On the Memory of Spray Measurements | TSTOF Spray Diagnostics – Lisbon 2026

This contribution was presented at the 22nd International Symposium on Application of Laser and Imaging Techniques to Fluid Mechanics, held in Lisbon, Portugal, from June 29 to July 2, 2026. The work introduces a new perspective on spray diagnostics, spray monitoring, and droplet measurement by investigating the memory of measurements in dynamically changing sprays.

22nd International Symposium on Application of Laser and Imaging Techniques to Fluid Mechanics – Lisbon 2026

Title: On the Memory of Measurements in Spray Diagnostics

Authors: M.R.O. Panão, P. Rehberg and W. Schäfer

Affiliations:
ADAI, University of Coimbra, Portugal
AOM-Systems GmbH, Germany
Department of Physics, TU Darmstadt, Germany
ai-quanton GmbH, Germany

Sprays are highly dynamic systems. During a measurement, operating conditions such as injection pressure, flow rate, or measurement position can change. At the same time, the measured droplet size, droplet velocity, and droplet arrival rate may also evolve. A spray measurement therefore cannot always be regarded as a collection of independent and stationary events.

This work investigates what happens when the spray changes while the measurement is still running. Instead of interpreting each detected droplet only as an isolated event, the measurement is treated as a time-dependent information record. In this context, the present measurement can carry traces of the recent past. The authors describe this concept as the memory of measurements in spray diagnostics.

The objective is to extend classical spray characterization with an additional infodynamic characterization layer. This layer is designed to describe how the informational state of a spray changes over time and how much information about previous droplet events remains detectable in subsequent measurements.

The experimental study uses a Time-Shift Time-of-Flight (TSTOF) measurement system for the characterization of individual droplets. TSTOF combines time-shift and time-of-flight principles and evaluates the time-dependent light-scattering signals generated when droplets pass through shaped laser beams.

TSTOF is a counting measurement technique. Individual droplet events are detected and characterized using parameters such as droplet size, droplet velocity, arrival time, and inter-arrival time. This event-based measurement principle is particularly suitable for investigating the temporal structure of spray processes.

The experimental setup consists of a closed-loop spray chamber, a TSTOF measurement probe, and a flat-fan nozzle from Lechler. Pressure, flow rate, and measurement position were recorded together with the droplet measurements. The measurement position was varied over a range of 50 mm, while the spray pressure was adjusted between 2 and 6 bar.

In total, 85 measurements were performed: 81 static measurements and 4 dynamic measurements. During the static measurements, the operating conditions remained constant. During the dynamic measurements, selected parameters were changed while droplet data continued to be recorded.

Classical spray diagnostics commonly describes sprays using mean values, distributions, and statistical moments of droplet size and velocity. These parameters remain essential, but they do not necessarily describe the complete internal diversity of a spray or how this diversity evolves during a measurement.

For example, two different droplet size or velocity distributions may produce similar mean values while representing different spray states. If the spray changes during data acquisition, cumulative statistical quantities can also react slowly to these changes.

The Lisbon contribution therefore introduces an additional description based on information theory and infodynamics. Individual size, velocity, and timing classes are interpreted as possible microstates of the spray. Their combined statistical distribution represents an informational macrostate of the local spray.

This additional layer does not replace established parameters such as mean droplet diameter or mean velocity. Instead, it complements them by describing the diversity and temporal evolution contained in the measurement data.

A central concept of the study is informature. It is used to quantify the amount of information associated with the distribution of measured spray characteristics. The paper also evaluates a differential form of informature to follow changes in the informational state of the spray.

The experimental results show that changes in injection pressure can significantly modify droplet velocity and the informational state of the spray. While conventional mean values describe the shift in velocity, the information-based parameter provides an additional measure of how the diversity of the measured droplet population changes.

The second major concept introduced in the work is the measurement memory trace. Each droplet event is described using droplet size, velocity, and inter-arrival time. The relationship between consecutive events is then investigated using mutual information.

In simple terms, the method asks: How much information about the next measured droplet is already contained in the present droplet event?

To distinguish a real temporal relationship from correlations caused by finite sample size, the measured event sequence is compared with randomly permuted sequences. The resulting corrected memory trace provides a quantitative measure of temporal dependence within the spray measurement.

The experiments demonstrate that sudden changes in spray operating conditions can produce characteristic responses in the corrected memory trace. Under comparatively stable operating conditions, the corrected memory trace remains close to zero. When the spray undergoes a rapid transformation, distinct changes in the memory signal can appear.

Gradual transformations are more complex. In these cases, the memory trace and the evolution of informature need to be interpreted together. This combination provides a more complete description of how the spray evolves during the measurement.

The important point is that a spray measurement is no longer considered only as a final statistical result. It is treated as an evolving sequence of droplet events in which the temporal order itself contains useful information.

This concept is particularly relevant for real-time spray diagnostics and spray monitoring. Industrial and scientific sprays frequently operate under transient or non-stationary conditions. A measurement system therefore needs to identify not only the actual droplet size and velocity, but also whether the underlying spray state is changing.

Combining conventional droplet characterization with information-based analysis can provide additional insight into spray transitions that may be difficult to recognize from averaged parameters alone.

Potential applications include model validation, sensor development, process monitoring, process control, atomization research, and the characterization of dynamically changing sprays.

The work presented in Lisbon extends classical TSTOF-based droplet measurement with an infodynamic temporal characterization layer. The objective is not to replace established spray parameters, but to add information about the temporal structure of the measurement.

This makes it possible to characterize a spray not only by what it is now—for example, its droplet size and velocity distributions—but also by how it is changing over time and by how much of its recent measurement history remains detectable in the present signal.

The concept opens a new research direction for laser-based spray diagnostics in which sprays are treated as complex, evolving systems rather than only as stationary statistical ensembles.