Colloid / Emulsion Stability

1 Introduksi

1.1 Latar Belakang

Emulsi adalah sistem dua-fase imiscible (oil-in-water O/W atau water-in-oil W/O) yang distabilkan oleh emulsifier (Tween, lesitin, protein, polisakarida). Stabilitas emulsi sangat menentukan shelf life produk seperti susu, krim, dressing, mayonnaise, dan minuman emulsi (McClements, 2015; Dickinson, 2003). Empat mekanisme destabilisasi utama: creaming (separasi gravitational), flocculation (agregasi tanpa coalescence), coalescence (merger droplet → fase terpisah), dan Ostwald ripening (transfer molekul dari droplet kecil ke besar).

Karakterisasi stabilitas memakai tiga metrik kunci: droplet size distribution ($d_{10}$, $d_{50}$, $d_{90}$ via laser diffraction atau DLS), zeta potential $\zeta$ (charge permukaan droplet, mV — indikator electrostatic stability; tipikal $|\zeta| > 30$ mV = stable, < 20 mV = aggregation prone), dan creaming index (visual % separasi setelah storage time). Hukum Stokes memprediksi creaming velocity dari droplet size + density difference + viscosity (McClements, 2015):

$$ v_S = \frac{2 r^2 (\rho_d - \rho_c) g}{9 \eta} $$

1.2 Tujuan Modul

Modul Colloid / Emulsion Stability di SQalytics ditujukan untuk:

Menerima droplet size data ($d_{10/50/90}$, span) + zeta potential + creaming index dari multi-sample.
Memprediksi Stokes creaming velocity dari size + density + viscosity.
Menampilkan stability matrix: classification per sample (stable / aggregation prone / coalescence risk).
Mendukung time-course tracking: $d_{50}$ vs storage time untuk Ostwald ripening kinetics.
Audiens: mahasiswa S2 ilmu pangan/farmasi, R&D produk emulsi (susu, minuman fungsional, drug delivery), peneliti emulsifier characterization.

1.3 Posisi di Antara Alternatif

Pilih Colloid / Emulsion Stability untuk integrated emulsion characterization. Untuk PSD alone (powder atau emulsi), pakai Particle Size Distribution. Untuk viskositas alir emulsi, gunakan Rheology / Flow Curve. Untuk statistical comparison formula, lanjut ke Compare Many Groups. Untuk multivariate optimization emulsifier, gunakan RSM Studio.

2 Metode

2.1 Dasar Teoretis

Hukum Stokes untuk creaming velocity $v_S$ droplet di Newtonian fluid (McClements, 2015):

$$ \boxed{\, v_S = \frac{2 r^2 (\rho_d - \rho_c) g}{9 \eta_c} \,} $$

dengan:

$r$ = droplet radius (m)
$\rho_d$, $\rho_c$ = density droplet (oil) dan continuous phase (water) (kg/m³)
$g$ = 9.81 m/s²
$\eta_c$ = viscosity continuous phase (Pa·s)

Velocity > 0: creaming (oil ke atas), < 0: sedimentation. Tipikal velocity untuk O/W emulsi: $v_S \sim 10^{-6}$–$10^{-9}$ m/s (1 mm/day to 0.1 mm/year).

Creaming index (visual setelah storage time $t$):

$$ \text{CI} (\%) = \frac{H_C}{H_T} \times 100 $$

dengan $H_C$ tinggi cream layer (mm) dan $H_T$ tinggi total emulsi (mm). CI = 0% = no creaming (stable), CI = 100% = total separation.

Zeta potential $\zeta$ — diukur via electrophoretic mobility (Henry equation):

$$ \zeta = \frac{3 \eta \mu}{2 \varepsilon \varepsilon_0 f(\kappa a)} $$

dengan $\mu$ electrophoretic mobility, $\varepsilon$ relative permittivity medium, $\varepsilon_0$ vacuum permittivity, $f(\kappa a)$ Henry function (≈ 1.5 for aqueous Smoluchowski limit). Tipikal interpretasi (McClements, 2015):

$\|\zeta\|$ (mV)	Stability
< 5	Maximum aggregation (isoelectric point)
5–15	Limited aggregation
15–20	Moderate stability
20–30	Good stability
> 30	Excellent stability
> 60	Outstanding stability (rare for emulsions)

Ostwald ripening rate ($\omega$) — Lifshitz-Slyozov-Wagner (LSW) theory:

$$ \omega = \frac{d r^3}{dt} = \frac{8 \sigma V_m^2 c_\infty D}{9 R T} $$

dengan $\sigma$ interfacial tension, $V_m$ molar volume oil, $c_\infty$ solubility oil di water, $D$ diffusion coefficient. Plot $r^3$ vs time menghasilkan slope = $\omega$ — Ostwald ripening rate.

Coalescence rate constant $k_c$ — first-order decay droplet number:

$$ \frac{1}{N(t)} - \frac{1}{N_0} = k_c \cdot t $$

Plot $1/N$ vs time linear → slope $k_c$ (coalescence rate, m³/s).

