---
title: "Solute activity from crystalline solubility to absorption: the amorphous ceiling, the drug-rich reservoir and the design target"
review: 2016-taylor-physical-chemistry-supersaturated-solutions
review_citation: "Taylor L.S., Zhang G.G.Z. (2016) Physical chemistry of supersaturated solutions and implications for oral absorption. Advanced Drug Delivery Reviews."
---
# Solute activity from crystalline solubility to absorption: the amorphous ceiling, the drug-rich reservoir and the design target

**What this page is.** Taylor and Zhang (2016) build one line of reasoning from the crystalline solubility through the amorphous solubility, liquid–liquid phase separation (LLPS), solubilization and membrane flux to the dissolution of amorphous solid dispersions (ASDs) and a set of absorption simulations, and end with "spring and plateau" as the target for enabling formulations. This page follows that line step by step; each step gives the review's argument and then what the library's papers, from 2010 to 2026, have measured since, with links to the findings. Where the review states a simulation or an interpretation, and where the library holds a measurement, is marked in each step.

## The chain at a glance

1. **Crystalline solubility as the reference state**: the chemical potential of crystal-saturated drug, with $S = C/C^{*}$ as its practical ratio → how far above it can a non-crystalline drug go?
2. **Amorphous solubility**: crystalline solubility, crystal–amorphous free energy and water uptake → a metastable equilibrium with a second, drug-rich phase.
3. **The amorphous solubility as a liquid–liquid equilibrium**: equal drug activity in a water-rich and a drug-rich phase → the drug-rich phase can form from solution and competes with the crystal.
4. **LLPS against crystallization**: crystal nucleation barriers against fast demixing of slow crystallizers → a two-phase solution persists at constant activity, whose effect on transport must be measured.
5. **Membrane flux and the ceiling of supersaturation**: $J \propto S\,D/(h\gamma_m)$ with a plateau at the amorphous solubility → total concentration fails once solubilizers are present.
6. **Solubilized against supersaturated drug**: free and micelle-bound drug, $K_m$ and the failure of $C/C^{*}$ → only free drug in the aqueous compartment drives absorption.
7. **The central compartment and the drug-rich reservoir**: nanodroplets resupply free drug at maximum activity → the formulation must deliver the dose into that state.
8. **ASD dissolution towards the ceiling**: loading, polymer, water in the solid and crystallization in solution → whether the ceiling holds also depends on removal by the membrane.
9. **Absorption with a sink**: removal against supply into the central compartment → scenarios can be compared by fraction absorbed in a finite residence time.
10. **The design target: spring and plateau**: fraction absorbed at 8 h and 4 h for stable LLPS, crystallization, slow dissolution and a crystalline suspension → reach the amorphous solubility quickly and hold it until the dose is absorbed.

## Step 1. Crystalline solubility as the reference state

**Question.** Against which state is supersaturation measured, and which terms of the dissolution rate can a formulation change?

**The review's reasoning (2016).** The review starts from the Noyes–Whitney equation with a Nernst–Brunner diffusion layer [review p. 2]:

$$\frac{dM}{dt} = \frac{DS}{h}\left(C_s - C\right) \approx \frac{DSC_s}{h} \tag{1}$$

The diffusion coefficient $D$ and the layer thickness $h$ are set by the molecule and the gastrointestinal tract, whereas surface area $S$ and solubility $C_s$ can be changed by formulation [review p. 2]. The crystalline solubility is a solid–liquid equilibrium with the supercooled liquid as standard state [review p. 3]:

$$\ln\left(x_D^{W(c)}\gamma_D^{W(c)}\right) = \frac{\mu_D^{(c)} - \mu_D^{0(a)}}{RT} \tag{2}$$

A solution is supersaturated when the chemical potential of the solute exceeds that of the solute in equilibrium with the most stable crystal [review p. 3]:

$$\ln S = \frac{\mu_D^{W(S)} - \mu_D^{(c)}}{RT} = \ln\frac{\gamma_D^{W(S)}x_D^{W(S)}}{\gamma_D^{W(c)}x_D^{W(c)}} \tag{3}$$

$$S_C = \frac{C}{C^{*}} \tag{4}$$

The concentration ratio of Eq. 4 approximates Eq. 3 only when $\gamma_D^{W(S)}/\gamma_D^{W(c)}$ is close to 1, which the authors expect at very low supersaturation and/or in very dilute solutions in simple media [review p. 3].

**What the library shows.** The reference $C^{*}$ has to be measured in the same medium, including dissolved polymer. At 1 mg/mL, HPMC and two HPMCAS grades raised the crystalline solubility of papaverine from 12.2 to 19.0–21.9 µg/mL [hsieh2014 R4] (2014), and 0.1% SDS raised that of 11 drugs 1.2- to about 266-fold [chen2015 R1] ([Crystallization from solution F19](../../dissolution/d-crystallization-from-solution/findings.md#f19)). A higher total concentration was not a higher activity: 5 µg/mL HPMCAS doubled the celecoxib solubility (1.2 → 2.4 µg/mL) without changing its membrane mass flow (0.44 µg/min) [li2016a R15] ([Crystallization from solution F19](../../dissolution/d-crystallization-from-solution/findings.md#f19)). At the mg/mL levels that a dispersion releases, dissolved HPMCAS raised crystalline resveratrol from 42 to about 1230 µg/mL at 20 mg/mL, which the authors attribute mainly to a soluble drug–polymer complex [wegiel2015 R2, R3, C41] (2015), whereas with 22 µg/mL to 1 mg/mL polymer felodipine, celecoxib and lopinavir kept their crystalline solubility within about 0.84–1.43 times [konno2008a R1; xie2015 R11; xie2016a R1; li2018 R1] ([Supersaturation from ASD dissolution F17](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f17)).

**Corrections and qualifications.**
- The review discusses changes of $C^{*}$ only for surfactants (Section 3.8). The library adds that dissolved polymers can raise $C^{*}$ by up to about threefold at 1 mg/mL, and that some papers called a 40–53% rise for celecoxib "negligible" although it would lower $S$ at 22 µg/mL from 14.7 to about 10.5 and 9.6 [ilevbare2013c R1, X7] ([Crystallization from solution F19](../../dissolution/d-crystallization-from-solution/findings.md#f19)). $S$ is therefore referred to the crystalline solubility in the polymer-containing medium.

**Next.** This step fixes the reference against which every activity is read; it does not say how far above the crystal a non-crystalline drug can go, which is the amorphous solubility.

**Pages.** [crystalline solubility](../../concepts/crystalline-solubility.md), [supersaturation](../../concepts/supersaturation.md), [chemical potential](../../concepts/chemical-potential.md), [thermodynamic activity](../../concepts/thermodynamic-activity.md), [activity coefficient](../../concepts/activity-coefficient.md), [Noyes–Whitney equation](../../formulas/noyes-whitney-equation.md), [solid–liquid equilibrium solubility equation](../../formulas/solid-liquid-equilibrium-solubility-equation.md), [activity-based supersaturation ratio](../../formulas/activity-based-supersaturation-ratio.md), [supersaturation ratio](../../formulas/supersaturation-ratio.md).

