phase-change problem

When ice cream warms from −18 to −12 °C, it does not simply become six degrees warmer.

Part of its ice melts.

That water joins unfrozen serum. Dissolved sugars and salts become less concentrated. Existing ice crystals lose mass. When product cools again, water freezes, but it does not reconstruct original crystal population perfectly.

Smaller crystals have higher curvature and chemical potential. During storage, water can migrate from smaller crystals toward larger ones. Under temperature cycling, partial melting and refreezing intensify redistribution. Controlled ice-cream experiments found cycling conditions produced more recrystallization than higher constant storage temperature, and that longer or more numerous cycles could matter more than amplitude alone (Flores and Goff, 1999).

Heat shock therefore connects thermodynamics to kinetics:

1. freezing profile determines how much water can change phase;
2. thermal history determines what product actually experiences;
3. serum mobility and microstructure influence how rapidly crystals reorganize;
4. repeated exposure changes crystal-size distribution and perceived smoothness.

Our chapters on ice fraction and creaminess establish first and final links. Here we focus on bridge between them.

Start with freezing profile

Ice fraction is not constant. It changes with temperature.

Let $f_{\mathrm{ice}}(T)$ be the fraction of total recipe water frozen at temperature $T$. Let $W$ be the total water fraction of the mix. Goff–Hartel equilibrium curve is used throughout this chapter. Remaining liquid water is solved from formulation composition at every temperature.

At cold bound:

$$f_{\mathrm{cold}}=f_{\mathrm{ice}}(T_{\mathrm{cold}})$$

At warm bound:

$$f_{\mathrm{warm}}=f_{\mathrm{ice}}(T_{\mathrm{warm}})$$

Because warmer ice cream normally contains less ice:

$$f_{\mathrm{cold}} \geq f_{\mathrm{warm}}$$

Difference is fraction of total water estimated to melt during excursion.

Texture Stability Index

On total-water basis:

$$TSI_{\mathrm{water}}= f_{\mathrm{ice}}(T_{\mathrm{cold}}) -f_{\mathrm{ice}}(T_{\mathrm{warm}})$$

On total-product basis:

$$TSI_{\mathrm{product}}= W\left[ f_{\mathrm{ice}}(T_{\mathrm{cold}}) -f_{\mathrm{ice}}(T_{\mathrm{warm}}) \right]$$

These bases answer different questions.

• Water basis: what fraction of recipe water changes phase?
• Product basis: how many grams per 100 g product change phase?

TSI is not temperature variance. It is finite difference between two points on freezing curve. It is also not temperature span itself.

Manual example

Consider a simplified 1 kg ice cream containing 620 g water, 110 g sucrose, 40 g dextrose, and 100 g MSNF. Goff–Hartel calculation gives an initial freezing point of −2.89 °C.

• At −18 °C, 80.77% of water is frozen.
• At −12 °C, 72.87% of water is frozen.

Water-basis TSI is:

$$TSI_{\mathrm{water}}=0.8077-0.7287=0.0790$$

Thus 7.90% of total recipe water changes phase.

Product-basis TSI is:

$$TSI_{\mathrm{product}}=0.62\times0.0790=0.0490$$

Thus 4.90% of product mass melts during warming and becomes available to refreeze during cooling.

This result supports formulation comparison under chosen temperature bounds. It does not establish final crystal size, sensory damage, or shelf life.

Try holding six-degree span constant, then slide both temperatures along curve. Same span does not produce same TSI because freezing profile is nonlinear.

Texture stability index

Goff–Hartel equilibrium curve

Reset

Water

620g

Sucrose

110g

Dextrose

40g

MSNF

100g

Cold temperature

-18.0°C

Warm temperature

-12.0°C

Ice fraction at cold bound80.8% water

Ice fraction at warm bound72.9% water

TSI on water basis7.90%

TSI on product basis4.90%

Temperature span6.0°C

Same excursion, different formulations

Two products exposed to same air temperatures may have different TSI because they differ in:

• total water;
• initial freezing point;
• sugar composition;
• dissolved solids;
• freezing-profile curvature.