2.2 Persamaan Inti

Stokes creaming: $v_S = 2 r^2 (\rho_d - \rho_c) g / (9 \eta_c)$

Creaming index: $\text{CI} (\%) = H_C / H_T \times 100$

Zeta potential interpretasi: $|\zeta| > 30$ mV = stable, $< 20$ mV = aggregation prone

Ostwald ripening LSW: $r^3(t) = r_0^3 + \omega t$

Coalescence first-order: $1/N(t) = 1/N_0 + k_c t$

2.3 Asumsi & Batas Validitas

Asumsi	Konsekuensi jika dilanggar	Cara cek di SQalytics
Droplet spherical	Stokes velocity bias	Mikroskopi konfirmasi shape
Continuous phase Newtonian	Velocity bias di non-Newtonian	Pakai effective viscosity (cek `Rheology / Flow Curve`)
Dilute emulsi ($\phi < 0.1$)	Stokes ignored crowding effect	Modul flag bila $\phi > 0.3$
Refractive index sesuai (Mie theory laser diffraction)	$d_{50}$ shifted	Catat RI di metadata
Zeta potential pH-dependent	$\zeta$ sangat berubah dengan pH	Catat pH assay
Ionic strength tidak terlalu tinggi (< 100 mM)	Electrostatic screening	Catat NaCl concentration
Time-course measurement $\geq 6$ titik untuk Ostwald	Slope $\omega$ tidak reliable	Modul flag minimum

3 Cara Kerja

3.1 Step-by-Step di SQalytics

Buka Colloid / Emulsion Stability dari domain Kimia.
Muat tabel: kolom Sample, d50_um, d10_um, d90_um, Zeta_mV, CI_pct, (opsional Time_day untuk time-course).
Atur parameter system:
- $\rho_d$ (oil density, default 920 kg/m³ untuk sunflower oil).
- $\rho_c$ (water density, 1000 kg/m³).
- $\eta_c$ (water viscosity, 0.001 Pa·s @ 25 °C).
Pilih mode:
- Single-point characterization — stability snapshot.
- Time-course tracking — kinetics Ostwald + coalescence.
Klik Run Emulsion Stability.
Tinjau hasil:
- Tab Stability Matrix — classification per sample (Stable/Moderate/Unstable).
- Tab Stokes Velocity — $v_S$ per sample + days to 50% creaming.
- Tab Time-course (jika multi-time) — $d_{50}^3$ vs time, slope = $\omega$ Ostwald.
- Tab Result Table.

Jika kurva stabilitas sudah representatif untuk laporan atau manuskrip, lanjutkan ke Step 5 opsional untuk mengirim Stability curves atau Droplet growth review ke Publication Graph Studio (PGS). Di sana Anda bisa melanjutkan pengaturan tipografi, legenda, pratinjau cetak, dan ekspor SVG / PNG / PDF.

3.2 Template Tabel Input + Contoh Data Sintetis

Kolom	Tipe	Wajib	Catatan
`Sample`	category	✓	ID emulsi/formulasi
`Time_day`	numeric	◯	Untuk time-course
`d50_um`	numeric	✓	Median droplet size
`d10_um`, `d90_um`	numeric	◯	Untuk span
`Zeta_mV`	numeric	✓	Surface charge
`CI_pct`	numeric	◯	Visual creaming index

Contoh data sintetis (3 formulasi minuman fungsional emulsi minyak omega-3):

Sample	d50_um	d10_um	d90_um	Zeta_mV	CI_pct (day 30)
Tween20-only	1.85	0.95	4.20	-18.5	25.0 (creaming jelas)
Tween20+WPI	0.85	0.45	1.95	-32.5	5.0 (stable)
Tween20+Soy lecithin	0.62	0.30	1.45	-38.5	2.0 (very stable)

Data sintetis — minuman fungsional emulsi minyak omega-3 (ω-3 fish oil 5% w/w) dengan 3 sistem emulsifier. Tween20 alone moderate; tambahan WPI (whey protein isolate) atau lecithin meningkatkan zeta potential dan menurunkan droplet size → stability lebih baik.

3.3 Contoh Luaran

Stability Matrix (snapshot day 30):

Sample	$d_{50}$ (μm)	Span	$	\zeta	$ (mV)	CI (%)	$v_S$ Stokes (m/s)
Tween20-only	1.85	1.76	18.5	25.0	$1.5 \times 10^{-7}$	$\sim$ 770 (theoretical)	⚠ Moderate-Unstable
Tween20+WPI	0.85	1.76	32.5	5.0	$3.2 \times 10^{-8}$	$\sim$ 3600	✓ Stable
Tween20+Soy lecithin	0.62	1.85	38.5	2.0	$1.7 \times 10^{-8}$	$\sim$ 6800	✓ Very Stable

Kesimpulan ringkas: "Tiga formulasi minuman fungsional emulsi ω-3 menunjukkan stability hierarchy clear: Tween20+Lecithin > Tween20+WPI > Tween20-only. Mekanisme: (i) droplet size turun dari 1.85 μm → 0.62 μm (3×) → Stokes velocity turun ~9× (proporsional $r^2$); (ii) zeta potential naik dari 18.5 mV (aggregation prone) ke 38.5 mV (electrostatic excellent stability per McClements 2015). Predicted shelf life (50% creaming threshold): Tween20-only ~ 2.1 tahun teoretik, tetapi visual CI 25% pada 30 hari menunjukkan accelerated destabilisasi (kemungkinan Ostwald ripening atau coalescence selain pure Stokes). Rekomendasi: pakai dual-emulsifier system Tween20+Lecithin untuk shelf life > 6 bulan komersial. Lanjut ke Rheology / Flow Curve untuk uji effective viscosity continuous phase, atau Compare Many Groups untuk uji statistik formulasi tambahan."