## Step 2. Amorphous solubility

**Question.** What concentration is reached when the amorphous form, not the crystal, is in contact with the solution, and what sets its ratio to the crystalline solubility?

**The review's reasoning (2016).** Strictly no equilibrium with amorphous material exists, but when crystallization is slow a metastable equilibrium can be treated as a liquid–liquid equilibrium, with the amorphous drug as a supercooled liquid, also for drugs that are glasses at the temperature of interest [review p. 3]. Assuming $\gamma_D^{W(c)} \cong \gamma_D^{W(a)}$ at these low concentrations, Eq. 2 gives the amorphous from the crystalline solubility [review p. 3]:

$$\ln x_D^{W(a)} = -\ln\gamma_D^{W(a)} \tag{5}$$

$$\ln x_D^{W(a)} = \ln x_D^{W(c)} - \frac{\mu_D^{(c)} - \mu_D^{0(a)}}{RT} \tag{6}$$

The chemical potential difference needs $\Delta H_f$ and $T_m$, and with constant $\Delta C_p$ is printed as [review p. 3]:

$$\mu_D^{(c)} - \mu_D^{0(a)} = -\frac{\Delta H_f}{R}\left(\frac{T_m - T}{T_m T}\right) + \frac{\Delta C_p}{R}\left(\frac{T_m - T}{T}\right) - \frac{\Delta C_p}{R}\left(\ln\frac{T_m}{T}\right) \tag{7}$$

Water absorbed by the amorphous drug lowers its chemical potential, so the activity of drug in the water-saturated amorphous phase enters (Eqs. 8–9) and the amorphous solubility becomes [review pp. 3–4]:

$$\ln x_D^{W(a)} = \ln x_D^{W(c)} - \frac{\mu_D^{(c)} - \mu_D^{0(a)}}{RT} + \ln\left(x_D^{L(a)}\gamma_D^{L(a)}\right) \tag{10}$$

$$C_{\text{amorphous}} = C_{\text{eq}} \cdot e^{-I(a_2)} \cdot e^{\frac{\Delta G_{c\to a}}{RT}} \tag{11}$$

where the water term comes from the sorption isotherm by the Gibbs–Duhem equation [review p. 4]. Amorphous phases generated in situ above the amorphous solubility give values on the line of slope 1 against prediction for 23 compounds [review p. 6, Fig. 4]. The amorphous-to-crystalline ratio grows with $T_m$ and $\Delta H_f$ and falls with water uptake: ibuprofen only 4 ($T_m$ ~77 °C), atazanavir ~65 ($T_m$ ~208 °C) [review p. 8]. Higher ionic strength lowers the amorphous solubility (ritonavir, Fig. 8), and for weak bases the un-ionized drug stays at the amorphous solubility, so the ratio "remains constant as a function of pH" [review pp. 8–9].

**What the library shows.** Across 17 compounds, 17 of 24 measured onsets lie between 0.91 and 1.15 times the value of Eq. 11; ritonavir in water gave 37.2 µg/mL against a predicted 39.2 [ilevbare2013a R8, R13] (2013), and atazanavir 70 against 68 µg/mL [indulkar2017a R5, R6] ([Amorphous solubility and LLPS F5](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f5)). The water term is not small: exp[−I(a2)] was 0.27 for ritonavir and 0.22 for atazanavir [ilevbare2013a M1; indulkar2015 M2]. For telaprevir, Eq. 11 gave 245 ± 5 µg/mL with the Hoffman equation and 97 ± 8 with the crystal-to-supercooled-liquid heat capacity, against 90–92 µg/mL measured [mosqueragiraldo2015 R13] (2015) ([Amorphous solubility and LLPS F7](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f7)). The ratio spans from 2.2 for efavirenz [ilevbare2013a R8] to about 603 for pazopanib at pH 6.5 [sugihara2018 R4] (2018) ([Amorphous solubility and LLPS F6](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f6)). The ritonavir onset fell from 37.2 µg/mL in water to 18.8, 14.3 and 4.7 µg/mL in 100, 200 and 500 mM phosphate [ilevbare2013a R13] ([Amorphous solubility and LLPS F9](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f9)), and for clotrimazole, atazanavir and nicardipine the total LLPS concentration rose 30- to 65-fold with ionization while the un-ionized part stayed near 5.6–8.4, 57–70 and 4.5–6.8 µg/mL [indulkar2015 R9] ([Amorphous solubility and LLPS F10](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f10)).

**Corrections and qualifications.**
- Eq. 7 is printed without the factor $RT$ on its left side (check R5); in Eq. 11 the activity of the water-saturated drug is $e^{-I(a_2)}$, not $-I(a_2)$ as the text calls it (check R6).
- Fig. 4 hides outliers: clotrimazole 1.30 and 1.57, tolnaftate 1.72 and ibuprofen 1.57 times the prediction, and telaprevir 0.38 with the Hoffman free energy; four of the eight 2013 predictions cannot be recomputed from the printed inputs [ilevbare2013a X1] ([Amorphous solubility and LLPS F5](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f5)).
- The ratio is constant with pH only while crystallization is slower than the measurement: clotrimazole gave about 8 at pH 4–4.5 against 12–17 from pH 5 [indulkar2015 X5], and pazopanib about 103 at pH 5 against 500–600 near neutral [sugihara2018 R1, R3, R4] ([Amorphous solubility and LLPS F10](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f10)).
- For high-melting drugs the Hoffman route overshoots (telaprevir 2.7-fold), and for pazopanib, which degrades on melting, no route could be run [sugihara2018 C17] ([Amorphous solubility and LLPS F7](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f7)).

**Next.** This step gives the ceiling as a number; to use it the review must show what phase coexists with the solution at that number and why reaching it from a solution gives the same state.

**Pages.** [amorphous solubility](../../concepts/amorphous-solubility.md), [amorphous solubility advantage](../../concepts/amorphous-solubility-advantage.md), [supercooled liquid](../../concepts/supercooled-liquid.md), [water sorption correction of amorphous solubility](../../concepts/water-sorption-correction-of-amorphous-solubility.md), [Hoffman equation](../../concepts/hoffman-equation.md), [Henderson–Hasselbalch equation](../../concepts/henderson-hasselbalch-equation.md), [amorphous solubility advantage with water-sorption correction](../../formulas/amorphous-solubility-advantage-with-water-sorption-correction.md), [amorphous–crystalline free energy difference from heat capacity](../../formulas/amorphous-crystalline-free-energy-difference-from-heat-capacity.md), [amorphous-to-crystalline solubility ratio](../../formulas/amorphous-to-crystalline-solubility-ratio.md).

