Connecting to two different network on single ESXi (Internal LAN and External DMZ)
You should use different vSwitch for each NIC
VMKernel should only be used for Management/vMotion/Shared storage (which is not need in your case)
(And you should not be connecting your Managment Network port to the DMZ)
EXAMPLE:
Internal LAN
vSwitch0 connected to a one physical NIC
1 Virtual Machine Port Group for VMs
1 VMKernel port for management
External DMZ
vSwitch1 connected to a one physical NIC
1 Virtual Machine Port Group for DMZ
SEE DIAGRAM FOR MORE DETAILS:
Raul.
VMware VDI Administrator.
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