Make-Up Consumption: ml/Hour by Nozzle & Duty Cycle

Written by: John LauChecked by: MarkOctober 10, 2025

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Make-Up Consumption: ml/Hour by Nozzle & Duty Cycle (v5.2 Reactive)

Make-up consumption in CIJ systems is the anchor metric that production, maintenance, and HSE teams monitor to keep costs stable and print quality predictable. In practice, your hourly solvent usage is a sum of two components: (1) active ejection through the nozzle during printing, purging, and cleaning; and (2) passive evaporation from the ink circuit while the printer maintains viscosity. This page translates nozzle physics and duty-cycle control into a practical, ml/hour calculator you can trust on the floor—plus realistic ranges for ethanol-, MEK-, and acetone-based make-up.

Before we dive into formulas, a quick orientation: CIJ sits inside your site-wide consumables plan alongside TIJ, TTO, and laser. If you need the bigger picture—inks, make-up, ribbons, beam time—bookmark the pillar page Coding & Marking Consumables (CIJ/TIJ/TTO/Laser) and come back here when you’re ready to quantify solvent cost per hour or per SKU run.

Why “ml/hour” matters more than anecdotal “one bottle a shift”

“One bottle a shift” sounds tidy, but it ignores shift length, standby time, ambient temperature, and purge habits. By converting everything into an hourly rate, you can: (a) forecast procurement with far less variance, (b) benchmark lines against each other independent of OEE, (c) set alert thresholds in the printer HMI/SCADA, and (d) negotiate better with suppliers using data that maps to physics rather than folklore.

Comparable across SKUs: Normalize by duty cycle to compare a sparse date code versus dense alphanumerics.
Actionable: Tie deviations to specific levers—pressure, nozzle wear, PWM settings, cabinet temperature, and purge routines.
Auditable: The calculation path is explainable (no black box). It uses standard orifice flow and a duty-cycle average.

If you’re also choosing solvents or switching families (MEK vs ethanol vs acetone vs dye/pigment blends), cross-check compatibility, dry time, and safety in CIJ Ink Families: MEK vs Ethanol vs Dye-Pigment after you finish the math here.

The two-part model: active ejection + passive evaporation

Think of make-up consumption as a dual engine:

Active ejection (Q_active): solvent pushed through the nozzle when you print, purge, or clean. It follows the orifice flow equation corrected by a discharge coefficient (C_d) and averaged by duty cycle.
Passive evaporation (Q_passive): solvent lost as vapor while the printer regulates viscosity. Driven mostly by temperature, exposed surface area, airflow, and solvent volatility.

Total make-up (ml/h) = Q_active + Q_passive. We’ll compute both and then combine them into a realistic hourly band for your line.

Nozzle physics you actually need (without the fog)

Instantaneous flow through a nozzle or orifice plate is well-described by the standard orifice equation:

Q_inst = C_d · A · sqrt( 2 · ΔP / ρ )

Where C_d = discharge coefficient (dimensionless), A = orifice area (m²), ΔP = pressure differential (Pa), and ρ = fluid density (kg/m³). CIJ make-up behaves as a low-viscosity solvent; for small orifices and the typical CIJ pressure regime, this model—empirically corrected by C_d—is robust and widely used in engineering practice.

About the discharge coefficient (C_d)

C_d condenses real-world losses (vena contracta, friction, turbulence) into a single multiplier. It depends on geometry and Reynolds number. In practice:

Typical C_d ranges by nozzle geometry (indicative)
Nozzle geometry	Typical C_d range	Notes
Sharp-edged hole (thin plate)	0.60–0.65	Strong vena contracta
Short tube, sharp inlet	0.70–0.80	Some flow guidance
Smoothly rounded inlet	0.90–0.98	Low separation, high efficiency
Convergent (7°–12°)	0.95–1.05	Occasional recovery >1.0 reported

CIJ nozzles are precision parts and their effective C_d shifts with fouling, partial clots, or wear. If your hourly usage creeps up at unchanged pressure/duty, suspect a C_d drift from contamination or erosion. For preventive practices that stabilize C_d, see Nozzle Clogging & Startup Failures: Preventive Playbook.

