Slide 1: Flow and Storage of Powders
Flow and Storage of Powders Greg Mehos, Ph.D., P.E. gmehos@uri.edu greg@mehos.net www.mehos.net https://www.linkedin.com/in/gmehos/ 978-799-7311 Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 2: Happiness Equals Reality Minus Expectations
Happiness Equals Reality Minus Expectations Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 3: Flow and Storage of Powders
Flow and Storage of Powders Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 4: Flow and Storage of Powders
Flow and Storage of Powders Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 5: Flow and Storage of Powders
Flow and Storage of Powders Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 6: Goals
Goals • Understand fundamental powder flow properties • Predict flow behavior of powders • Know how to design/modify equipment for reliable powder handling Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 7: Goals
Goals Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 8: Goals
Goals Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 9: Definitions
Definitions Bulk solid “Powder” Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 10: Definitions
Definitions Biomass Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 11: Definitions
Definitions Hopper, bin, or silo Axisymmetric Planar Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 12: Definitions
Definitions • Normal stress • Shear stress • Major principal stress Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 13: Classification of liquids
Classification of liquids Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 14: Classification of bulk solids
Classification of bulk solids Neurotic move awkwardly - poor flowability - sticky or tacky Sadistic attack their surroundings - abrasive - explosive Masochistic suffer from their surroundings - friable - degradable Schizophrenic change their behavior pattern - hygroscopic - electrostatic Woodcock an
Slide 15: Flow problems
Flow problems • Ratholing Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 16: Flow problems
Flow problems • Ratholing • Arching/bridging Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 17: Bridging
Bridging Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 18: Flow problems
Flow problems • Ratholing • Arching • Caking Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 19: Flow problems
Flow problems • Ratholing • Arching • Caking • Flooding Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 20: Flow problems
Flow problems • Ratholing • Arching • Caking • Flooding • Segregation Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 21: Flow problems
Flow problems • Ratholing • Arching • Caking • Flooding • Segregation • Limiting discharge rate Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 22: Flow problems
Flow problems • Ratholing • Arching • Caking • Flooding • Segregation • Limiting discharge rate • Structural Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 23: Solids flow patterns
Solids flow patterns • Funnel flow • Mass flow Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 24: Funnel flow
Funnel flow Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 25: Mass flow
Mass flow Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 26: Mass flow
Mass flow Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 27: Funnel flow
Funnel flow Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 28: No flow
No flow Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 29: Preventing flow problems
Preventing flow problems • Ensure properly sized outlet • Design/modify to allow mass flow • Need powder flow properties Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 30: Fundamental properties
Fundamental properties • Viscosity • Density • Vapor pressure Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 31: Fundamental properties
Fundamental properties • Cohesive strength • Internal friction • Compressibility • Wall friction • Permeability Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 32: Andrew Jenike
Andrew Jenike Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 33: Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 34: Shear cell testers
