## Deborah Number

### Quick Start

You have a PSA property measured in a time tmeasure, and you happen to know that some property of your PSA has a response, or relaxation, time of trelax. The Deborah Number D tells you whether that property is of any significance in that timescale.

### Deborah Number

trelax s
tmeasure s
D
Comment
//One universal basic required here to get things going once loaded
Main();
};
//Any global variables go here

//Main is hard wired as THE place to start calculating when input changes
//It does no calculations itself, it merely sets them up, sends off variables, gets results and, if necessary, plots them.
function Main() {
saveSettings();

//Send all the inputs as a structured object
//If you need to convert to, say, SI units, do it here!
const inputs = {
trelax: sliders.Slidetrelax.value,
tmeasure: sliders.Slidetmeasure.value,
}

//Get all the resonses as a structure
const result = CalcIt(inputs)

//Set all the text box outputs
document.getElementById('D').value = result.D
document.getElementById('Comment').value = result.Comment
}

//Here's the real app calculation
function CalcIt({ trelax, tmeasure }) {
//The structure automatically has the names provided from input
//By convention the values are provided with the correct units within CalcIt
var D = trelax / tmeasure
var Comment = "Balanced"
if (D < 0.1) Comment = "Relaxed"
if (D > 10) Comment = "Unresponsive"
return {
D: D.toPrecision(3),
Comment: Comment
}
}


We don't really need an app, but it's here for reference. In the Bible, Judges 5:5 the prophetess Deborah made a profound rheological observation. She noted that “The mountains flowed before the Lord”, i.e. even mountains are liquid if you sit around long enough. What she didn't go on to say was that mountains are liquid if you heat them hot enough. As discussed in WLF time and temperature are highly inter-related. The opposite to Deborah's observation is also true. If you look at a liquid in a short-enough timescale it's a solid.

The relative values of the response or relaxation time, trelax and the observation time, tmeasure is the Deborah Number, D:

D=t_(relax)/t_(measure)

As a rough guide, if D < 0.1 then that property is relaxed in the observational timescale so is irrelevant. Conversely, if D > 10 then the property will be unresponsive to that specific process so is equally irrelevant.