Density and area: simple but sensitive

Area (A): for a circular orifice of diameter d, use A = π(d²/4). A 60 µm nozzle (0.00006 m) has A ≈ 2.827e-9 m².
Density (ρ): ethanol ≈ 789 kg/m³ at 20 °C; MEK ≈ 805 kg/m³; acetone ≈ 784 kg/m³. Heavier fluids reduce Q at a given pressure; lighter fluids increase it.

From instantaneous to hourly: the duty-cycle average

CIJ doesn’t flow continuously at the nozzle when you’re coding sparse content; rather, the solenoid/deflection/charge system “works” in bursts. If the printer is “on” for a fraction of each cycle, your average flow is:

Q_active = Q_inst · DutyCycle

Duty cycle is the “on” time divided by the total cycle time, often manipulated via PWM. Convert to ml/h using 3600 s/h and 10⁶ ml/m³.

Worked example: 60 µm, 2 bar, ethanol, C_d=0.97, duty = 15%

Let ΔP = 2 bar (2×10⁵ Pa), ρ = 789 kg/m³, A = 2.827e-9 m². Then:

Q_inst ≈ 0.97 · 2.827e-9 · sqrt( 2·2e5 / 789 ) ≈ 6.18e-8 m³/s

Q_active ≈ 6.18e-8 · 0.15 = 9.27e-9 m³/s → ~33.4 ml/h.

Duty cycle & PWM: the clean lever for average flow

PWM (pulse-width modulation) lets you change average flow without chasing pump pressure. It’s responsive, digital, and repeatable. Keep these realities in mind:

Response time: at very high PWM frequencies the valve may not fully open; your effective Q_inst is lower than theory. Validate with a capture test.
Print quality trade-off: extreme PWM patterns can alter drop charge/deflection stability; always pair flow changes with a quick code-legibility audit.
Energy & wear: constant pressure + PWM often uses simpler hardware and can reduce mechanical stress compared with frequent pressure modulation.

Acceptance criteria for a good PWM setup

At three duty settings (e.g., 10%, 30%, 50%), measured ml/h tracks linearly within ±7% of calculation.
Code quality (contrast, edge raggedness, overspray) remains in spec across the same points.
Start/stop stability: first 30 s after resume doesn’t overshoot more than 10% of steady state.

Use your plant’s print QC routine here. For visual failure modes and fast fixes, reference CIJ Print Quality Troubleshooting Checklist when PWM changes ripple into character defects.

Active Make-Up Consumption (ml/hour)

Compute hourly solvent ejection from nozzle physics and duty cycle.

Orifice diameter (µm)

Pressure differential (bar)

Fluid density (kg/m³)

Duty cycle (%)

Discharge coefficient

Passive evaporation: the quiet, continuous draw on your bottle

Even when the nozzle is idle, make-up is consumed to restore solvent lost to evaporation from the ink reservoir and circuit. Volatility is the feature (fast dry on the part) and the cost (constant loss to air). Four factors dominate:

Temperature: higher cabinet/ambient temperature raises solvent vapor pressure—evaporation climbs sharply.
Exposed surface area: larger liquid–air interface drives loss. Lids, baffles, and well-sealed circuits matter.
Air exchange: fans and drafts carry vapor away, maintaining the gradient that sustains evaporation.
Solvent type: MEK typically evaporates faster than ethanol at the same conditions; acetone is faster still.

Quick rules of thumb (use to sanity-check your logs)

For an ethanol system, Q_passive commonly sits around 4–12 ml/hour at 20–25 °C with modest air movement.
MEK systems often run higher, 6–18 ml/hour, and are more temperature-sensitive.
Open doors, hot enclosures, or frequent purges can double those baselines.

A simple estimator for Q_passive (for scheduling and alerts)

This tool scales baseline losses by temperature, approximate air exchange, surface area, and solvent family. It’s not a vapor-diffusion solver; it’s a practical scheduler for when to expect top-ups and when to ring an alert if consumption deviates too far from norms.

Planning Tool: Est. Passive Consumption

Estimate bottle usage based on shift hours and temperature.