Shear cell testers Jenike Schulze Brookfield Anton Paar Freeman Direct RST PFT MCR Technology FT4 Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 35: Compressibility
Compressibility Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 36: Compressibility
Compressibility Normal Force Bulk Density ρb Cover Bulk Solid Consolida)on Pressure σ Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 37: Wall friction
Wall friction mg sin θ = μ mg cos θ µ = tanθ Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 38: Wall friction
Wall friction Normal Force φ! = angle of wall friction Cover Shearing Force Bulk Solid Coupon of Wall Material Shear Stress tanφ ' = =µ Normal Stress Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 39: Wall friction
Wall friction Wall yield locus 25 20 (kPa) StressStress 15 ShearShear 10 5 0 0 5 10 15 20 25 Normal Normal Stress(kPa) Pressure Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 40: Mass flow hopper angle
Mass flow hopper angle Conical Funnel Flow Mass Flow Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 41: Mass flow hopper angle
Mass flow hopper angle Conical Funnel Flow Mass Flow Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 42: Mass flow hopper angles
Mass flow hopper angles Conical Planar Length > 2-3 x Width Funnel Flow Wall Friction Wall Friction Angle Angle Mass Flow Hopper Angle from Vertical Hopper Angle from Vertical From Jenike Bulletin 123 Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 43: Mass flow hopper angle
Mass flow hopper angle 30° Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 44: Mass flow hopper angle
Mass flow hopper angle 30° 20° Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 45: Valley angles
Valley angles Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 46: Pressure distribution
Pressure distribution D r πD2 πD2 πD2 (σ V + dσ V ) + σH µπDdh = σ V + ρbg dh h 4 4 4 σV(πD2/4) σ Force from powder below H Force due to wall friction dh σHμπDdh Force from powder above (σV + dσV)(πD2/4) Force due to gravity ρbg(πD2/4)dh Cylinder Greg Mehos & Associates LLC • www.mehos.net • greg@me
Slide 47: Pressure distribution
Pressure distribution D r πD2 πD2 πD2 (σ V + dσ V ) + σH µπDdh = σ V + ρbg dh h 4 4 4 Janssen coefficient σV(πD2/4) σ σH H k= ≅ 0.4 − 0.6 σV dh σHμπDdh D dσ V ρDg + kµσ V = b ρbg (σV + dσV)(πD2/4) 4 dh g4c ρbg(πD2/4)dh 1st order linear differential equation Cylinder Greg Mehos & Associates LLC • www
Slide 48: Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 49: Pressure distribution
Pressure distribution DD r r πD 2 2 πD πD 2 2 πD πD πD 2 2 (σ(σV V++dσ dσV )V ) + +σσ = =σ σ µ πDdh H µπDdh V V ++ρ ρgbg dhdh hh 44 H 44 b 44 Janssen coefficient V(πD σVσ(πD 2/4) 2/4) σ σH σ σH H k = k H=≅ 0.4 ≅−00.6 .4 σ V σV dhdh HμπDdh σHσμπDdh DDdσdσ ρg + kµσ V V + kµσ = Dbρbbgg V V =ρ (σσVV++dσ
Slide 50: Pressure distribution
Pressure distribution 0 ρb gD ⎡ ⎛ 4k tan φʹh ⎞⎤ ⎢1− exp ⎜ − ⎟⎥ 4k tan φʹ ⎣ ⎝ D ⎠⎦ 25 D = 10 ft Liquid - Hydrostatic head ρ or ρb = 62.4 lb/cu ft φʹ = 20° Depth (ft) 50 ρgh H = 100 ft 75 Bulk Solid - Janssen Eq 100 0 2000 4000 6000 8000 Stress Vertical Pressure (lb/sq ft) Greg Mehos & Associates LLC
Slide 51: Pressure distribution
Pressure distribution 0 ρb gD ⎡ ⎛ 4k tan φʹh ⎞⎤ ⎢1− exp ⎜ − ⎟⎥ 4k tan φʹ ⎣ ⎝ D ⎠⎦ 25 D = 10 ft Liquid Liquid: Hydrostatic - Hydrostatic head Pressure ρ or ρb = 62.4 lb/cu ft sv = rgh φʹ = 20° Depth (ft) 50 ρgh H = 100 ft Janssen Equation: 75 ρbgD ⎡ ⎛ −4kµh ⎞⎤ σv = ⎢1− exp ⎜ ⎟⎥ 4kµ ⎣ ⎝ D ⎠⎦ Bulk Soli
Slide 52: Pressure distribution
Pressure distribution Initial fill Stress Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 53: Pressure distribution
Pressure distribution After discharge (mass flow) Stress Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 54: Transfer chutes and diverter valves
Transfer chutes and diverter valves 45° 60° Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 55: Transfer chutes
Transfer chutes a = g(sin θ − cosθ tan φ ʹ) = g cosθ (tan θ − tan φ ʹ) mg For dependable flow, set θ = ϕ’ + 5 -10° For dependable flow, θ’ = ϕ’ + 5° Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 56: Transfer chutes
Transfer chutes For dependable flow, set θ = ϕ’ + 5 -10° a = g cosθ (tan θ − tan φ ʹ) Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 57: Transfer chutes
