How to change a column values from dataframe comparing value from another dataframe only if the new value is not empty?

I have a dataframe with this info let call it df1:

Patient Id      Email5628        mapy@gmail.com17433       ssdx@gmail.com861415336       cris@yahoo.es17604       avasallo@yahoo.com8635        carolinavi@gmail.com1542415393       TAM20@YAHOO.COM

also have df2 which is bigger but for sure it have the patient id but It may have a different email or even dont have it at all. so what I want to do is replace the email in df1 with the one in df2 where the patient ids match and if the df2 email is not empty.

so I have tried with this:

df1['Email'] = df1['Patient Id'].map(df2.set_index('patient_id')['email_address'])

it locate correctly the match of the patient ids and replace the email but it replace it even when df2 email is empty ending up like this:

Patient Id      Email                   email nuevo5628        mapy@gmail.com          mapy@gmail.com17433       ssdx@gmail.com          ssdx002gmail.com8614        15336       cris@yahoo.es       17604       avasallo@yahoo.com      avasallo@yahoo.com8635        carolinavi@gmail.com    carolinavictoria.md@gmail.com15424       15393       TAM20@YAHOO.COM         TACM2010@YAHOO.COM

as you can see, it the email ssdx@gmail.com and TAM20@YAHOO.com but also overwrite cris@yahoo.es with an empty cell that's what i want to avoid.

any help is appreciated, thank you!