Avg Temp (°C)

Shift Hours

Nozzle Size

Make-Up Cost ($)

Putting it together: total ml/hour bands you can plan around

Let’s combine active and passive components for a typical small-character CIJ:

Light coding (date only), ethanol, 60 µm, 2 bar, duty 5–10%: Q_active ≈ 10–25 ml/h; Q_passive ≈ 4–12 ml/h; Total ≈ 14–37 ml/h.
Dense coding (batch + time + logo), ethanol, duty 15–25%: Q_active ≈ 30–60 ml/h; Q_passive ≈ 6–12 ml/h; Total ≈ 36–72 ml/h.
MEK environments 25–35 °C: Q_passive rises; expect +20–60% vs ethanol numbers if airflow is not mitigated.

Acceptance bands and alerting

For a given SKU and speed, log your last 5 stable runs and compute the mean and standard deviation of total ml/h. Set HMI/SCADA alerts at mean ± 2σ. A spike above the band flags leaks, doors left open, clogged filters, or drift in C_d (from nozzle fouling). A dip flags a failed make-up pump or mis-scaled duty cycle.

30-minute bench method: verify your numbers today

Stabilize the printer at target ΔP and duty cycle (simulate the SKU if needed).
Record bottle mass before/after 30 minutes (±0.1 g scale). Correct for any purge.
Convert g→ml using the solvent density (e.g., ethanol ≈ 0.789 g/ml).
Double the 30-minute result to get ml/h and compare to calculated Q_active+Q_passive.

This half-hour check is often enough to catch a silently rising evaporation load or an inadvertently aggressive purge routine.

Solvent choice and storage habits shape consumption

Solvent families differ in density, vapor pressure, and viscosity-versus-temperature behavior. That translates into different active flow (through ρ) and different passive loss (through volatility).

Indicative properties at ~20 °C (for planning)
Solvent	Density (kg/m³)	Volatility (qual.)	Notes
Ethanol	~789	Medium	Common in food, lower odor
MEK (Butanone)	~805	High	Fast dry; flammable; higher passive loss
Acetone	~784	Very high	Very fast dry; aggressive

To compare full pros/cons (dry time, adhesion synergies with ink families, EHS handling), see the cluster CIJ Ink Families: MEK vs Ethanol vs Dye-Pigment you opened earlier.

Pressure, nozzle, and health of the ink circuit

Three levers dominate Q_active variance at fixed duty cycle: ΔP, nozzle diameter, and C_d (which is sensitive to cleanliness and wear). A 10 µm change in diameter is non-trivial—area scales with d².

Nozzle cleanliness: schedule preventive cleaning; keep start/stop purges consistent and minimal.
Filter integrity: clogged filters distort pressure and ripple into spray stability and consumption.
Seal leaks: any air ingress increases evaporation; dye halos around fittings are clues.

For deeper maintenance practices across startup/shutdown and long stops, cross-reference Nozzle Clogging & Startup Failures: Preventive Playbook.

Temperature, enclosure, and storage discipline

Every degree over ~20 °C amplifies evaporation. Simple steps help:

Ensure fans blow across heat sinks, not across reservoir openings.
Keep cabinet doors latched; add a “door ajar” micro-switch alarm if operators frequent the panel.
Use baffles/lids to shrink the exposed surface area of the ink reservoir.
Relocate makeup bottle away from hot drives; shield from direct sun or HVAC discharge.

Storage and thermal control are also crucial for ink stability and consistent viscosity management. For practical limits and good-practice ranges, see Ink Shelf Life, Storage & Temperature Control.

Purge policy: an invisible line-item in your hourly consumption

Purge volumes can dwarf passive evaporation if used as a catch-all fix. Institute a purge policy:

Define when purges are allowed (e.g., after 30 min idle, after filter swap).
Set a purge volume cap per shift; track it in SCADA.
Investigate repeated purges as a symptom (nozzle wear, ink contamination, wrong pressure).

