How Does Liquid Entrainment Impact Solid-Liquid Separation And Mass Balances? Improve Freeze Desalination Recovery

Liquid entrainment directly reduces both product purity and apparent water recovery in freeze desalination. When harvested ice crystals retain a fraction of concentrated brine, the brine’s dissolved salt enters the melter with the ice. If the retained-liquid fraction is (\beta) and the retained brine contains a salt mass fraction (\sigma), the melted product salt fraction is approximately (\varepsilon=\beta\sigma), assuming the ice itself contains negligible salt.

Core takeaway: Ice is not automatically salt-free after separation. A realistic pilot-plant balance must treat the ice stream as pure ice plus entrained brine, and must define boundaries around the slusher, separator, and melter to predict product salinity and recoverable water correctly.

How Entrainment Changes Separation Performance

Retained brine carries salt into the product

During solid-liquid separation, ice crystals can retain liquid between particles, inside voids, or on their surfaces. That liquid contains dissolved salt and travels with the nominal ice stream.

When the ice is melted, the retained brine becomes part of the desalinated-water product. The result is residual salinity even when salt rejection during ice formation is otherwise effective.

Product salinity depends on two variables

Let:

(\beta) = mass fraction of retained liquid in the harvested ice stream
(\sigma) = salt mass fraction in the retained brine
(\varepsilon) = salt mass fraction in the melted product

Under the idealized assumption that the ice crystals contain no salt:

[ \varepsilon=\beta\sigma ]

This relationship shows why a small amount of entrained liquid can have a large effect when the brine is highly concentrated.

For a potable-product limit of (0.05) wt% salt:

[ \varepsilon \leq 0.0005 ]

Therefore, the allowable entrainment is constrained by:

[ \beta \leq \frac{0.0005}{\sigma} ]

The more concentrated the retained brine, the lower the acceptable liquid retention.

Separation efficiency is more than salt rejection

A separator can produce visually clean ice while still performing poorly in terms of product quality. The relevant metrics include:

Ice recovery
Water recovery
Salt rejection
Melted-product salinity
Liquid retention or cake moisture
Salt loss with the rejected brine

Entrainment can make the solid stream appear to have high mass recovery while reducing the amount of water that meets the product specification.

How to Represent Entrainment in the Mass Balance

Define the unit-operation boundaries first

A useful pilot-plant boundary includes three linked operations:

Slusher or crystallizer outlet, where ice and brine are present
Solid-liquid separator, where free brine is removed from the ice
Melter, where the separated ice is converted to product water

The balance should not treat the separator outlet as pure ice unless liquid retention has been measured or deliberately assumed to be zero.

Split the harvested ice into two parts

Let (P) be the total mass flow of the harvested ice stream leaving the separator. Represent it as:

[ P=P_{\text{ice}}+P_{\text{retained brine}} ]

If (\beta) is the retained-brine mass fraction:

[ P_{\text{retained brine}}=\beta P ]

[ P_{\text{ice}}=(1-\beta)P ]

This split is the central correction to an idealized mass balance.

Track water and salt separately

The retained brine contains:

[ \text{salt flow}=\beta P\sigma ]

[ \text{water flow}=\beta P(1-\sigma) ]

The salt-free ice contributes:

[ \text{water flow}=(1-\beta)P ]

After melting, the product stream therefore contains:

[ \text{total salt}=\beta P\sigma ]

[ \text{total water}=P(1-\beta\sigma) ]

and its total mass is (P). Consequently:

[ \varepsilon=\frac{\beta P\sigma}{P}=\beta\sigma ]

This component balance is more informative than a total-mass balance alone because total mass is conserved even when product quality fails.

Balance the rejected brine separately

If (F) is the feed entering the slusher or crystallizer, the overall balance can be written as:

[ F=P+B ]

where (B) is the brine stream leaving the defined system boundary. The component balances are:

[ F_{\text{water}}=P_{\text{water}}+B_{\text{water}} ]

[ F_{\text{salt}}=P_{\text{salt}}+B_{\text{salt}} ]

For a realistic model, the salt in the product is not zero:

[ P_{\text{salt}}=\beta P\sigma ]

That salt must be subtracted from the salt sent to the rejected brine. Setting (P_{\text{salt}}=0) artificially overstates salt rejection and understates brine salinity.

Why Small Retention Changes Can Matter Disproportionately

Entrainment affects both purity and usable yield

Reducing (\beta) lowers the salt entering the melter. It can also increase the fraction of feed water that becomes specification-grade product because less product water must be rejected, diluted, or recycled.

The effect is especially important when the product specification is close to the predicted salinity. A small change in separator performance can move the product from acceptable to off-specification.