A formulation with lower freezing point may retain more liquid water at both bounds. What matters for TSI is not ice fraction at one temperature alone, but difference between two states.

This creates an important trade-off. A softer product may have lower ice fraction at serving temperature yet still mobilize substantial water during excursion if relevant section of curve is steep.

Compare two formulations below. Bounds remain shared. Change water and dextrose; initial freezing point and complete freezing curves are recalculated from each composition.

Compare formulations under one heat shock

Goff–Hartel equilibrium curves

Reset

Shared cold temperature

-18°C

Shared warm temperature

-12°C

Formulation A

WaterDextroseTSI on product basis4.90%Relative ranking#1

Formulation B

WaterDextroseTSI on product basis6.12%Relative ranking#2

Lower TSI means less water estimated to change phase for that excursion. It does not prove greater resistance to recrystallization because water mobility, stabilizer system, initial crystal distribution, and time remain outside index.

What happens to crystals?

Mean crystal size often grows with storage time. Donhowe and Hartel found recrystallization rates rose with storage temperature and depended on sweetener and stabilizer system (1996). Later work showed sweetener-stabilizer interactions were conditional rather than universal (1997).

TSI describes amount of phase change available to drive this process. It does not describe rate at which redistribution occurs.

Air temperature is not product temperature

A freezer may warm quickly during defrost cycle. Ice cream centre warms more slowly.

Package size, geometry, thermal conductivity, convection, contact surfaces, and phase-change enthalpy all create thermal inertia. Treating air-temperature extremes as product-temperature extremes can overstate short excursions and misrepresent long ones.

A simple first-order explanatory model is:

$$\frac{dT_{\mathrm{product}}}{dt} =\frac{T_{\mathrm{air}}(t)-T_{\mathrm{product}}(t)}{\tau}$$

where $\tau$ is the thermal time constant.

Large $\tau$ means a slow product response. Small $\tau$ means the product follows the air more rapidly.

This lumped model ignores spatial gradients, but it demonstrates why time matters. A short warm pulse may barely reach product core. Long hold may bring product close to warm-air temperature and expose nearly full air-defined TSI.

Thermal-history explorer

Explanatory thermal model · Goff–Hartel ice equilibrium

Reset

Cold air temperature

-18°C

Warm air temperature

-8°C

Warm hold

30 min

Cold hold

60 min

Number of cycles

3

Thermal time constant

20 min

Peak product temperature-10.1°C

Air-temperature span10.0°C

Product-experienced span7.9°C

Experienced TSI7.56% product

Use module as thought experiment. Increase warm hold while keeping temperature bounds fixed. Air span remains unchanged, but product-experienced span and TSI rise as product has time to warm.

Toward a state-dependent thermal model

First-order model keeps one constant time scale. More physical extension would let ice fraction modify enthalpy, apparent heat capacity, and thermal conductivity:

$$X_{ice}(T)\rightarrow H(T),\ C_p(T),\ k(T)$$

and then solve heat equation with temperature-dependent properties. Cogné et al. used this connection to model ice-cream freezing and storage thermophysics. Such model could connect ambient history to internal temperature, latent heat, changing ice fraction, and heat-shock exposure. It belongs beyond current TSI because it needs geometry, density, boundary conditions, and validated thermal-property relationships.

Why cycle count and duration matter

TSI is defined for one pair of bounds. It contains no clock and no memory.

Two cold-chain histories can share same per-cycle TSI:

• one excursion lasting ten minutes;
• ten excursions lasting two hours each.

They are not kinetically equivalent.

In cycling experiments, increasing number or duration of cycles had greater impact than increasing amplitude under studied conditions (Flores and Goff, 1999). This does not create universal weighting formula. It shows amplitude alone cannot represent damage.

Useful reporting therefore separates:

1. air temperature bounds;
2. product temperature bounds;
3. TSI per experienced excursion;
4. warm-hold and cold-hold durations;
5. number of cycles;
6. total observation time.