## Step 3. The amorphous solubility as a liquid–liquid equilibrium

**Question.** What phase coexists with the solution at the amorphous solubility, and what lowers that solubility once other components are present?

**The review's reasoning (2016).** Drug and water have a miscibility gap: between the binodal compositions $x_{DW}$ (drug-rich) and $x_{WD}$ (water-rich) the mixture splits into two liquids, by nucleation and growth between binodal and spinodal and spontaneously inside the spinodal ($\partial^2G/\partial x^2 = 0$) [review p. 4, Fig. 1]. If the drug-rich phase is below its water-plasticized $T_g$ the process is glass–liquid phase separation (GLPS) [review p. 4]. At equilibrium the drug has the same activity in both phases [review p. 5]:

$$a_D^{W(a)} = a_D^{L(a)} \tag{12}$$

$$\ln x_D^{W(a)}\gamma_D^{W(a)} = \ln x_D^{L(a)}\gamma_D^{L(a)} \tag{13}$$

so the amorphous solubility $x_{WD}$ is set by the activity of drug in the water-saturated drug-rich phase, the water term of Eq. 10 [review p. 5]. Equilibrating amorphous drug with water and adding drug to water until LLPS end in the same two phases; the second route is the one relevant to drug delivery [review p. 5]. A second drug that mixes into the drug-rich phase lowers the drug's activity there and hence the amorphous solubility; for ritonavir and lopinavir ideal mixing predicts that each is halved at a mole fraction of 0.5, while the diclofenac anion had no effect [review p. 9, Fig. 9]. PVP, HPMC and HPMCAS had no detectable effect on the amorphous solubility of danazol, and by NMR PVPVA and HPMCAS made up less than 7 wt.% of a drug-rich phase, "confirming" that the polymers do not mix substantially with it [review p. 9].

**What the library shows.** The isolated ritonavir drug-rich phase held 94.85–95.97% drug and 4.03–5.15% water, matching the 5.21% that amorphous ritonavir sorbs at 100% RH by extrapolation [ilevbare2013a R6, E14] (2013) ([Amorphous solubility and LLPS F1](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f1)). Whether it is a liquid or a glass follows its wet $T_g$: 0.4 °C for ritonavir, about 14 °C for clotrimazole and about 51 and 52 °C for atazanavir and telaprevir [ilevbare2013a R5; indulkar2015 R22; mosqueragiraldo2015 R2]; the glassy telaprevir phase still redissolved within about 2 min on dilution [mosqueragiraldo2015 R8] ([Amorphous solubility and LLPS F2](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f2)). A second drug lowered the onset as the review states: with 10 µM lopinavir, paclitaxel or felodipine, ritonavir separated at about 14, 10 and 12 µg/mL instead of about 26 µg/mL, while with diclofenac it stayed at about 25 µg/mL [trasi2015a R7, R11] (2015) ([Amorphous solubility and LLPS F11](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f11)). For danazol, 1–1000 µg/mL PVP, HPMC or HPMC-AS left the onset at 7–9.1 µg/mL and the maximum flux unchanged [jackson2016 R8, R11] ([Crystallization from solution F22](../../dissolution/d-crystallization-from-solution/findings.md#f22)). Later papers found polymers that do lower the ceiling: 300 µg/mL HPMC and PVP-VA lowered the amorphous solubility of ibuprofen from 177.1 to 96.9 and 90.7 µg/mL [ueda2020b R1, R13] (2020) ([Amorphous solubility and LLPS F19](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f19)); HPMCAS-HF lowered atazanavir from 81.5 to 35.5 µg/mL and clozapine from 233.0 to 95.0 µg/mL, while AS-LF moved them only to 75.8 and 219.0 µg/mL [ueda2020a R1] ([Bioperformance F19](../../bioperformance/bioperformance/findings.md#f19)); and HPMCAS and Eudragit E PO lowered dissolved enzalutamide from 42 to about 20.5–36.5 and 23.5–30.5 µg/mL [wilson2021 R8] (2021) ([Crystallization from solution F19](../../dissolution/d-crystallization-from-solution/findings.md#f19)).

**Corrections and qualifications.**
- The statement that dissolved ASD polymers do not mix with the drug-rich phase (check R24, verdict "differs") holds for danazol but not as a rule: the results above lower the ceiling by a quarter to more than half, and the polymer weight fraction in the posaconazole drug-rich phase rose from about 0.05 to 0.31 from HPMCAS-L to -H [shah2025 R17] (2025) ([Bioperformance F19](../../bioperformance/bioperformance/findings.md#f19)); in telaprevir ASD pellets it was about 0.9 for cellulose acetate suberate [mosqueragiraldo2018b R14] ([Amorphous solubility and LLPS F19](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f19)), so "less than 7 wt.%" holds for the systems of ref. [49].
- The ideal-mixing line is approximate: ritonavir points lie mostly 2–4 µg/mL above it [trasi2015a R16, X9], and the bile salts STCDC and SGCDC cut the maximum telaprevir flux to about 0.8–0.9 of its buffer value [lu2017b R13] (2017) ([Amorphous solubility and LLPS F11](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f11)).

**Next.** This step establishes that a drug-rich liquid or glass can coexist with a solution at a fixed activity; whether that state appears in practice depends on whether the crystal forms first.

**Pages.** [liquid–liquid phase separation](../../concepts/liquid-liquid-phase-separation.md), [binodal](../../concepts/binodal.md), [spinodal decomposition](../../concepts/spinodal-decomposition.md), [free energy of mixing](../../concepts/free-energy-of-mixing.md), [drug-rich phase](../../concepts/drug-rich-phase.md), [glass–liquid phase separation](../../concepts/glass-liquid-phase-separation.md), [ideal mixing](../../concepts/ideal-mixing.md), [polymer partitioning into the drug-rich phase](../../concepts/polymer-partitioning-into-the-drug-rich-phase.md), [ideal-mixing reduction of amorphous solubility](../../formulas/ideal-mixing-reduction-of-amorphous-solubility.md).

## Step 4. Liquid–liquid phase separation against crystallization

**Question.** When a solution is pushed above the amorphous solubility, does it form the drug-rich phase or crystals, and how long does the two-phase state last?

**The review's reasoning (2016).** Between the crystalline and the amorphous solubility curves only crystals can form; above the amorphous curve either LLPS or crystallization can take place [review p. 5, Fig. 2]. Because crystal nucleation and growth have kinetic barriers, "slow crystallizers" given a rapidly generated high supersaturation split into two liquids, and the amorphous phase is a precursor expected to crystallize later, as in the "oiling out" of process chemistry [review p. 5, Fig. 3]. The drug-rich species measure 100–500 nm by DLS when formed and can grow unless additives such as polymers inhibit growth [review p. 6]. In a study of about 50 compounds, about a third crystallized within 2.5 min of solvent shift and a third had not crystallized after 1 h [review p. 6]. Light scattering at a non-absorbing wavelength, polarity probes and ultracentrifugation locate the onset, the droplets redissolve rapidly below the amorphous solubility, and agreement between methods suggests little overshoot before separation [review pp. 6–8]. Droplets coarsen and agglomerate, and their interfaces may favour heterogeneous nucleation [review pp. 13–14].