Kuadran stability droplet vs zeta dan kecepatan Stokes 3 formulasi emulsi omega-3 — Gambar 1. Stabilitas tiga formulasi minuman fungsional emulsi minyak omega-3 (5% w/w fish oil; data sintetis snapshot day 30). **(a)** Kuadran stabilitas $|\zeta|$ vs $d_{50}$: latar belakang berwarna menandakan zona elektrostatik per McClements (2015) — aggregation prone ($|\zeta|$ < 20 mV), marginal (20–30 mV), electrostatic stable (> 30 mV). Ukuran *marker* proporsional dengan visual creaming index (CI%) pada day 30. Sistem Tween20-only ($d_{50}$ = 1.85 μm, $|\zeta|$ = 18.5 mV) jatuh di zona aggregation prone (CI 25%); dual emulsifier Tween20+WPI dan Tween20+Lecithin masuk zona stabil (CI 5% dan 2%). **(b)** Kecepatan creaming Stokes (skala log) menurun ~9× dari sistem Tween20-only (1.5×10⁻⁷ m/s, ~770 day to 50% creaming) ke Tween20+Lecithin (1.7×10⁻⁸ m/s, ~6800 day) — konsekuensi $v_S \propto r^2$ pada hukum Stokes.

4 Kesimpulan

4.1 Relevansi Real-World

Minuman fungsional emulsi (ω-3 drink, CBD beverage, vitamin emulsi) — shelf life > 6 bulan target.
Salad dressing & mayonnaise — viscosity + droplet size untuk mouth feel.
Susu UHT — homogenisasi 1–2 μm dengan caseinate stabilizer.
Es krim — fat globule destabilization terkontrol untuk aerasi optimal.
Pharmaceutical lipid emulsi parenteral — droplet < 1 μm untuk IV admin.
Pestisida formulasi — agricultural emulsi.
Krim kosmetika — water-in-oil dengan zeta + visco kontrol.

4.2 Where to Go from Here

Particle Size Distribution — drill-down ke PSD detail dari laser diffraction.
Rheology / Flow Curve — viscosity continuous phase + emulsion.
Compare Many Groups — uji statistik $d_{50}$ atau $\zeta$ antar emulsifier.
Predict One Result from Many Variables — model CI dari $d_{50}$, $\zeta$, $\phi$.
ISO 13320 untuk PSD; ISO/TR 13097 untuk emulsion stability methods.

⚙ Troubleshooting Cepat

$|\zeta|$ rendah (< 15 mV). Tambah charged emulsifier (lecithin, protein) atau adjust pH jauh dari isoelectric point.

Stokes velocity sangat tinggi. Reduksi droplet size via high-pressure homogenization (>800 bar), atau tambah viscosifier (xanthan gum).

CI inconsistent dengan Stokes prediction. Indikasi coalescence atau Ostwald — pakai time-course tracking.

Droplet size bimodal. Indikasi inadequate homogenization atau emulsifier kompetisi — optimasi rasio.

i Riwayat Revisi

Tanggal	Revisi	Penulis
2026-05-12	Migrasi MD v2 → HTML final dengan figure publikasi + caption Elsevier-style (W1 batch malam 12 Mei)	Claude
2026-05-12	Draft v2 publikasi (KaTeX Stokes/CI/zeta/Ostwald LSW + APA McClements/Dickinson/Tadros)	Claude

4 Referensi

McClements, D. J. (2015). Food emulsions: Principles, practices, and techniques (3rd ed.). CRC Press. https://doi.org/10.1201/b18868
Dickinson, E. (2003). Hydrocolloids at interfaces and the influence on the properties of dispersed systems. Food Hydrocolloids, 17(1), 25–39. https://doi.org/10.1016/S0268-005X(01)00120-5
Tadros, T. F. (2013). Emulsion formation and stability. Wiley-VCH. https://doi.org/10.1002/9783527647941
Robins, M. M., Watson, A. D., & Wilde, P. J. (2002). Emulsions — creaming and rheology. Current Opinion in Colloid & Interface Science, 7(5–6), 419–425. https://doi.org/10.1016/S1359-0294(02)00089-4
Hunter, R. J. (2001). Foundations of colloid science (2nd ed.). Oxford University Press.
Lifshitz, I. M., & Slyozov, V. V. (1961). The kinetics of precipitation from supersaturated solid solutions. Journal of Physics and Chemistry of Solids, 19(1–2), 35–50. https://doi.org/10.1016/0022-3697(61)90054-3