Stabilizers do not necessarily change TSI

TSI follows freezing profile. Stabilizers may have limited effect on equilibrium amount of ice at given temperature while still changing recrystallization kinetics through serum viscosity, molecular mobility, and interactions at crystal interfaces.

Sutton and Wilcox observed smaller crystals after heat shock with locust bean gum or guar than without stabilizer, with formulation-dependent response and evidence of concentration plateau for locust bean gum (1998).

This distinction prevents common error:

Same TSI does not mean same crystal-growth rate.

TSI quantifies thermodynamic exposure. Stabilizer system influences kinetic response.

The same phase change also concentrates and dilutes the unfrozen serum. For the related risk of sugar crystals, see why lactose crystallization depends on available liquid water.

What index does not capture

Model does not include:

• initial crystal-size distribution from freezing and hardening;
• spatial temperature gradients inside package;
• real thermal properties and changing latent heat;
• serum rheology and water diffusivity;
• stabilizer-specific interactions;
• air-cell destabilization, fat network, shrinkage, or meltdown;
• door openings, transport vibration, or pressure change;
• sensory threshold for coarseness.

Therefore TSI does not predict shelf life. It screens formulations and thermal scenarios before experimental validation.

How to use TSI

For formulation work:

1. define realistic cold and warm product temperatures;
2. calculate ice fraction at both bounds using one shared composition-aware model;
3. report TSI on water and product bases;
4. compare formulations under identical bounds;
5. examine product thermal response for realistic hold times and package inertia;
6. retain cycle duration and count as separate variables;
7. validate promising formulations with controlled heat-shock storage;
8. measure crystal-size distribution, texture, and sensory acceptance.

Lower TSI is favourable when other factors remain comparable. But formulation with slightly higher TSI may still recrystallize more slowly if serum mobility is better controlled.

Final thoughts

Temperature fluctuation damages ice cream through amount of water it mobilizes, not through degrees alone.

Texture Stability Index makes this visible by comparing ice fractions at two temperatures. It converts freezing curve into practical quantity: grams of water per 100 g product that can melt and refreeze.

Time then changes question. Product may never reach air-temperature peak. Repeated or prolonged cycles create more opportunity for crystal redistribution. Stabilizers alter kinetics without necessarily changing TSI.

Best interpretation is layered:

• freezing profile tells how much water can move;
• thermal history tells what product experiences;
• formulation structure tells how quickly crystals respond;
• experiments tell whether consumer will notice.

References

1. Donhowe, D. P., and Hartel, R. W. “Effect of Sweetener, Stabilizer, and Storage Temperature on Ice Recrystallization in Ice Cream.” Journal of Dairy Science 79, no. 5 (1996): 735–744. https://doi.org/10.3168/jds.S0022-0302(96)76420-2
2. Flores, A. A., and Goff, H. D. “Recrystallization in Ice Cream After Constant and Cycling Temperature Storage Conditions as Affected by Stabilizers.” Journal of Dairy Science 82, no. 7 (1999): 1408–1415. https://doi.org/10.3168/jds.S0022-0302(99)75367-1
3. Donhowe, D. P., and Hartel, R. W. “Ice Recrystallization in Ice Cream: Interactions Between Sweeteners and Stabilizers.” Journal of Dairy Science 80, no. 3 (1997): 447–456. https://doi.org/10.3168/jds.S0022-0302(97)75956-3
4. Sutton, R. L., and Wilcox, J. “Recrystallization in Ice Cream as Affected by Stabilizers.” Journal of Food Science 63, no. 1 (1998): 104–107. https://doi.org/10.1111/j.1365-2621.1998.tb15686.x
5. Sipple, B., and Young, S. “A guide to differentiating and comparing mixes for frozen desserts.” Dairy Foods (2023). https://www.dairyfoods.com/articles/96311-a-guide-to-differentiating-and-comparing-mixes-for-frozen-desserts
6. Cogné, C., Andrieu, J., Laurent, P., Besson, A., and Nocquet, J. “Experimental data and modelling of thermal properties of ice creams.” Journal of Food Engineering 58, no. 4 (2003): 331–341. https://doi.org/10.1016/S0260-8774(02)00396-5