**What the library shows.** For ritonavir the drug-rich phase lies far inside the metastable zone (37.2 against 2.4 µg/mL crystalline solubility in water at 37 °C) [ilevbare2013a R8, R11] (2013) ([Amorphous solubility and LLPS F3](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f3)). Lifetimes without polymer run from minutes to hours: telaprevir gave birefringent particles after about 15 min, while 5 µg/mL HPMCAS-MF kept the turbid solution for hours [mosqueragiraldo2015 R1], and pazopanib held its supersaturation for 5 ± 2 min without and about 39 min with 50 µg/mL HPMC [sugihara2018 R22] (2018) ([Amorphous solubility and LLPS F3](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f3)). Unseeded induction times at the calculated amorphous solubility were about 2.4 min for celecoxib and 120 min for ritonavir, although their seeds grew at almost the same rate per area (6.23 and 6.14 mg min⁻¹ m⁻²), so the difference lies in nucleation [ilevbare2013c R8; ilevbare2013b R7] ([Crystallization from solution F3](../../dissolution/d-crystallization-from-solution/findings.md#f3)). Fresh droplets measured 116–387 nm for three weak bases [indulkar2015 R14], and ritonavir droplets grew from about 345 to about 842 nm in 64 min [ilevbare2013a R3] ([Amorphous solubility and LLPS F1](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f1)). With 300 µg/mL HPMC or PVP-VA fresh ibuprofen droplets measured 268–345 nm instead of 3182–5313 nm, but over 3 h the droplet-phase drug fell from about 264 to 67 µg/mL with PVP-VA against about 260 to 183 µg/mL with HPMC [ueda2020b R5, R15] (2020) ([Amorphous solubility and LLPS F22](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f22)). For ritonavir the induction time was about 284 min at 17 µg/mL, below the LLPS concentration of 18.2 µg/mL, against 119.3 min at 20 µg/mL, and SDS and Tween 80 shortened it only when droplets were present [ilevbare2013d R16, R12] ([Supersaturation from ASD dissolution F13](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f13)).

**Corrections and qualifications.**
- The 100–500 nm range is drug- and additive-specific: pazopanib droplets measured 496 nm (145 nm with HPMC) [sugihara2018 R15] and ibuprofen droplets several µm without polymer [ueda2020b R5] ([Amorphous solubility and LLPS F1](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f1), [F22](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f22)).
- A drug-rich phase that disappears is not necessarily a crystal precursor: in buffer the ibuprofen droplet phase was lost within 1–2 h by creaming, and crystals appeared only after 24 h [ueda2020b R8, R15] ([Amorphous solubility and LLPS F3](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f3)).
- The ritonavir evidence for nucleation in the droplets compares bulk supersaturations of about 13 and 15, and mixed ritonavir–lopinavir drug-rich phases did not crystallize within 5 h [trasi2015b R15] ([Supersaturation from ASD dissolution F13](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f13)); the 50-compound study is not in the library (check R12).

**Next.** This step shows that a two-phase solution can persist at a constant activity for minutes to hours; the review then needs a read-out of that activity, which is membrane flux.

**Pages.** [metastable zone](../../concepts/metastable-zone.md), [crystallization tendency](../../concepts/crystallization-tendency.md), [nucleation induction time](../../concepts/nucleation-induction-time.md), [drug-rich nanodroplets](../../concepts/drug-rich-nanodroplets.md), [drug-rich phase coarsening](../../concepts/drug-rich-phase-coarsening.md), [heterogeneous nucleation](../../concepts/heterogeneous-nucleation.md), [light scattering by particles](../../concepts/light-scattering-by-particles.md), [pyrene I1/I3 polarity ratio](../../concepts/pyrene-i1-i3-polarity-ratio.md), [temperature–composition phase diagram](../../concepts/temperature-composition-phase-diagram.md).

## Step 5. Membrane flux and the ceiling of supersaturation

**Question.** Does membrane transport follow concentration or activity, and is there a highest flux that supersaturation can give?

**The review's reasoning (2016).** Dissolution-limited bioavailability is addressed by faster dissolution, solubility-limited bioavailability only by supersaturation [review p. 9]. Crystal-saturated solutions of very different concentration gave nearly constant flux, and solubility and membrane–solution partition coefficient are reciprocal, so a solubilizer does not raise flux; following Higuchi, flux is written in terms of activity [review p. 9]:

$$J \propto S * \frac{D}{h\gamma_m} \tag{14}$$

with $D$, $h$ and $\gamma_m$ constant for a given system. For danazol (crystalline solubility about 1 µg/mL) flux rose linearly to about 8 µg/mL and stayed constant above, about an order of magnitude above the crystalline flux; the plateau is the amorphous solubility, above which added drug enlarges the drug-rich phase at constant activity, and solutions made by dissolving ASDs with 90 wt.% PVP, HPMC or HPMCAS gave a flux similar to antisolvent solutions [review pp. 9–10, Fig. 10]. The authors then state that the amorphous solubility caps the supersaturation of any formulation: temperature change, antisolvent addition, pH swing, ASD and salt dissolution all gave a drug-rich phase, lipolysis may, and prodrugs and co-crystals are "unexplored potential routes"; the cap is the amorphous solubility, "or strictly speaking, the spinodal decomposition point" [review p. 10, Fig. 11]. The ratio "probably should be considered during lead optimization and candidate selection" [review p. 10].

**What the library shows.** The flux plateau is repeated in every drug tested: telaprevir flux rose linearly to about 0.97 µg/min at 90 µg/mL and reached only about 1.07 µg/min at 130 µg/mL [mosqueragiraldo2015 R12] (2015); ritonavir, lopinavir and paclitaxel broke at 27.3, 16.1 and 30.1 µg/mL, matching three other onset estimates [trasi2015a R1, R2]; and atazanavir rose linearly to 70 µg/mL and stayed at about 0.114–0.121 µg/min·cm² up to 200 µg/mL [indulkar2017a R10] (2017) ([Amorphous solubility and LLPS F8](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f8)). The cap holds for dispersions: every danazol dispersion that formed a drug-rich phase gave 7.1–9.1 µg/mL free drug by flux, like antisolvent solutions (7.2–8.2 µg/mL), whereas the 50:50 HPMCAS dispersion, which formed none, gave 5.4 ± 0.8 µg/mL [jackson2015 R9]; felodipine flux relative to the crystal was 10.5, 9.5 and 8.5 for 90:10 and 50:50 HPMC dispersions and pure amorphous drug against a predicted factor of about 9 [alonzo2011 R14]; and six marketed 5-mg tacrolimus capsules all levelled off at about 46–50 µg/mL, the amorphous solubility measured four ways [trasi2016 R10, R4] (2016) ([Supersaturation from ASD dissolution F7](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f7)).