Transfer chutes For dependable flow, set θ = ϕ’ + 5 -10° a = g cosθ (tan θ − tan φ ʹ) Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 58: Cohesive strength
Cohesive strength Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 59: Cohesive strength
Cohesive strength Normal Stress σ Shear Stress τ Time Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 60: Cohesive strength
Cohesive strength Flow Function Strength or Stress Consolidation Pressure Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 61: Pressure distribution
Pressure distribution After discharge (mass flow) Stress Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 62: Cohesive strength
Cohesive strength Strength Strength or Cohesive Stress Stress Consolidation Pressure Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 63: Cohesive strength
Cohesive strength Cohesive strength Solids Stress Stress or Strength Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 64: Arch stress
Arch stress Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 65: Arch stress
Arch stress Stress on abutments of arch: ρb gB σ1 ≈ 2 θ′ s1 s1 B rb g Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 66: Arch stress
Arch stress Stress on abutments of arch: ρb gB σ1 = H (θ ʹ) θ′ Conical: H (θ ʹ) ≈ 2 s1 s1 Slot: B H (θ ʹ) ≈ 1 rb g Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 67: Arch stress
Arch stress Cohesive strength Arch supporting stress Stress or Strength Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 68: Arch stress
Arch stress Cohesive strength Arch supporting stress Stress > Strength Strength > Stress Stress or Strength Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 69: Critical arching diameter
Critical arching diameter Cohesive strength Arch stress ρ gB σ= b H(θʹ) σ Critical Critical stress Stress = Strength Stress or Strength Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 70: Critical arching diameter
Critical arching diameter Cohesive strength Arch stress ρ gB σ= b H(θʹ) H(θ ʹ)σ Critical Bmin = ρb g σ Critical Critical stress Stress = Strength Stress or Strength Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 71: Flow factor
Flow factor • Flow function (FF) – Relationship between consolidation stress and cohesive strength • Flow factor (ff) – Ratio of consolidation stress and arch supporting stress consolidation stress ff = arch stress Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 72: Critical flow factor
Critical flow factor 2.5 Axisymmetric (Conical) Planar 2.2 1.9 Flow Factor 1.6 1.3 1.0 20 30 40 50 60 70 Effective Angle of Friction (deg) from Jerry Johanson’s chapter in McGlinchey, Bulk Solids Characterization, 2005 Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 73: Flow function
Flow function Strength Strength or Cohesive Stress Flow Function Consolidation Stress Consolidation Pressure Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 74: Flow factor
Flow factor Flow Factor Slope = 1/ff Stress or Stress ⎛1⎞ σ 1 = ⎜ ⎟σ 1 Strength or ⎝ ff ⎠ Strength Flow Function Consolidation Stress Consolidation Pressure Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 75: Critical stress
Critical stress No Flow Flow Flow Factor Slope = 1/ff Stress or Stress H(θ ʹ)σ Critical Bmin = Strength or ρb g Strength Flow Function σ Critical Consolidation Major Principal Consolidation Stress Stress Pressure Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 76: Example
Example Design a hopper that reliable handles 67/29/4 blend of acetaminophen/Avicel/hydroxypropyl cellulose Flow Function Wall Friction Cohesive Strength (kPa) Shear Stress (kPa) Consolidation Stress (kPa) Normal Stress (kPa) Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-731
Slide 77: Example
Example Shear Stress (kPa) Wall Fric.on Angle (deg) (δ = 43o) 30° 9° Normal Stress Normal Stress (kPa) (kPa) Hopper Angle from Ver.cal (deg) From Jenike Bulletin 123 Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 78: Example
Example 2.5 Axisymmetric (Conical) Planar 2.2 1 ff = 1.38 1 Strength or Strength (kPa) σ critical = 900Pa Factor 1.9 Flow Factor Flow 1.6 1.38 1.3 1.0 20 30 40 43° 50 60 70 Effective Angle of Friction (deg) Effective Angle of Friction (deg) Major Major Principle Principal Stress Stress (kPa) (kPa) G