Safety and compliance notes that affect “real” consumption

Flammability class, ventilation, and labeling rules often drive enclosure airflow and cabinet layout. Those constraints, in turn, change evaporation. When you tighten safety, you often lower make-up usage too:

Ground and bond containers; eliminate static discharge points.
Keep lids tight; choose fittings that don’t weep under vibration.
Train on SDS for the exact make-up SKU in use (MEK, ethanol, acetone—each has distinct exposure and ignition profiles).

Safety Tool: SDS Transport Check

Quickly validate SDS integrity for air shipments.

UN Number

PSN

Class

Ship via Air?

Troubleshooting cheat-sheet (ml/h points of failure)

Symptom → likely cause → quick check
Symptom	Likely cause	Quick check
Total ml/h drifts up week over week	Nozzle fouling; door left open; filter clog; ΔP creep	Weigh 30 min bottle loss; inspect nozzle; check door logs; ΔP trend
Active ml/h < calc at high PWM freq	Valve not fully opening; inertia; timing skew	Lower PWM freq; scope signal; verify valve stroke time
Large spikes at shift start	Overshoot on restart purge; cold ink	Cap purge volume; warm-up timer; viscosity target check
Make-up bottle empties faster on hot days	Passive evaporation surge	Measure cabinet temp; add baffles; reduce airflow across reservoir

Deployment checklist (so your numbers stick)

Log ΔP, nozzle diameter, solvent family, and duty cycle in your job recipe.
Pin a PWM frequency range that respects valve response time.
Calibrate your C_d with a one-time weigh test; reuse until hardware changes.
Attach an hourly alert at mean + 2σ for your SKU; investigate before purging.
Label cabinet doors; enable an interlock or alarm if left open beyond 60 s.

Mini case studies (what teams actually fixed)

CS-1: 22 ml/h saved by PWM + door discipline

A beverage line coding 36,000 bph saw total make-up drop from 64 to 42 ml/h by (a) cutting PWM frequency from 1.2 kHz to 600 Hz (valve reached full stroke), and (b) adding a door-ajar alarm. Active fell 14 ml/h; passive fell 8 ml/h.

CS-2: MEK in summer—evaporation doubled until airflow was rerouted

An HVAC diffuser pointed at the printer cabinet increased passive from ≈8 to ≈16 ml/h. Redirecting airflow and adding a lid baffle returned it to 9–10 ml/h.

CS-3: Nozzle wear masquerading as “bad batch of ink”

After 5 months, a 60 µm nozzle had eroded to ≈66 µm. Area increased ~20%; active consumption and edge raggedness rose together. A simple microscope check plus replacement restored both quality and ml/h.

When your consumption math touches ink choice, storage practice, or visual QC, read next:

Inks & solvent families: CIJ Ink Families: MEK vs Ethanol vs Dye-Pigment
Nozzle maintenance: Nozzle Clogging & Startup Failures: Preventive Playbook
Ink storage & thermal control: Ink Shelf Life, Storage & Temperature Control
Quality diagnostics: CIJ Print Quality Troubleshooting Checklist

FAQ

Q: Does higher pressure always increase consumption?
A: Yes for active ejection (it grows with √ΔP), but not for passive. If your total rises with pressure while print density is constant, it’s active—not evaporation.

Q: Why doesn’t viscosity appear in the main equation?
A: Its effect is wrapped into C_d. Viscosity drops with temperature; the practical signal is that warm days often show higher C_d and thus higher Q at the same ΔP.

Q: Can I use K-factors instead?
A: Yes, if your nozzle vendor provides a K constant (and exponent). It’s an empirical way to get Q from ΔP for a reference fluid; adjust for your solvent’s specific gravity.

Q: How do purges figure into ml/h?
A: Treat them as discrete adds: sum purge volumes per hour and add to your model. Better: limit purges by policy and fix the root cause (nozzle, filters, ΔP).

Glossary

Make-up: the solvent bottle added to maintain ink viscosity; not pigment/ dye.
Duty cycle: fraction of time the system is “actively ejecting” within a cycle.
Vena contracta: the contracted jet cross-section just downstream of an orifice.
K-factor: vendor constant summarizing nozzle geometry + fluid reference to map ΔP→Q.