**Corrections and qualifications.**
- Not every route reaches the cap. The CRH1 co-crystal at pH 4.6 peaked at about 2.9 µg/mL without and 6.2 µg/mL with 20 µg/mL HPMC and formed no drug-rich phase, while the salts and the ASD did, against an estimated amorphous solubility of 11.2–12.5 µg/mL; the authors attribute this to crystallization outpacing dissolution [almeidaesousa2016 R8, R9, R11, C31] (2016) ([Amorphous solubility and LLPS F14](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f14)) (check R30). Ritonavir from mesoporous silica plateaued at about 24 µg/mL, about 85% of its amorphous solubility of 27.9 µg/mL, without a drug-rich phase [dening2018 R22] (2018) ([Mesoporous silica F15](../../mesoporous-silica/mesoporous-silica/findings.md#f15)). The cap is a ceiling, not a value every route attains.
- The library uses the binodal as the ceiling and does not test the spinodal qualification; the one overshoot is kinetic, danazol read 15 s after each addition giving 10–14 µg/mL against about 8 µg/mL after 1–5 min [jackson2016 R13, R12] ([Crystallization from solution F22](../../dissolution/d-crystallization-from-solution/findings.md#f22)) (check R29).
- For felodipine the dispersion authors note that the equality of dispersion and amorphous activity "may be purely coincidental" [alonzo2011 C48] ([Supersaturation from ASD dissolution F7](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f7)).

**Next.** Flux reads activity and the amorphous solubility caps it in simple buffers; the intestine and most formulations contain solubilizers, which raise the total concentration without raising the activity, so the review has to separate the two.

**Pages.** [membrane flux](../../concepts/membrane-flux.md), [membrane transport](../../concepts/membrane-transport.md), [thermodynamic activity](../../concepts/thermodynamic-activity.md), [solubility–permeability interplay](../../concepts/solubility-permeability-interplay.md), [dissolution-rate-limited absorption](../../concepts/dissolution-rate-limited-absorption.md), [supersaturating drug delivery systems](../../concepts/supersaturating-drug-delivery-systems.md), [membrane flux in terms of solute activity](../../formulas/membrane-flux-in-terms-of-solute-activity.md), [supersaturation from membrane flux ratio](../../formulas/supersaturation-from-membrane-flux-ratio.md).

## Step 6. Solubilized against supersaturated drug

**Question.** When micelles or other solubilizers are present, which part of the dissolved drug sets the driving force, and does the concentration ratio still measure it?

**The review's reasoning (2016).** Micellar solubilization is described by a micelle–water partition coefficient [review pp. 10–11]:

$$K_m = \frac{C_m}{C_w} \tag{15}$$

$$S_{tot} = S_w + K_m S_w \tag{16}$$

so the total solubility rises while the free drug in water, which alone partitions into the membrane, does not. For felodipine with Vit E TPGS the crystalline solubility rose from about 1 to 40 µg/mL and the amorphous solubility from about 10 to 177 µg/mL; the ratio fell from about 9 to about 4.5, Eq. 4 under-predicted the supersaturation in TPGS and in FaSSIF, and the maximum flux was the same as in buffer [review pp. 10–11]. A micelle–water partition coefficient that decreases as drug concentration rises is called "the most plausible explanation" [review p. 11]. This is the review's interpretation; the coefficient was not measured in the work it cites.

**What the library shows.** The felodipine data are those of Raina 2015: onsets 10.4, 177.3 and 214.6 µg/mL in buffer, 0.04% Vit E TPGS and FaSSIF, ratios 9.2, 4.5 and 5.0, and the buffer flux band of about 0.11–0.15 µg/min reached only at 175–200 and from 250 µg/mL [raina2015c R11, R9] (2015) ([Bioperformance F4](../../bioperformance/bioperformance/findings.md#f4)); above their critical micelle concentration six additives cut the flux of 50 µg/mL felodipine from about 0.14 to 0.010–0.12 µg/min [raina2015c R7] ([Bioperformance F3](../../bioperformance/bioperformance/findings.md#f3)). The partition coefficient was measured in 2017: for atazanavir in 3.6 mg/mL SDS, Km/w fell from about 327 to about 99 as total drug rose to 100 µg/mL and then stayed at about 90–114 up to 1450 µg/mL, and the amorphous solubility rose only half as much as predicted from the crystal (κ 0.183 against 0.351) [indulkar2017a R14, R9] ([Amorphous solubility and LLPS F18](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f18)). At the amorphous solubility the concentration ratio was 37.5, 35.9 and 33.0 at 1, 2 and 3.6 mg/mL SDS, while the flux-derived activity ratio was 70.0, 66.1 and 65.0, as in buffer (66.0) [indulkar2017a R13]; in five simulated media and pooled human intestinal fluid the flux-based maximum stayed at about 50–56 for atazanavir and 29–37 for posaconazole, while the concentration-based value fell to about 14 and 5 in human fluid [elkhabaz2019b R8, R9] (2019) ([Amorphous solubility and LLPS F16](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f16)).

**Corrections and qualifications.**
- The ratio does not always fall. Ritonavir with 500 µg/mL Tween 80 raised the crystalline solubility from 1.3 to 3.5 µg/mL and the LLPS concentration from 18.8 to 46.1 µg/mL, leaving ratios of about 14.5 and 13.2, and telaprevir with dihydroxy bile salts kept a ratio of about 28–32 [ilevbare2013a R16, X5; lu2017b R1, R2] ([Amorphous solubility and LLPS F12](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f12)). The activity-based ceiling is conserved in all of these; the concentration ratio is conserved only for some drug–solubilizer pairs.
- The fall of Km/w ends at about three times the crystalline solubility and is read as a change from adsorption at the micelle surface to dissolution in the core, a mechanism the authors call "speculation" [indulkar2017a C24, X6] ([Amorphous solubility and LLPS F18](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f18)).

**Next.** With free and solubilized drug separated, the review can place the formulation in the intestine as a set of compartments around one aqueous phase from which drug is absorbed.

**Pages.** [micellar solubilization](../../concepts/micellar-solubilization.md), [free drug concentration](../../concepts/free-drug-concentration.md), [bile-salt micelles](../../concepts/bile-salt-micelles.md), [supersaturation ratio](../../concepts/supersaturation-ratio.md), [critical micelle concentration](../../concepts/critical-micelle-concentration.md), [activity from concentration](../../formulas/activity-from-concentration.md), [activity-based supersaturation ratio](../../formulas/activity-based-supersaturation-ratio.md).

## Step 7. The central compartment and the drug-rich reservoir

**Question.** How do drug-rich droplets, micelles and undissolved solid in the gut lumen feed the free drug that is absorbed?