Illustrative pilot-plant implication

The supplementary reference describes a 100 kg/min feed example in which reducing retained brine from 1.0 wt% to 0.5 wt% substantially increases potable-water production, with reported values changing from approximately 30 kg/min to 65 kg/min.

Those values should be treated as illustrative system results, not universal performance factors. The actual improvement depends on brine salinity, ice fraction, separator design, washing losses, recycle, and the product-quality cutoff.

Separation data must include retention

Measuring only the mass of recovered ice is insufficient. A pilot plant should also estimate the liquid retained in that ice, using measurements such as:

Moisture or liquid content of the separated ice
Salt concentration of the retained liquid
Salt concentration of the melted product
Flow rates of ice, product water, and rejected brine

The measured product salinity can also be used as a consistency check:

[ \beta \approx \frac{\varepsilon}{\sigma} ]

This estimate is valid only when the assumptions behind (\varepsilon=\beta\sigma) are reasonable.

Operational Factors That Control Entrainment

Separator performance

Improved drainage, longer drainage time, suitable centrifugation, and effective solid-liquid separation can reduce free brine carried with the ice.

However, stronger separation may also increase ice loss or energy consumption. The operating objective is not simply to maximize dry solids; it is to maximize on-specification water recovery.

Washing or displacement steps

An enhanced washing step can displace concentrated brine from the ice surface and reduce salt carryover. The wash liquid itself must be included in the balance because it can dilute the product, increase water demand, or create an additional brine stream.

A wash may improve purity while reducing net recovery if too much ice melts or too much wash water must be discarded.

Ice morphology and handling

Crystal size, agglomeration, surface area, and compaction influence how much liquid remains attached to the solid phase. Handling conditions between crystallization and separation can therefore change the effective value of (\beta).

For pilot studies, retention should be measured at the same operating conditions used to generate performance data.

Understanding the Trade-offs

Lower entrainment versus higher ice loss

Aggressive separation can remove more brine but may also remove or melt more ice. A lower (\beta) is beneficial only if the corresponding loss of solid water does not outweigh the purity improvement.

The correct optimization target is typically potable-water production rate, not separator dryness alone.

Product purity versus process simplicity

Treating all recovered ice as pure simplifies calculations but produces optimistic predictions. Including entrainment requires more measurements, yet it gives a model that can explain off-specification product and support scale-up.

For educational units, the non-ideal model is particularly valuable because it connects equipment performance to component balances.

Apparent recovery versus true recovery

A high ice-stream flow can be misleading if much of the feed water remains in entrained brine that must later be rejected. Recovery should be reported using a clearly defined basis, such as:

Total water entering the ice stream
Water recovered as melted product
Water recovered as product below the salt limit

These are different quantities when product salinity is controlled by a specification.

Treating (\beta) as constant

Using a fixed retention value, such as 1.0 wt%, is acceptable for an initial model but not necessarily for all operating conditions. Retention may change with feed rate, crystal characteristics, separator settings, and washing conditions.

Sensitivity calculations should evaluate how predicted product flow and salinity change over a realistic range of (\beta).

How to Apply This to Your Pilot Plant

Start by measuring or estimating the retained-brine fraction and its salt concentration, then use component—not just total—mass balances across the slusher, separator, and melter.

If your primary focus is product purity: Calculate (\varepsilon=\beta\sigma) and verify that the melted product remains below the specified salt limit.
If your primary focus is potable-water recovery: Optimize separator and washing conditions for specification-grade water production, not simply maximum ice-stream mass.
If your primary focus is accurate mass-balance modeling: Represent the harvested ice as separate ice and entrained-brine fractions, and track water and salt independently.
If your primary focus is scale-up or equipment comparison: Measure liquid retention under each operating condition and compare changes in (\beta), product salinity, and usable recovery.
If your primary focus is pilot-plant teaching: Use the entrainment term to demonstrate how a non-ideal separator changes operating performance even when total mass is conserved.

Accurate entrainment measurement turns a nominal ice-recovery calculation into a credible prediction of desalinated-water quality and yield.

Summary Table:

Key factor	Impact	Recommended approach
Retained-brine fraction (β)	Increases product salinity and reduces usable water recovery	Measure liquid retention under each operating condition
Brine salt fraction (σ)	Higher salinity makes small entrainment more damaging	Analyze the salt concentration of retained brine
Product salinity (ε)	Indicates whether melted ice meets specifications	Use ε = βσ and verify with product testing
Mass balance	Assuming pure ice overstates salt rejection and recovery	Track ice, water, and salt separately
Separator operation	Drainage, centrifugation, and residence time affect entrainment	Optimize for specification-grade water, not dryness alone
Washing and handling	Can reduce salt carryover but add water demand or ice loss	Include wash streams, recycle, and losses in the balance

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