I was having trouble with your definition of gravity, so I just replaced it with the internal definition of the physical constant. The manipulate appears to work as intended.

gamma = ChemicalData["Water", "SurfaceTension"];
mu = ChemicalData["Water", "Viscosity"];
rho = ChemicalData["Water", "Density"];
g = Quantity["StandardAccelerationOfGravity"];
darcyEqn[d_, c_, eps_, Rb_, L_, theta_, 
  phi_] := ((Pi (d/2)^2 c eps^3 Rb^2)/((1 - 
         eps)^2 mu)) (((3 (1 - eps) gamma Cos[theta])/(eps L Rb)) + 
    g rho Sin[phi])
Manipulate[
 UnitConvert[
  darcyEqn[d Quantity[1, "Millimeters"], c, eps, 
   Rb Quantity[1, "Microns"], L Quantity[70, "Millimeters"], 
   theta \[Degree], phi \[Degree]], 
  "mL/min"], {{L, 70, "wick length"}, 1, 
  100}, {{d, 6.8, "wick diameter"}, 1, 8}, {c, 1/60, 1/
  30}, {{eps, 0.5, "porosity"}, 0.3, 0.9}, {{Rb, 100, "fiber radius"},
   10, 200}, {{theta, 70, "contact angle"}, 0, 
  90}, {{phi, 90, "wick orientation"}, 0, 90}]

Hey Tim Thanks for your reply. I altered my code slightly to make it more readable and may have accidentally removed a bracket. It evaluates correctly in my notebook document. I'm confident that's not the issue here. I have tried the ctrl= method of adding units with the same level of success as using the Quantity[] syntax. Sorry, I didn't mention that in my original post, I'd forgotten about that. Bill

When I copied your Manipulate expression, Mathematica indicates that the your parentheses are unbalanced (one more right paren than left). You will need to check that first.

Second, you may want to use the Unit Discovery feature by typing ctrl+=. You may want to check out my post https://community.wolfram.com/groups/-/m/t/1560271?ppauth=e8bMDzPu for an example of using Units Discovery and UnitConvert.