**The review's reasoning (2016).** The gastrointestinal tract is simplified to a central aqueous compartment in contact with the membrane, from which only the un-ionized drug is thought to be absorbed passively, surrounded by compartments (micelles, lipid vesicles, crystals, drug-rich droplets) that exchange drug with it as drug is absorbed [review pp. 11–12, Fig. 12]. Ideally an ASD dissolves rapidly and completely into a supersaturated solution in equilibrium with drug-rich nanodroplets, which exchange fast because they are pre-wetted and have a very high specific surface area [review p. 14]. For clotrimazole (amorphous solubility 7.5 µg/mL) donors of 0.5–7 µg/mL gave flux proportional to concentration that declined with time, whereas above 7.5 µg/mL 200–250 nm droplets formed and the flux stayed at its maximum for a time that "roughly correlates" with the excess over the amorphous solubility; the authors conclude that the activity in the aqueous phase is "maintained at its maximum value of 1" until the droplets are consumed [review pp. 14–15, Figs. 13–14]. The review also states that "a well-designed formulation will rely on transferring the drug into drug-rich liquid droplets and compartments such as micelles" [review pp. 12–13].

**What the library shows.** The clotrimazole data are Indulkar 2016: the steady receiver period was about 1 h at 10 µg/mL, 5 h at 15 and at least 13 h at 20 µg/mL, and 7.5 mg/mL of 150–250 µm amorphous particles gave no plateau, falling from about 0.63 to 0.42 µg/mL, below the one-phase control [indulkar2016 R6, R7] (2016) ([Bioperformance F5](../../bioperformance/bioperformance/findings.md#f5)). The effect was carried to ASD-derived droplets: 90:10 HPMCAS and HPMC atazanavir ASDs held the hollow-fibre receiver above the level of an amorphous-solubility solution for 120 min, with maxima of about 10.0 and 9.4 µg/mL [hate2018 R13] (2018). In the same module the transfer kept rising above the amorphous solubility, the AUC slope falling from 5.51 to 1.29 at 78 µg/mL without a plateau, as droplet count rose from about 2.3 × 10⁹ to 1.06 × 10¹⁰ per mL; the authors read this as a higher mass transfer coefficient and leave the mechanism untested [hate2018 E3, E4, R7, C56] ([Bioperformance F15](../../bioperformance/bioperformance/findings.md#f15)).

**Corrections and qualifications.**
- Micelles are not an equivalent reservoir. They resupply free drug, but at the lower activity of the micellar solution (Step 6), and the clotrimazole authors state that micelle-solubilized drug is not equivalent [indulkar2016 C26] ([nanodroplet reservoir effect](../../concepts/nanodroplet-reservoir-effect.md)) (check R39).
- The evidence for plateau length is moderate: replicates are not stated, and the back-calculated depletion times do not match a mass balance with the stated volumes [indulkar2016 X3] ([Bioperformance F5](../../bioperformance/bioperformance/findings.md#f5)). With mesoporous silica the amorphous solubility can be reached without droplets, and then no reservoir exists [hate2020a C54; dening2018 C44].

**Next.** The reservoir works only if the formulation delivers the dose into the droplet state rather than into crystals, so the review turns to what happens while an ASD dissolves.

**Pages.** [nanodroplet reservoir effect](../../concepts/nanodroplet-reservoir-effect.md), [drug-rich nanodroplets](../../concepts/drug-rich-nanodroplets.md), [drug-rich phase](../../concepts/drug-rich-phase.md), [sink conditions](../../concepts/sink-conditions.md), [membrane mass transfer coefficient](../../concepts/membrane-mass-transfer-coefficient.md), [mass transferred from receiver AUC](../../formulas/mass-transferred-from-receiver-auc.md).

## Step 8. ASD dissolution towards the ceiling

**Question.** Which processes during ASD dissolution decide whether the solution reaches the amorphous solubility and forms the reservoir, or loses its supersaturation to crystals?

**The review's reasoning (2016).** Copovidone and HPMC matrices tend to erode in water while HPMCAS formulations can be designed to disintegrate [review p. 12]. The driving force for dissolution of a multicomponent solid is "poorly understood": felodipine ASDs at low drug:polymer ratio dissolved rapidly under non-sink conditions and generated nanoparticles, read as the amorphous solubility being exceeded, whereas at higher ratios dissolution was slower, no nanoparticles formed and the concentration approached but did not exceed the amorphous solubility [review pp. 12–13]. For sulfathiazole–PVP the polymer dissolved faster than the drug, and the drug-enriched surface lowered the rate [review p. 13]. Water lowers the Tg of the wetted solid: amorphous nifedipine crystallized immediately in water, but not with HPMC, and water-induced amorphous–amorphous phase separation, to which PVP dispersions are susceptible, is "a precursor to crystallization" [review p. 13]. Felodipine–PVP dispersions gave high but short-lived supersaturation, so an effective crystallization inhibitor is "essential"; with one, dissolution continues until the solution splits into two liquid phases [review p. 13]. The droplets can grow, agglomerate and nucleate crystals heterogeneously, and surfactants can inhibit or promote this [review pp. 13–14].

**What the library shows.** The two loss routes were separated in situ: neat amorphous felodipine at 37 °C was about 54% crystalline at 1 min and dissolved no higher than the crystal (about 0.9–1.1 µg/mL), whereas amorphous indomethacin at 25 °C stayed amorphous while needles grew in the liquid [alonzo2010 R2, R1, R11] (2010), and nifedipine glass crystallized within minutes with or without dissolved polymer while its 50:50 dispersions crystallized from the solution instead [raina2014b R2, R13] (2014) ([Supersaturation from ASD dissolution F1](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f1)). The loading effect was named the limit of congruency: ritonavir–PVPVA tablets released about 97% at 60 min at 25% loading, about 29% at 30% and at most about 2% at 35–50% [indulkar2019a R11] (2019), and in PVPVA the limit lay between 2% and 40% for the drug forms tested to 2022 ([Release mechanism and LoC F6](../../dissolution/a-release-mechanism-and-loc/findings.md#f6)). In 2017–2020 only release under polymer control passed the amorphous solubility and formed 190–370 nm droplets [purohit2017b R10, R11] ([Release mechanism and LoC F4](../../dissolution/a-release-mechanism-and-loc/findings.md#f4)); droplets from a ritonavir–PVP dispersion vanished on dilution and had a Tg of about 1 °C [ilevbare2013d R1, R2] (2013) ([Supersaturation from ASD dissolution F9](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f9)).

**Corrections and qualifications.**
- The felodipine nanoparticles of the cited study (ref. [44]) were read by their authors as crystalline, from growth, birefringence at about 1 µm and spectra (not shown); no diffraction was made, and no paper in the library shows them to be amorphous [alonzo2011 C33, X7] ([Supersaturation from ASD dissolution F9](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f9)) (check R42). Their formation shows that the dispersion released past the crystalline solubility quickly; it is not evidence that the amorphous solubility was exceeded.
- From 2021 partly incongruent release of low-Tg drugs also passed the amorphous solubility (loratadine–PVPVA at 35%) [yang2021 R19, C15], and HPMCAS felodipine dispersions showed no limit up to 50% [saboo2020a R15], so the loading switch is drug- and polymer-specific.
- The disintegration-against-erosion statement is not tested in the library (check R40).