Slide 79: Example
Example H (θ ʹ)σ Critical (2.14)(900) Bmin = = = 0.28 m = 11 in. ρb g (690)(9.8) Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 80: Example
Example 6” Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 81: Example
Example Unconfined Yield Strength (kPa) Consolidation Stress (kPa) Shear Stress (kPa) Normal Stress (kPa) Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 82: Example
Example Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 83: Funnel flow bins
Funnel flow bins Major Principal Stress ρb gRH ⎡ ⎛ −k tan φ ʹz ⎞⎤ σ v (z) = ⎢1− exp ⎜⎜ ⎟⎟⎥ k tan φ ʹ ⎢⎣ ⎝ RH ⎠⎥⎦ D = diameter of round outlet or Stress diagonal of slotted outlet Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 84: Funnel flow bins
Funnel flow bins Major Principal Stress Cohesive Strength D = diameter of round outlet or Stress or Strength diagonal of slotted outlet Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 85: Funnel flow bins
Funnel flow bins Unstable Rathole Flow Channel Stress ρb gD σ= G(φt ) fC Stable Rathole Cohesive Strength D = diameter of round outlet or Stress or Strength diagonal of slotted outlet Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 86: Funnel flow bins
Funnel flow bins Unstable Rathole Flow Channel Stress ρb gD σ= G(φt ) fC Stable Rathole Cohesive Strength Maximum strength fC D = diameter of round outlet or Stress or Strength diagonal of slotted outlet Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 87: Funnel flow bins
Funnel flow bins Unstable Rathole Flow Channel Stress ρb gD σ= G(φt ) fC Stable Rathole Cohesive Strength Maximum strength fC Stress or Strength G(φt )fC D = diameter of round outlet or DF = diagonal of slotted outlet ρb g Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 88: Mass flow vs. funnel flow
Mass flow vs. funnel flow To prevent arching in a mass flow bin: Strength or Stress H(θ ʹ)σ critical Bmin = ρb g fc To prevent a stable rathole in a 1/ff funnel flow bin: G(φt )fC σcritical DF = ρb g Major Principal Stress Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 89: Permeability
Permeability Darcy’s Law KA Δ P qg = ρb g h Darcy’s Law valid ΔP/h KA Slope = ρbg qg Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 90: Solids discharge rates
Solids discharge rates Permeability θ’ Mehos, G., “Maximum Solids Discharge Rates from Hoppers”, Chem. Engr. Res. Des., 191, 564 (2023) B Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 91: Summary
Summary • Flow problems – Arching and ratholing – Caking – Segregation – Flooding and erratic discharge • Flow properties – Cohesive strength – Internal friction – Compressibility – Wall friction – Permeability • Design – Outlet dimension – Hopper angle Greg Mehos & Associates LLC • www.mehos.net •
Slide 92: Rand Corporation Study
Rand Corporation Study • Study by independent organization • 40 solids processing plants in U.S. and Canada • Six-year duration Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 93: Planned vs. actual start-up
Planned vs. actual start-up Average Start-Up Time (months) 35 30 Planned Actual 25 20 15 10 5 0 Liquid/Gas Solids Feedstock Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 94: Planned vs. actual start-up
Planned vs. actual start-up Average Start-Up Time (months) 35 30 Planned Actual 25 20 15 10 5 0 Liquid/Gas Solids Feedstock Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 95: Planned vs. actual start-up
Planned vs. actual start-up Average Start-Up Time (months) 35 30 Planned Actual 25 20 15 10 5 0 Liquid/Gas Solids Feedstock Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 96: Rand conclusions
Rand conclusions • 80% experienced solids handling problems • Average startup time ca. 20 months (vs. 4 mo. for fluids) • Typical performance 40 to 50% of design Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 97: Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 98: Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311
Slide 99: Flow and Storage of Powders
Flow and Storage of Powders Greg Mehos, Ph.D., P.E. gmehos@uri.edu greg@mehos.net www.mehos.net https://www.linkedin.com/in/gmehos/ 978-799-7311 Greg Mehos & Associates LLC • www.mehos.net • greg@mehos.net • 978-799-7311