**Next.** A dispersion that reaches the ceiling and forms droplets still has to hold it while the membrane removes drug, so the review adds absorption to the picture.

**Pages.** [limit of congruency](../../concepts/limit-of-congruency.md), [congruent release](../../concepts/congruent-release.md), [polymer-controlled release](../../concepts/polymer-controlled-release.md), [matrix crystallization](../../concepts/matrix-crystallization.md), [solution crystallization](../../concepts/solution-crystallization.md), [plasticization by water](../../concepts/plasticization-by-water.md), [drug-rich nanodroplets](../../concepts/drug-rich-nanodroplets.md), [surface-normalized release rate](../../formulas/surface-normalized-release-rate.md).

## Step 9. Absorption with a sink

**Question.** How does removal of drug by the membrane change the activity in the central compartment, and for which drugs does activity matter?

**The review's reasoning (2016).** Membrane flux links all earlier processes to passive absorption and is set by the activity of the drug in the central compartment, which, not the total concentration, should be measured or estimated [review p. 14]. For BCS class IV drugs slow permeation is likely rate-determining and activity "may not be the most critical parameter"; for BCS class II drugs a higher activity by supersaturation drives transport [review p. 14]. Removal from the central compartment may be fast compared with entry by dissolution, so that the effective activity is lowered and, in the extreme, absorption is dissolution-rate-limited; a reservoir with a low barrier for entering the central compartment overcomes this [review p. 14]. In the simulations the activity with and without absorption is compared for a slowly dissolving ASD (Fig. 18) [review pp. 16–17]. This is the review's argument and simulation; it reports no measurement with a sink.

**What the library shows.** Measurements with an absorptive sink came from 2017. With 0.05% HPMC-AS a nevirapine tablet donor stayed at about 525 µg/mL for 270 min in a closed vessel but fell to about 253 µg/mL with absorption, and with 0.1% PVPVA the total drug stayed at about 44–49 mg with absorption while the dissolved drug of the closed vessel fell to about 26 mg [hate2017 R15, R7, R17] (2017); 50% atazanavir ASDs released about 6200, 6300 and 5000 µg at 120 min with a sink against about 4200, 4600 and 3600 µg without (HPMCAS, HPMC, PVPVA) [hate2018 R18] (2018) ([Bioperformance F14](../../bioperformance/bioperformance/findings.md#f14)). A sink also raised atazanavir release from SBA-15 at 240 min from about 46.5 to 89.5% [hate2020a R20] (2020) ([Overview F14](../../overview/findings.md#f14)). These measure the review's point, and add that removal also raises the release of slow dispersions.

**Corrections and qualifications.**
- A sink does not prevent crystallization that starts within minutes: without polymer the closed and absorptive nevirapine donors fell alike [hate2017 C51] ([Bioperformance F14](../../bioperformance/bioperformance/findings.md#f14)). The lower driving force for nucleation is inferred, not measured, and replicates are mostly not stated [hate2017 X17, C57].
- The BCS class II / IV distinction is not tested; the library's flux and absorption data concern high-permeability drugs, enzalutamide being called BCS class II [wilson2018 C30] ([Bioperformance F23](../../bioperformance/bioperformance/findings.md#f23)) (check R50).

**Next.** With supply, removal and crystallization each given a rate, the review can compare whole scenarios by the fraction of the dose absorbed in a finite residence time.

**Pages.** [absorptive sink](../../concepts/absorptive-sink.md), [absorptive dissolution testing](../../concepts/absorptive-dissolution-testing.md), [non-sink dissolution](../../concepts/non-sink-dissolution.md), [dissolution-rate-limited absorption](../../concepts/dissolution-rate-limited-absorption.md), [desupersaturation](../../concepts/desupersaturation.md), [hollow-fibre donor depletion](../../formulas/hollow-fibre-donor-depletion.md).

## Step 10. The design target: spring and plateau

**Question.** Which dissolution and phase behaviour gives the largest fraction of a high dose-number drug absorbed, and what should an enabling formulation aim for?

**The review's reasoning (2016): a simulation.** The assumptions are a crystalline solubility of 1 µg/mL and an amorphous solubility of 10 µg/mL (activity 1 for the amorphous and 0.1 for the crystalline phase); a 5 mg dose; a central compartment of 100 mL, after a human study [109]; passive absorption only; and a flux chosen for high permeability, absorption being limited by free drug [review p. 15]. The simulations "do not contain sufficient parameters to represent the complex biological situation" and serve to compare scenarios [review p. 15]:

- **Case 1**: LLPS reached at once, droplets stable; 20% of the dose in the aqueous compartment and 80% in the droplets. Flux and activity (1) are constant for 6 h, 96% is absorbed at 6 h and 100% at 8 h, and 80% of the absorbed molecules come from the droplets [review pp. 15–16, Fig. 15].
- **Case 2a**: as Case 1, but crystals deplete the solution from 30 min and reach the crystalline solubility after another 30 min; the small crystals hold 1 µg/mL. Activity falls from 1 to 0.1 within an hour; at 1 h the compartment holds 2% of the dose, less than 12% is absorbed and more than 86% is in crystals; another 11% is absorbed over the next 7 h, 23% in all at 8 h [review pp. 15–16].
- **Case 2b**: as 2a, but the recrystallized solid has an apparent solubility of 3 µg/mL (metastable polymorph, low crystallinity or defects); 34% is absorbed over the last 7 h, 46% at 8 h [review p. 16]. (The text says the first hour is "the same as for Case 1a", read here as Case 2a.)
- **Case 2c**: depletion starts at 2 h and takes 2 h to reach 3 µg/mL; activity is 1 for 2 h, falls to 0.3 and stays there; over 32% is absorbed in the first 2 h, over 51% at 4 h and 71% at 8 h. The authors identify this with "spring and parachute" [76] [review p. 16, Fig. 16].
- **Case 3**: a slowly dissolving ASD that never reaches the amorphous solubility and does not crystallize; activity reaches the crystalline value in about an hour and almost plateaus at 0.29; 30% is absorbed at 8 h and about 6% of the dose is in the compartment at 8 h [review pp. 16–17, Figs. 17–18].
- **Case 4**: a crystalline suspension holding 1 µg/mL; activity 0.1, 2% of the dose in the compartment, 13% absorbed over 8 h [review p. 17, Fig. 19].

Shortening the residence time from 8 h to 4 h lowers every case (Table 1; introduced on p. 18 of the review, and placed on p. 2 of the extracted text) [review p. 18]:

| Case | % absorbed, 8 h | % absorbed, 4 h |
|---|---|---|
| 1 | 100 | 65 |
| 2a | 23 | 17 |
| 2b | 46 | 27 |
| 2c | 71 | 52 |
| 3 | 30 | 11 |
| 4 | 13 | 6 |

From Case 1 the authors define "spring and plateau": fast dissolution to the LLPS/GLPS concentration, the thermodynamic limit, held by replenishment from the drug-rich phase with crystallization inhibited; they "believe that this should be the goal of every enabling formulation with high dose number", rather than the "spring and parachute" of Case 2c [review pp. 16, 18]. They add that the 8 h window is "somewhat long", that constant permeability "is unlikely to be valid for a majority of compounds", and that in the stomach enteric polymers (HPMCAS, Eudragit L 100-55) do not dissolve while PVP, HPMC and Eudragit E PO begin to, so fasted and fed states differ [review p. 18].

**What the library shows.**
- *Tested in vitro: the plateau.* Droplet donors held the maximum flux for a time that grew with the excess (Step 7) ([Bioperformance F5](../../bioperformance/bioperformance/findings.md#f5)). With crystals already present after a gastric stage, a 10% posaconazole–HPMCAS dispersion at 200 µg/mL held about 22–24 µg/mL to 120 min, while a fifth of the dose fell to about 8 µg/mL by 120 min, read by the authors as a reservoir offsetting crystal growth ("most likely", not measured) [elkhabaz2019a R6, R12, C48] (2019) ([Supersaturation from ASD dissolution F26](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f26)), a mixture of Cases 1 and 2 that the simulation does not include.
- *Tested in rats: ceiling against crystals.* Enzalutamide ASDs that reached the amorphous solubility gave AUC0–48 of about 770 and 575 µg·h/mL against about 91 for crystalline drug, and the 10% HPMCAS ASD that crystallized gave about 61 [wilson2018 R17, R18] (2018) ([Bioperformance F23](../../bioperformance/bioperformance/findings.md#f23)), the direction of Cases 1 and 2a against Case 4.
- *Tested in rats: how long the plateau must last.* The polymer that delayed crystallization longest in solution (CA Sub) gave an ASD with the exposure of the crystals (45 against 43.1 µg·h/mL), while CPHPC-106, with an induction time of about 0.7 h, gave 516 and 305 µg·h/mL at 10% and 50% loading; with an absorption half-life of about 1 h the authors conclude that absorption before crystallization made short inhibition sufficient [wilson2020 R1, R6, C48] (2020) ([Bioperformance F24](../../bioperformance/bioperformance/findings.md#f24)). For this fast-absorbed drug a "spring and parachute" profile was enough, which qualifies the review's "every".
- *Partly tested: absorption against growth.* In the hollow-fibre module absorption scaled with $S$ and growth on seeds with the excess concentration to the power 1.677, placing the crossover near $S$ = 18.5 for tacrolimus; the constants do not reproduce from the printed values, and the strength is weak [hate2019 R18, R19, X4] (2019) ([Bioperformance F29](../../bioperformance/bioperformance/findings.md#f29)). Cases 2a–2c impose crystallization times; this finding shows that absorption itself lowers the supersaturation that drives growth, a coupling the simulation leaves out.
- *Tested in monkeys: the fed state.* A 20% pretomanid–HPMCAS-HF ASD gave 155% of the crystalline product's exposure fasted but fell to 72.2% of its fasted exposure with food, while the crystalline product rose to 163% [nguyen2023a R23] (2023) ([Bioperformance F26](../../bioperformance/bioperformance/findings.md#f26)), an example of the review's fasted–fed caution for an enteric polymer.
- *Not tested.* No paper in the library reproduces the fractions absorbed of Table 1, the 20/80 split, the 100 mL compartment or the 4 h against 8 h comparison, and the library holds no human exposure for a dispersion ([Overview F14](../../overview/findings.md#f14)) (checks R53, R56).

**Corrections and qualifications.**
- The simulation is the review's own illustration; its percentages are model outputs for an assumed drug, not measurements.
- The rat comparisons rest on one drug and three rats per arm in the 2020 study, and the aggregate benefit in the 2018 study is a trend without a statistical test [wilson2020 K1; wilson2018 C46, X6] ([Bioperformance F23](../../bioperformance/bioperformance/findings.md#f23), [F24](../../bioperformance/bioperformance/findings.md#f24)).

**Next.** The chain ends here; the points along it that the library has not tested are listed below.

**Pages.** [nanodroplet reservoir effect](../../concepts/nanodroplet-reservoir-effect.md), [crystallization inhibition](../../concepts/crystallization-inhibition.md), [crystal seeding](../../concepts/crystal-seeding.md), [food effect](../../concepts/food-effect.md), [oral bioavailability](../../concepts/oral-bioavailability.md), [in vitro–in vivo correlation](../../concepts/in-vitro-in-vivo-correlation.md), [power-law crystal growth rate](../../formulas/power-law-crystal-growth-rate.md), [non-compartmental AUC](../../formulas/non-compartmental-auc.md).

## Open questions along the chain

- Is the ceiling the binodal or, as the review allows, the spinodal? — Step 5 — the library uses the binodal and has only a kinetic overshoot for danazol ([Crystallization from solution F22](../../dissolution/d-crystallization-from-solution/findings.md#f22), [Amorphous solubility and LLPS F3](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f3)).
- Do co-crystals, lipid formulations and prodrugs reach the amorphous solubility? — Step 5 — the one co-crystal tested did not; lipid and prodrug routes are absent ([Amorphous solubility and LLPS F14](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f14)).
- Is the activity at the amorphous solubility kept in every micellar medium? — Step 6 — it was for atazanavir with SDS and in human intestinal fluid, but the partition mechanism rests on indirect probes ([Amorphous solubility and LLPS F16](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f16), [F18](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f18)).
- Were the nanoparticles of low-loading felodipine dispersions crystalline or amorphous? — Step 8 — the crystalline reading has no diffraction behind it ([Supersaturation from ASD dissolution F9](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f9)).
- Does supersaturation matter less for low-permeability drugs? — Step 9 — all flux and absorption data concern high-permeability drugs ([Bioperformance F14](../../bioperformance/bioperformance/findings.md#f14)).
- How do absorption and growth on seeds trade off quantitatively? — Steps 9–10 — the one model has constants that do not reproduce from the printed values ([Bioperformance F29](../../bioperformance/bioperformance/findings.md#f29)).
- Is "spring and plateau" better than "spring and parachute" for a slowly absorbed drug? — Step 10 — short inhibition sufficed for enzalutamide (absorption half-life about 1 h), and no slow-absorption comparison exists ([Bioperformance F24](../../bioperformance/bioperformance/findings.md#f24)).
- Do the simulated fractions absorbed, and the loss at 4 h, hold in humans? — Step 10 — the library has animal data for three drugs and no human data for a dispersion ([Overview F14](../../overview/findings.md#f14)).